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If the students were awarded only three grades-A, B and C-how many students in the class got grade A?(1) 20% of the class got grade B and 50% of the class got grade C. (2) The 12 girls in the class make up 40% of the class. a+b+c=T- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- d)EACH statement ALONE is sufficient.
- e)Statements (1) and (2) TOGETHER are NOT sufficient.
Correct answer is option 'C'. Can you explain this answer?
If the students were awarded only three grades-A, B and C-how many students in the class got grade A?
(1) 20% of the class got grade B and 50% of the class got grade C.
(2) The 12 girls in the class make up 40% of the class.
a+b+c=T
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
c)
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
d)
EACH statement ALONE is sufficient.
e)
Statements (1) and (2) TOGETHER are NOT sufficient.
|
Divey Sethi answered |
Steps 1&2: Understand question and draw inferences
This question involves the creation of two trees.
In the first tree, the node ‘Total Students’ is branched on the basis of gender. So, we get two branches: Girls and Boys.
Let the number of Girls in the class be g, and the number of boys in the class be b.
Let the total number of students in the class be T.
So, we can write:
g+b=T
. . . Equation 1
In the second tree, the node ‘Total Students’ is branched out on the basis of grades.
So, we get three branches: Grade A, Grade B and Grade C.
Let the number of students who got grades A, B and C be a, b and c respectively.
So, we can write:
a+b+c=T. . . Equation 2
We need to find the value of a.
Step 3: Analyze Statement 1
As per Statement 1,
20% of the class got grade B and 50% of the class got grade C
b = 20% of T and c = 50% of T
⇒ b = 0.2T and c = 0.5T
Substituting these values of b and c in Equation 2:
a + 0.2T + 0.5T = T
a=0.3 T
Since we don’t know the value of T, we will not be able to find the value of a.
Therefore, Statement 1 is not sufficient.
Step 4: Analyze Statement 2
As per Statement 2,
The 12 girls in the class make up 40% of the class
⇒ g=12
and g=40% of T
⇒ 12 = 40100T
⇒ T = 30
However, this statement gives us no clue about the value of a. Therefore, this statement is clearly not sufficient.
Step 5: Analyze Statement 1 and Statement 2 together (if needed)
From Statement 1,
a=0.3 T
From Statement 2,
T = 30
Thus, by combining the two statements,
We get a = 9
Thus, we are able to get a unique value by combining the two statements.
Correct Answer - Choice C
70 % of all the staff members in a college are administrators and remaining are teachers. If the total number of teachers is 60, then what is the total number of staff members in the college?- a)60
- b)140
- c)180
- d)200
- e)300
Correct answer is option 'D'. Can you explain this answer?
70 % of all the staff members in a college are administrators and remaining are teachers. If the total number of teachers is 60, then what is the total number of staff members in the college?
a)
60
b)
140
c)
180
d)
200
e)
300
|
Aspire Academy answered |
70% of all the staff members in a college are administrators and the remaining are teachers. If the total number of teachers is 60, then what is the total number of staff members in the college?
30% of staff members are teachers = 60
=> total number of staff members in the college = 60/0.3 = 200.
=> total number of staff members in the college = 60/0.3 = 200.
Candidate A, B and C are contesting elections. Each voter can only vote for a single candidate. 20% of the voters refrained from voting and candidates A, B and C received votes in the ratio 4 :3: 1 respectively. If there were no invalid votes and Candidate C got 2 million votes, then how many voters (in millions) refrained from voting?- a)2
- b)2.4
- c)3.2
- d)4
- e)8
Correct answer is option 'D'. Can you explain this answer?
Candidate A, B and C are contesting elections. Each voter can only vote for a single candidate. 20% of the voters refrained from voting and candidates A, B and C received votes in the ratio 4 :3: 1 respectively. If there were no invalid votes and Candidate C got 2 million votes, then how many voters (in millions) refrained from voting?
a)
2
b)
2.4
c)
3.2
d)
4
e)
8
|
Sameer Rane answered |
ratio = a:b:c=4:3:1
but c =2 million
thus multiplying the ratio with 2 we get = 8:6:2
thus total = 16 million
As 16 million is 20% decreased value of total X(let) voters
16 = X(1-20/100)
thus X= 20 million
thus number of people not voted = 20-16 million =4 million
A total of 500 students applied to a college for admission to its MBA program. The applicants were either freshers or experienced professionals. If 70% of all applicants were freshers and 20% of the experienced professionals had an experience of at least 2 years, then how many experienced professionals had an experience of less than 2 years?- a)30
- b)90
- c)120
- d)150
- e)180
Correct answer is option 'C'. Can you explain this answer?
A total of 500 students applied to a college for admission to its MBA program. The applicants were either freshers or experienced professionals. If 70% of all applicants were freshers and 20% of the experienced professionals had an experience of at least 2 years, then how many experienced professionals had an experience of less than 2 years?
a)
30
b)
90
c)
120
d)
150
e)
180
|
Avantika Sengupta answered |
Given:
- Total number of applicants = 500
- 70% of all applicants were freshers
- 20% of the experienced professionals had an experience of at least 2 years
To find:
- The number of experienced professionals with less than 2 years of experience
Approach:
1. Calculate the number of freshers.
2. Calculate the number of experienced professionals.
3. Calculate the number of experienced professionals with at least 2 years of experience.
4. Calculate the number of experienced professionals with less than 2 years of experience.
Calculation:
1. Calculate the number of Freshers:
- Freshers = 70% of 500 = 0.7 * 500 = 350
2. Calculate the number of experienced professionals:
- Experienced professionals = Total applicants - Freshers = 500 - 350 = 150
3. Calculate the number of experienced professionals with at least 2 years of experience:
- Experienced professionals with at least 2 years of experience = 20% of experienced professionals
- Experienced professionals with at least 2 years of experience = 0.2 * 150 = 30
4. Calculate the number of experienced professionals with less than 2 years of experience:
- Experienced professionals with less than 2 years of experience = Experienced professionals - Experienced professionals with at least 2 years of experience
- Experienced professionals with less than 2 years of experience = 150 - 30 = 120
Therefore, the number of experienced professionals with less than 2 years of experience is 120.
Hence, the correct answer is option C) 120.
- Total number of applicants = 500
- 70% of all applicants were freshers
- 20% of the experienced professionals had an experience of at least 2 years
To find:
- The number of experienced professionals with less than 2 years of experience
Approach:
1. Calculate the number of freshers.
2. Calculate the number of experienced professionals.
3. Calculate the number of experienced professionals with at least 2 years of experience.
4. Calculate the number of experienced professionals with less than 2 years of experience.
Calculation:
1. Calculate the number of Freshers:
- Freshers = 70% of 500 = 0.7 * 500 = 350
2. Calculate the number of experienced professionals:
- Experienced professionals = Total applicants - Freshers = 500 - 350 = 150
3. Calculate the number of experienced professionals with at least 2 years of experience:
- Experienced professionals with at least 2 years of experience = 20% of experienced professionals
- Experienced professionals with at least 2 years of experience = 0.2 * 150 = 30
4. Calculate the number of experienced professionals with less than 2 years of experience:
- Experienced professionals with less than 2 years of experience = Experienced professionals - Experienced professionals with at least 2 years of experience
- Experienced professionals with less than 2 years of experience = 150 - 30 = 120
Therefore, the number of experienced professionals with less than 2 years of experience is 120.
Hence, the correct answer is option C) 120.
In a village 40% of the men are above 25-years of age. Among these, 50% are married and 60% of these married men have at least one kid. If there are a total of 72000 men who are at most 25-year-old, how many of the married men does not have any kids?- a)9600
- b)14400
- c)19200
- d)28800
- e)81600
Correct answer is option 'A'. Can you explain this answer?
In a village 40% of the men are above 25-years of age. Among these, 50% are married and 60% of these married men have at least one kid. If there are a total of 72000 men who are at most 25-year-old, how many of the married men does not have any kids?
a)
9600
b)
14400
c)
19200
d)
28800
e)
81600
|
|
Niharika Sen answered |
Given:
- 40% of the men are above 25 years of age.
- Among these, 50% are married.
- 60% of these married men have at least one kid.
- Total number of men who are at most 25-year-old is 72000.
To find:
- Number of married men who do not have any kids.
Solution:
Let's assume the total number of men in the village = 100x.
Then, the number of men above 25 years of age = 40x.
The number of married men above 25 years of age = 20x (50% of 40x).
And, the number of married men above 25 years of age with at least one kid = 12x (60% of 20x).
Now, we know that the total number of men in the village = 100x.
And, the number of men above 25 years of age = 40x.
So, the number of men at most 25-year-old = 60x.
Given that the number of men at most 25-year-old is 72000.
So, 60x = 72000.
Therefore, x = 1200.
Now, we can find the number of married men who do not have any kids as follows:
- Total number of married men above 25 years of age = 20x = 20*1200 = 24000.
- Number of married men above 25 years of age with at least one kid = 12x = 12*1200 = 14400.
- Number of married men above 25 years of age with no kids = Total number of married men above 25 years of age - Number of married men above 25 years of age with at least one kid
= 24000 - 14400
= 9600.
Therefore, the number of married men who do not have any kids is 9600, which is option (a).
- 40% of the men are above 25 years of age.
- Among these, 50% are married.
- 60% of these married men have at least one kid.
- Total number of men who are at most 25-year-old is 72000.
To find:
- Number of married men who do not have any kids.
Solution:
Let's assume the total number of men in the village = 100x.
Then, the number of men above 25 years of age = 40x.
The number of married men above 25 years of age = 20x (50% of 40x).
And, the number of married men above 25 years of age with at least one kid = 12x (60% of 20x).
Now, we know that the total number of men in the village = 100x.
And, the number of men above 25 years of age = 40x.
So, the number of men at most 25-year-old = 60x.
Given that the number of men at most 25-year-old is 72000.
So, 60x = 72000.
Therefore, x = 1200.
Now, we can find the number of married men who do not have any kids as follows:
- Total number of married men above 25 years of age = 20x = 20*1200 = 24000.
- Number of married men above 25 years of age with at least one kid = 12x = 12*1200 = 14400.
- Number of married men above 25 years of age with no kids = Total number of married men above 25 years of age - Number of married men above 25 years of age with at least one kid
= 24000 - 14400
= 9600.
Therefore, the number of married men who do not have any kids is 9600, which is option (a).
A premier Film and Performing Arts school has a total class strength of 770. Two-third of the male students and three-fourth of the female students have opted for acting courses. The remaining students have opted for other courses. If the number of female students who opted for other courses was 55 less, then there would be 2 male students who opted for other courses for every female student who opted for other courses. How many students have opted for the acting courses?- a)220
- b)330
- c)440
- d)550
- e)600
Correct answer is option 'D'. Can you explain this answer?
A premier Film and Performing Arts school has a total class strength of 770. Two-third of the male students and three-fourth of the female students have opted for acting courses. The remaining students have opted for other courses. If the number of female students who opted for other courses was 55 less, then there would be 2 male students who opted for other courses for every female student who opted for other courses. How many students have opted for the acting courses?
a)
220
b)
330
c)
440
d)
550
e)
600
|
|
Nandita Chauhan answered |
Step 1: Question statement and Inferences
We are given that in a certain school, there are a total of 770 students. Let’s say the number of male students is x and the number of female students is y. So,
x + y = 770 …………… (1)
The number of male students in acting courses = 2x/3
The number of male students in other courses = x/3
The number of female students in acting courses = 3y/4
The number of female students in other courses = y/4
Thus,
The total number of students in acting courses =
And, the total number of students in other courses=
It is also given that, If there were 55 less female students who opted for other courses, then the number of male students who opted for other courses will be twice that of the female students who opted for other courses. So,
Step 2: Finding required values
Adding equations (1) and (4), we get y = 440 from which we can calculate x = 330.
Step 3: Calculating the final answer
Now, from equation (2),
The total number of students in acting courses
Correct choice : D
A book publishing company released 100 books last year. Three-fifth of the released books were fiction and all the remaining were non-fiction. 20% of fiction has at least 350 pages. And 80% of the non-fiction has less than 350 pages. How many of the released books has less than 350 pages?- a)12
- b)20
- c)32
- d)48
- e)80
Correct answer is option 'E'. Can you explain this answer?
A book publishing company released 100 books last year. Three-fifth of the released books were fiction and all the remaining were non-fiction. 20% of fiction has at least 350 pages. And 80% of the non-fiction has less than 350 pages. How many of the released books has less than 350 pages?
a)
12
b)
20
c)
32
d)
48
e)
80
|
Arjun Iyer answered |
Given:
- 100 books were released last year.
- Three-fifth of the released books were fiction and all the remaining were non-fiction.
- 20% of fiction has at least 350 pages.
- 80% of the non-fiction has less than 350 pages.
To find: How many of the released books have less than 350 pages?
Solution:
Number of fiction books released = (3/5) x 100 = 60
Number of non-fiction books released = 100 - 60 = 40
Number of fiction books with at least 350 pages = (20/100) x 60 = 12
Number of non-fiction books with less than 350 pages = (80/100) x 40 = 32
Total number of books with less than 350 pages = 12 + 32 = 44
Therefore, option (E) 80 is incorrect. The correct answer is option (D) 48.
- 100 books were released last year.
- Three-fifth of the released books were fiction and all the remaining were non-fiction.
- 20% of fiction has at least 350 pages.
- 80% of the non-fiction has less than 350 pages.
To find: How many of the released books have less than 350 pages?
Solution:
Number of fiction books released = (3/5) x 100 = 60
Number of non-fiction books released = 100 - 60 = 40
Number of fiction books with at least 350 pages = (20/100) x 60 = 12
Number of non-fiction books with less than 350 pages = (80/100) x 40 = 32
Total number of books with less than 350 pages = 12 + 32 = 44
Therefore, option (E) 80 is incorrect. The correct answer is option (D) 48.
Numbers
All numbers used are real numbers.
Figures
A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).
Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.
You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.
All figures lie in a plane unless otherwise indicated.
Q.Is y = 3?
1. (y - 3)(x - 4) = 0
2. (x - 4) = 0- a)Statement (1 ) ALONE is sufficient, but statement (2 ) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed
Correct answer is option 'E'. Can you explain this answer?
Numbers
All numbers used are real numbers.
Figures
A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).
Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.
You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.
All figures lie in a plane unless otherwise indicated.
Q.
All numbers used are real numbers.
Figures
A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).
Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.
You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.
All figures lie in a plane unless otherwise indicated.
Q.
Is y = 3?
1. (y - 3)(x - 4) = 0
2. (x - 4) = 0
1. (y - 3)(x - 4) = 0
2. (x - 4) = 0
a)
Statement (1 ) ALONE is sufficient, but statement (2 ) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed
|
|
Anirban Das answered |
Evaluate Statement (1) ALONE: (y - 3)(x - 4) = 0
If product of the two terms (y - 3) and (x - 4) is 0, then at least one of the two terms equals 0.
(y - 3) = 0 or (x - 4) = 0 or both (y - 3) and (x - 4) equal 0.
i.e., either y = 3 or x = 4 or that both y = 3 and x = 4.
If x = 4, y could take any value. The value of 'y' could be 3 or it could be some other value and the product will still be a 0.
Example: x = 4 and y = 5. The equation holds good. y ≠ 3.
Counter example: x = 4 and y = 3. The equation holds good. y = 3
We CANNOT determine whether 'y' is 3 from this statement.
If product of the two terms (y - 3) and (x - 4) is 0, then at least one of the two terms equals 0.
(y - 3) = 0 or (x - 4) = 0 or both (y - 3) and (x - 4) equal 0.
i.e., either y = 3 or x = 4 or that both y = 3 and x = 4.
If x = 4, y could take any value. The value of 'y' could be 3 or it could be some other value and the product will still be a 0.
Example: x = 4 and y = 5. The equation holds good. y ≠ 3.
Counter example: x = 4 and y = 3. The equation holds good. y = 3
We CANNOT determine whether 'y' is 3 from this statement.
Statement 1 ALONE is NOT sufficient.
Eliminate choices A and D. Choices narrow down to B, C or E
Evaluate Statement (2) ALONE: (x - 4) = 0
The statement provides no information about y.
Eliminate choices A and D. Choices narrow down to B, C or E
Evaluate Statement (2) ALONE: (x - 4) = 0
The statement provides no information about y.
Statement 2 ALONE is NOT sufficient.
Eliminate choice B. Choices narrow down to C or E.
Eliminate choice B. Choices narrow down to C or E.
Evaluate Statements (1) & (2) Together: (y - 3)(x - 4) = 0 & (x - 4) = 0
When x = 4, (y - 3)(x - 4) will be 0 irrespective of the value that y takes.
When x = 4, (y - 3)(x - 4) will be 0 irrespective of the value that y takes.
Can 'y' be 3? Yes 'y' can be 3.
Is y = 3? Not necessary.It can take values other than 3 and the data in the two statements will still hold good.
Is y = 3? Not necessary.It can take values other than 3 and the data in the two statements will still hold good.
Eliminate choice C.
Statements TOGETHER are NOT sufficient. Choice E is the answer.
Statements TOGETHER are NOT sufficient. Choice E is the answer.
Numbers
All numbers used are real numbers.
Figures
A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).
Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.
You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.
All figures lie in a plane unless otherwise indicated.
Q.What is the value of X, if X and Y are two distinct integers and their product is 30? - X is an odd integer
- X > Y
- a)Statement (1 ) ALONE is sufficient, but statement (2 ) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed
Correct answer is option 'E'. Can you explain this answer?
Numbers
All numbers used are real numbers.
Figures
A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).
Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.
You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.
All figures lie in a plane unless otherwise indicated.
Q.
All numbers used are real numbers.
Figures
A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).
Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.
You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.
All figures lie in a plane unless otherwise indicated.
Q.
What is the value of X, if X and Y are two distinct integers and their product is 30?
- X is an odd integer
- X > Y
a)
Statement (1 ) ALONE is sufficient, but statement (2 ) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed
|
|
Anirban Das answered |
Values of X and Y that satisfy both the conditions are
More than one value exists for X. Because we are not able to deduce a UNIQUE value for X using the information provided in the two statements together, the given data is NOT sufficient.
More than one value exists for X. Because we are not able to deduce a UNIQUE value for X using the information provided in the two statements together, the given data is NOT sufficient.
Statements TOGETHER are NOT sufficient.
Choice E is the answer.
Numbers
All numbers used are real numbers.
Figures
A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).
Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.
You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.
All figures lie in a plane unless otherwise indicated.
Q.
Is y an integer?
1. y3 is an integer
2. 3y is an integer
- a)Statement (1 ) ALONE is sufficient, but statement (2 ) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed
Correct answer is option 'C'. Can you explain this answer?
Numbers
All numbers used are real numbers.
Figures
A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).
Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.
You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.
All figures lie in a plane unless otherwise indicated.
Q.
All numbers used are real numbers.
Figures
A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).
Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.
You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.
All figures lie in a plane unless otherwise indicated.
Q.
Is y an integer?
1. y3 is an integer
2. 3y is an integer
1. y3 is an integer
2. 3y is an integer
a)
Statement (1 ) ALONE is sufficient, but statement (2 ) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed
|
|
Palak Saha answered |
Step 1 of solving this GMAT DS question:
Evaluate Statement (1) ALONE: y3 is an integer
Evaluate Statement (1) ALONE: y3 is an integer
We know that y3 is an integer.
However, that does not necessarily mean that y is an integer.
Let us say, y3 = 2, then y is not an integer.
However, if y3 = 8, then y = 2 and is an integer.
However, that does not necessarily mean that y is an integer.
Let us say, y3 = 2, then y is not an integer.
However, if y3 = 8, then y = 2 and is an integer.
Statement 1 ALONE is NOT sufficient.
Eliminate choices A and D. Choices narrow down to B, C, or E.
Eliminate choices A and D. Choices narrow down to B, C, or E.
Step 2 of solving this GMAT DS question:
Evaluate Statement (2) ALONE: 3y is an integer
Evaluate Statement (2) ALONE: 3y is an integer
We know that 3y is an integer.
Let us say 3y = 2, then y is not an integer.
However, if 3y = 3, then y will be an integer.
Let us say 3y = 2, then y is not an integer.
However, if 3y = 3, then y will be an integer.
Statement 3 ALONE is NOT sufficient.
Eliminate choice B. Choices narrow down to C or E.
Step 4 of solving this GMAT DS question:
Evaluate Statements (1) & (2) Together: y3 is an integer and 3y is an integer.
Statements TOGETHER are sufficient. Choice C is the answer.
Eliminate choice B. Choices narrow down to C or E.
Step 4 of solving this GMAT DS question:
Evaluate Statements (1) & (2) Together: y3 is an integer and 3y is an integer.
Statements TOGETHER are sufficient. Choice C is the answer.
If 80% employees of a company play soccer, what percent of the employees play golf?(1) 25% of the employees who play soccer also play golf.(2) 50% of the employees who play golf also play soccer. - a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- d)EACH statement ALONE is sufficient.
- e)Statements (1) and (2) TOGETHER are NOT sufficient.
Correct answer is option 'C'. Can you explain this answer?
If 80% employees of a company play soccer, what percent of the employees play golf?
(1) 25% of the employees who play soccer also play golf.
(2) 50% of the employees who play golf also play soccer.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
c)
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
d)
EACH statement ALONE is sufficient.
e)
Statements (1) and (2) TOGETHER are NOT sufficient.
|
|
Nandita Chauhan answered |
Steps 1 & 2: Understand Question and Draw Inferences
We are given that 80% employees of a company play soccer. We have to find the percentage of the employees who play golf.
Since this question only talks about the percentage, not the absolute numbers, let’s say the number of employees in the company is 100.
80% of these employees play soccer. Now, these 80% employees include the employees who play only soccer and the employees who play soccer and golf both.
So, the employees who play soccer = 80% of 100 = 80
Let’s say the number of employees who play both soccer and golf = x
Thus, the number of employees who play only soccer = 80 – x
Also, let the number of employees who play only golf = y
If there are any employees who play neither soccer nor golf = 20 – y
The total number of employees who play golf = x + y
We have to find the value of (x + y).
Step 3: Analyze Statement 1
Statement (1) says: 25% of the employees who play soccer also play golf.
The number of employees who play soccer and golf is x.
Per this statement:
x = 25% of 80
x = 20 ………….. (1)
However, since we do not know the value of y, we cannot get the value of (x + y).
Hence, statement (1) is not sufficient to answer the question: What is the value of (x + y)?
Step 4: Analyze Statement 2
Statement (2) says: 50% of the employees who play golf also play soccer.
The employees who play golf and soccer are (x + y). 50% of these employees also play soccer. Out of these (x + y) employees, the employees who play soccer = x
50% of (x + y) = x
x + y = 2x
y = x …… (2)
However, we don’t know the value of x and y. so, we can’t determine the value of (x + y).
Hence, statement II is not sufficient to answer the question: What is the value of (x + y)?
Step 5: Analyze Both Statements Together (if needed)
Since step 3 and step 4 were not able to provide the answer to the question, let’s analyse both the statements together:
Statement (1):
x = 20 ………….. (1)
Statement (2):
y = x ………… (2)
Thus,
y = 20
Hence,
x + y = 20 + 20 = 40
So, statement (1) and (2) combined are sufficient to answer the question.
Answer: Option (C)
Numbers
All numbers used are real numbers.
Figures
A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).
Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.
You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.
All figures lie in a plane unless otherwise indicated.
Q.Is ab positive?
1. (a + b)2 < (a - b)2
2. a = b- a)Statement (1 ) ALONE is sufficient, but statement (2 ) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed
Correct answer is option 'A'. Can you explain this answer?
Numbers
All numbers used are real numbers.
Figures
A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).
Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.
You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.
All figures lie in a plane unless otherwise indicated.
Q.
All numbers used are real numbers.
Figures
A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).
Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.
You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.
All figures lie in a plane unless otherwise indicated.
Q.
Is ab positive?
1. (a + b)2 < (a - b)2
2. a = b
1. (a + b)2 < (a - b)2
2. a = b
a)
Statement (1 ) ALONE is sufficient, but statement (2 ) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed
|
|
Palak Saha answered |
STATEMENT 1:
Expanding both sides of the inequality, we get a2 + b2 + 2ab < a2 + b2 - 2ab
Simplifying we get, 4ab < 0 or ab < 0.
So, we can conclude that ab is not positive. We have got a definite NO as the answer.
Statement 1 ALONE is SUFFICIENT.
Expanding both sides of the inequality, we get a2 + b2 + 2ab < a2 + b2 - 2ab
Simplifying we get, 4ab < 0 or ab < 0.
So, we can conclude that ab is not positive. We have got a definite NO as the answer.
Statement 1 ALONE is SUFFICIENT.
Eliminate choices B, C, and E. Answer choices narrow down to A or D.
STATEMENT 2:
STATEMENT 2:
This is actually the statement that could trick you.
a = b.
So, either both a and b or positive or both a and b are negative. In either case ab is positive.
We will certainly be "tempted" to decide that statement 2 is also sufficient.
The catch is that, both a and b could be 0. In that case ab = 0, which is not positive.
As we are not able to conclude whether ab is positive with statement 2, it is not sufficient. Statement 2 ALONE is NOT sufficient.
a = b.
So, either both a and b or positive or both a and b are negative. In either case ab is positive.
We will certainly be "tempted" to decide that statement 2 is also sufficient.
The catch is that, both a and b could be 0. In that case ab = 0, which is not positive.
As we are not able to conclude whether ab is positive with statement 2, it is not sufficient. Statement 2 ALONE is NOT sufficient.
In an interview for a certain job, 120 candidates appeared and two questions were asked to each candidate. How many candidates did not answer any question correctly?(1) Of all the candidates who appeared for the interview, 20% of the candidates who answered at least one question correctly, answered both questions correctly.(2) Of all the candidates who appeared for the interview, 25% of the candidates who answered none or both questions correctly, answered both questions correctly.- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- d)EACH statement ALONE is sufficient.
- e)Statements (1) and (2) TOGETHER are NOT sufficient.
Correct answer is option 'C'. Can you explain this answer?
In an interview for a certain job, 120 candidates appeared and two questions were asked to each candidate. How many candidates did not answer any question correctly?
(1) Of all the candidates who appeared for the interview, 20% of the candidates who answered at least one question correctly, answered both questions correctly.
(2) Of all the candidates who appeared for the interview, 25% of the candidates who answered none or both questions correctly, answered both questions correctly.
a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
c)
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
d)
EACH statement ALONE is sufficient.
e)
Statements (1) and (2) TOGETHER are NOT sufficient.
|
|
Nandita Chauhan answered |
Steps 1&2: Understand question and draw inferences
Let the number of candidates who gave 0 correct answers, 1 correct answer and 2 correct answers = A, B and C respectively
A + B + C = 120 -----(1)
We have to find the value of A.
To do so, we need to find:
(i) Either the value of B and C
(ii) Or the value of (B + C)
Step 3: Analyze Statement 1
Number of students who answered at least one question correctly = B + C
We derive a relation between B and C, but we cannot find the value of B or C or (B + C) from equation (1) and (2).
INSUFFICIENT.
Step 4: Analyze Statement 2
Number of students who answered none or all questions correctly = A + C
We derive a relation between A and C, but we cannot find the value of B or C or (B + C) from equation (1) and (3).
Step 5: Analyze Statement 1 and Statement 2 together (if needed)
We have equations (1), (2) and (3) when we combine the two statements.
Substituting A and B from equation (2) and (3) in equation (1),
3C + 4C + C = 120
We can find the value of C from this equation and substitute the value in equation (3) the find the required value of A.
SUFFICIENT.
(C) is the correct answer.
A certain university spends all the money donated by The Goodwill Foundation in a certain year to fund three research projects P, Q and R. Project P receives a funding of $40,000. Both projects P and Q receive 100% more funding than Project R. The donation made by The Goodwill Foundation to the university is 25% of the total donation received by the university during the year. If the university invests in projects P, Q and R only from the money received from The Goodwill Foundation, then what is the total amount, in dollars, of donation that is not received by the university from The Goodwill Foundation?- a)50000
- b)100000
- c)200000
- d)300000
- e)400000
Correct answer is option 'D'. Can you explain this answer?
A certain university spends all the money donated by The Goodwill Foundation in a certain year to fund three research projects P, Q and R. Project P receives a funding of $40,000. Both projects P and Q receive 100% more funding than Project R. The donation made by The Goodwill Foundation to the university is 25% of the total donation received by the university during the year. If the university invests in projects P, Q and R only from the money received from The Goodwill Foundation, then what is the total amount, in dollars, of donation that is not received by the university from The Goodwill Foundation?
a)
50000
b)
100000
c)
200000
d)
300000
e)
400000
|
|
Navya Yadav answered |
Step 1: Question statement and Inferences
The first step will be to draw the tree structure that depicts the question statement.
The next step will be to find the value at each node and branch of the tree.
Step 2: Finding required values
Let the money donated by The Goodwill Foundation be $x
It is given that
Amount donated by Goodwill Foundation =25% of Total Donation
Total Donation=4x
So, Donations by others=4x–x=3x
We need to find the value of
We are also given that
Funding received by P = Funding Received by Q = $40,000
Also,
Funding received by P= Funding received by R+100 of Funding received by R
Thus,x=40,000 + 40,000 + 20,000 = $100,000
Step 3: Calculating the final answer
Donation that is not received by the university from The Goodwill Foundation = 3x = $300,000
(D) is the correct answer.
A real estate broker booked 1200 apartments for sale. All of them were either 2-bedroom or 3-bedroom apartments. Out of the 2-bedroom apartments, 20% had terrace gardens and out of the 3-bedroom apartments, 80% had terrace gardens. If there were 600 apartments with terrace gardens, how many 3-bedroom apartments were booked by the broker?- a)400
- b)600
- c)800
- d)900
- e)1000
Correct answer is option 'B'. Can you explain this answer?
A real estate broker booked 1200 apartments for sale. All of them were either 2-bedroom or 3-bedroom apartments. Out of the 2-bedroom apartments, 20% had terrace gardens and out of the 3-bedroom apartments, 80% had terrace gardens. If there were 600 apartments with terrace gardens, how many 3-bedroom apartments were booked by the broker?
a)
400
b)
600
c)
800
d)
900
e)
1000
|
|
Nandita Chauhan answered |
Step 1: Question statement and Inferences
We are given that a broker booked 1200 apartments for sale. There are only two types of apartments in these 1200: either 2-bedroom apartments or 3-bedroom apartments.
Let’s say:
The number of 2-bedroom apartments = x
And the number of 3-bedroom apartments = y
Thus,
x + y = 1200 ………….. (1)
Next the question says, 20% of the 2-bedroom apartments have terrace gardens, and 80% of the 3-bedroom apartments have terrace gardens. So,
The number of 2-bedroom apartments with terrace gardens = 20% of x = 0.2x
And the number of 3-bedroom apartments with terrace gardens = 80% of y = 0.8y
It is also given that there are 600 apartments with terrace gardens. So,
0.2x + 0.8y = 600
2x + 8y = 6000 ……………… (2)
We have to find the number of 3-bedroom apartments booked i.e. the value of y.
Step 2: Finding required values
Now, we have two equations and two variables. So, let’s solve them to get the value of y.
x + y = 1200 ……………… (1)
2x + 8y = 6000 ……………… (2)
Multiplying equation (1) by 2, and then subtracting it from equation (2), we get:
6y = 3600
Thus,y = 600
Step 3: Calculating the final answer
So, the number of 3-bedroom apartments = 600
Answer: Option (B)
Numbers
All numbers used are real numbers.
Figures
A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).
Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.
You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.
All figures lie in a plane unless otherwise indicated.
Q.Is the positive integer X divisible by 21?
1. When X is divided by 14, the remainder is 4
2. When X is divided by 15, the remainder is 5- a)Statement (1 ) ALONE is sufficient, but statement (2 ) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed
Correct answer is option 'D'. Can you explain this answer?
Numbers
All numbers used are real numbers.
Figures
A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).
Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.
You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.
All figures lie in a plane unless otherwise indicated.
Q.
All numbers used are real numbers.
Figures
A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).
Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.
You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.
All figures lie in a plane unless otherwise indicated.
Q.
Is the positive integer X divisible by 21?
1. When X is divided by 14, the remainder is 4
2. When X is divided by 15, the remainder is 5
1. When X is divided by 14, the remainder is 4
2. When X is divided by 15, the remainder is 5
a)
Statement (1 ) ALONE is sufficient, but statement (2 ) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed
|
|
Kiran Nambiar answered |
Evaluating Statement (1) ALONE
Statement (1) : When X is divided by 14, the remainder is 4
The number is, therefore, of the form 14k + 4.
It will leave a remainder of 4 when divided by 7. (14k is divisible by 7. When 4 is divided by 7, the remainder is 4.)
Statement (1) : When X is divided by 14, the remainder is 4
The number is, therefore, of the form 14k + 4.
It will leave a remainder of 4 when divided by 7. (14k is divisible by 7. When 4 is divided by 7, the remainder is 4.)
This number is definitely not divisible by 7.
To be divisible by 21, the number must be divisible by both 3 and 7. This number is not divisible by 7. Hence, X is not divisible by 21.
To be divisible by 21, the number must be divisible by both 3 and 7. This number is not divisible by 7. Hence, X is not divisible by 21.
We have a DEFINITE NO as the answer to the question using statement 1.
Statement 1 ALONE is sufficient.
Eliminate choices B, C and E. Choices narrow down to A or D.
Eliminate choices B, C and E. Choices narrow down to A or D.
Evaluating Statement (2) ALONE
Statement (2) : When X is divided by 15, the remainder is 5
The number X is of the form 15m + 5
Therefore, the number will leave a remainder of 2 when divided by 3.
Statement (2) : When X is divided by 15, the remainder is 5
The number X is of the form 15m + 5
Therefore, the number will leave a remainder of 2 when divided by 3.
Hence, it is not divisible by 3.
To be divisible by 21, the number must be divisible by both 3 and 7. This number is not divisible by 3. Hence, X is not divisible by 21.
To be divisible by 21, the number must be divisible by both 3 and 7. This number is not divisible by 3. Hence, X is not divisible by 21.
We have a DEFINITE NO as the answer to the question using statement 2 as well.
Statement 2 ALONE is also sufficient.
Eliminate choice A.
Eliminate choice A.
Each statement is INDEPENDENTLY sufficient. Choice D is the answer.
In a day care, 80% of the kids are American. 60% of the kids have started speaking. Of these, only 20% are under the age of 2 years. If the number of non-American kids at the day care is 40, what is the number of kids who can speak and are not under 2 years of age?- a)24
- b)50
- c)96
- d)120
- e)160
Correct answer is option 'C'. Can you explain this answer?
In a day care, 80% of the kids are American. 60% of the kids have started speaking. Of these, only 20% are under the age of 2 years. If the number of non-American kids at the day care is 40, what is the number of kids who can speak and are not under 2 years of age?
a)
24
b)
50
c)
96
d)
120
e)
160
|
|
Maya Choudhury answered |
Step 1: Question statement and Inferences
Let the total number of kids at the day care be N
So, number of American kids = 80% of N = 0.8N
Number of non-American kids = N-0.8N = 0.2N
It is given that 0.2N = 40
From here, we calculate that N = 200
Step 2: Finding required values
Number of kids who speak = 60% of N = 60% of 200 = 120
Of these, 20% are under 2 years of age.
Remaining 80% are not under 2 years of age
Step 3: Calculating the final answer
Number of kids who are not under 2 years of age = 80% of 120
= 96
Looking at the answer options, we see that option C is correct.
Mid-way through their MBA, the students of the Class of 2012 in a business school were surveyed for career preferences. One-third of the students chose consulting as their first preference. When the survey was repeated upon completion of the MBA, it was found that two-third of the students who earlier preferred consulting had changed their mind. Among the students who chose consulting in both the surveys, three-fifths became entrepreneurs and opened consulting startups and the remaining 12 joined consulting firms as employees. How many students did the Class of 2012 have?- a)90
- b)180
- c)210
- d)270
- e)360
Correct answer is option 'D'. Can you explain this answer?
Mid-way through their MBA, the students of the Class of 2012 in a business school were surveyed for career preferences. One-third of the students chose consulting as their first preference. When the survey was repeated upon completion of the MBA, it was found that two-third of the students who earlier preferred consulting had changed their mind. Among the students who chose consulting in both the surveys, three-fifths became entrepreneurs and opened consulting startups and the remaining 12 joined consulting firms as employees. How many students did the Class of 2012 have?
a)
90
b)
180
c)
210
d)
270
e)
360
|
|
Maya Choudhury answered |
Step 1: Question statement and Inferences
Let the number of students in the Class of 2012 be x.
So, number of students who chose consultancy in the first survey = x/3.
Two-third out of the students who chose consultancy as their first career choice, changed their mind by the completion of the course.
So, the number of students who changed their mind
Step 2: Finding required values
Out of the students who chose consulting in the second survey as well, three-fifth started their careers as entrepreneurs and 12 as employee to firms.
The number of students who still chose consulting in the second survey = 
The number of student who became entrepreneurs = 3/5 x The number of students who stayed with their first choice 
The number of student who joined firms = 12
That is,
Step 3: Calculating the final answer
Thus, the total number of students in the class = 270.
Answer: Option (D)
Numbers
All numbers used are real numbers.
Figures
A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).
Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.
You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.
All figures lie in a plane unless otherwise indicated.
Q.If m, s are the average and standard deviation of integers a, b, c, and d, is s > 0?
1. m > a
2. a + b + c + d = 0- a)Statement (1 ) ALONE is sufficient, but statement (2 ) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed
Correct answer is option 'A'. Can you explain this answer?
Numbers
All numbers used are real numbers.
Figures
A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).
Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.
You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.
All figures lie in a plane unless otherwise indicated.
Q.
All numbers used are real numbers.
Figures
A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).
Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.
You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.
All figures lie in a plane unless otherwise indicated.
Q.
If m, s are the average and standard deviation of integers a, b, c, and d, is s > 0?
1. m > a
2. a + b + c + d = 0
1. m > a
2. a + b + c + d = 0
a)
Statement (1 ) ALONE is sufficient, but statement (2 ) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed
|
|
Athul Joshi answered |
STATEMENT 1:
If a = b = c = d, the average m will be the same as a.
Since m > a, all the elements in the set cannot be the same, and therefore, s > 0.
Statement 1 ALONE is sufficient.
Eliminate choices B, C and E. Choices narrow down to A and D.
STATEMENT 2:
Statement 1 ALONE is sufficient.
Eliminate choices B, C and E. Choices narrow down to A and D.
STATEMENT 2:
Approach: Look for a counter example
Example: When a = b = c = d = 0, s = 0
Counter Example: When a = -4, b = 0, c = 0, and d = 4, s > 0
Statement 2 ALONE is NOT sufficient.
Eliminate choice D. Choice A is the answer.
Example: When a = b = c = d = 0, s = 0
Counter Example: When a = -4, b = 0, c = 0, and d = 4, s > 0
Statement 2 ALONE is NOT sufficient.
Eliminate choice D. Choice A is the answer.
Numbers
All numbers used are real numbers.
Figures
A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).
Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.
You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.
All figures lie in a plane unless otherwise indicated.
Q.Is the two digit positive integer P a prime number?
1. (P + 2) and (P - 2) are prime.
2. (P - 4) and (P + 4) are prime- a)Statement (1 ) ALONE is sufficient, but statement (2 ) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed
Correct answer is option 'D'. Can you explain this answer?
Numbers
All numbers used are real numbers.
Figures
A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).
Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.
You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.
All figures lie in a plane unless otherwise indicated.
Q.
All numbers used are real numbers.
Figures
A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).
Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.
You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.
All figures lie in a plane unless otherwise indicated.
Q.
Is the two digit positive integer P a prime number?
1. (P + 2) and (P - 2) are prime.
2. (P - 4) and (P + 4) are prime
1. (P + 2) and (P - 2) are prime.
2. (P - 4) and (P + 4) are prime
a)
Statement (1 ) ALONE is sufficient, but statement (2 ) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed
|
|
Palak Saha answered |
STATEMENT 1:
(P - 2), P and (P + 2) are 3 consecutive odd integers because (P - 2) and (P + 2) are prime.
One out of 3 consecutive odd integers, (P - 2), P, and (P + 2) will definitely be a multiple of '3'. If (P + 2) and (P - 2) are prime, then P has to be a multiple of '3', which is not prime.
The only exception is if the 3 consecutive odd numbers are 3, 5 and 7. However, we are dealing with two digit positive integers. So that possibility is ruled out.
Statement 1 ALONE is SUFFICIENT.
STATEMENT 2:
This is a brilliant statement.
1. The remainder when (P - 4) and (P - 1) are divided by 3 will be the same.
2. Similarly, the remainder when (P + 4) and (P + 1) are divided by 3 will be the same.
If (P - 4) and (P + 4) are prime, both (P - 4) and (P + 4) will leave a remainder when divided by 3.
Therefore, (P - 1) and (P + 1) will leave a remainder when divided by 3. i.e., they are not divisible by 3.(P - 1), P, (P + 1) are 3 consecutive positive integers.
One out of 3 consecutive integers, (P - 1), P, and (P + 1) will definitely be a multiple of '3'.
If (P - 1) and (P + 1) are not divisible by 3, then P has to be a multiple of '3'.
P cannot be 3 because when P is 3, (P - 4) will not be prime. So, that possiblity is ruled out.
Therefore, P is not prime.
Statement 2 ALONE is SUFFICIENT.
Statement 1 ALONE is SUFFICIENT.
STATEMENT 2:
This is a brilliant statement.
1. The remainder when (P - 4) and (P - 1) are divided by 3 will be the same.
2. Similarly, the remainder when (P + 4) and (P + 1) are divided by 3 will be the same.
If (P - 4) and (P + 4) are prime, both (P - 4) and (P + 4) will leave a remainder when divided by 3.
Therefore, (P - 1) and (P + 1) will leave a remainder when divided by 3. i.e., they are not divisible by 3.(P - 1), P, (P + 1) are 3 consecutive positive integers.
One out of 3 consecutive integers, (P - 1), P, and (P + 1) will definitely be a multiple of '3'.
If (P - 1) and (P + 1) are not divisible by 3, then P has to be a multiple of '3'.
P cannot be 3 because when P is 3, (P - 4) will not be prime. So, that possiblity is ruled out.
Therefore, P is not prime.
Statement 2 ALONE is SUFFICIENT.
Numbers
All numbers used are real numbers.
Figures
A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).
Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.
You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.
All figures lie in a plane unless otherwise indicated.
Q.What is the standard deviation (SD) of the four numbers p, q, r, s? - The sum of p, q, r and s is 24
- The sum of the squares of p, q, r and s is 224
- a)Statement (1 ) ALONE is sufficient, but statement (2 ) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed
Correct answer is option 'C'. Can you explain this answer?
Numbers
All numbers used are real numbers.
Figures
A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).
Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.
You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.
All figures lie in a plane unless otherwise indicated.
Q.
All numbers used are real numbers.
Figures
A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).
Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.
You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.
All figures lie in a plane unless otherwise indicated.
Q.
What is the standard deviation (SD) of the four numbers p, q, r, s?
- The sum of p, q, r and s is 24
- The sum of the squares of p, q, r and s is 224
a)
Statement (1 ) ALONE is sufficient, but statement (2 ) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed
|
|
Palak Saha answered |
From statement 1 we know that the square of the means is 36.
From statement 2 we know that the mean of the squares is 56.
From statement 2 we know that the mean of the squares is 56.
Using the formula, Standard deviation =
we can find the SD of the 4 numbers
we can find the SD of the 4 numbers
Statements TOGETHER are SUFFICIENT.
Choice C is the answer.
Numbers
All numbers used are real numbers.
Figures
A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).
Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.
You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.
All figures lie in a plane unless otherwise indicated.
Q.Is the positive integer m divisible by 6?
1. m is divisible by 3
2. m is divisible by 4- a)Statement (1 ) ALONE is sufficient, but statement (2 ) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed
Correct answer is option 'C'. Can you explain this answer?
Numbers
All numbers used are real numbers.
Figures
A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).
Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.
You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.
All figures lie in a plane unless otherwise indicated.
Q.
All numbers used are real numbers.
Figures
A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).
Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.
You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.
All figures lie in a plane unless otherwise indicated.
Q.
Is the positive integer m divisible by 6?
1. m is divisible by 3
2. m is divisible by 4
1. m is divisible by 3
2. m is divisible by 4
a)
Statement (1 ) ALONE is sufficient, but statement (2 ) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed
|
|
Soumya Iyer answered |
Evaluate Statement (1) ALONE: x is divisible by 6
Approach: Look for a counter example
Approach: Look for a counter example
Example: x = 6. It is divisible by 6. However, it is NOT divisible by 12.
Counter Example: x = 12. It is divisible by 6. It is divisible by 12 as well.
Knowing that x is divisible by 6 is not enough to answer the question.
Counter Example: x = 12. It is divisible by 6. It is divisible by 12 as well.
Knowing that x is divisible by 6 is not enough to answer the question.
If x is divisible by 6, we can infer that it is divisible by 3 and 2. But we cannot deduce whether it is also divisible by 22 - which is essential to deduce that x is divisible by 12.
tatement 1 ALONE is NOT sufficient.
Eliminate choices A and D. Choices narrow down to B, C or E.
tatement 1 ALONE is NOT sufficient.
Eliminate choices A and D. Choices narrow down to B, C or E.
Evaluate Statement (2) ALONE: x is divisible by 8
If x is divisible by 8, then x will definitely be divisible by 4.
However, from statement (2) alone we do not know if x is divisible by 3.
Alternative Approach: Look for a counter example
If x is divisible by 8, then x will definitely be divisible by 4.
However, from statement (2) alone we do not know if x is divisible by 3.
Alternative Approach: Look for a counter example
Example: x = 8. It is divisible by 8. However, it is NOT divisible by 12.
Counter Example:x = 24. It is divisible by 8. It is divisible by 12 as well.
Knowing that x is divisible by 8 is not enough to answer the question.
Counter Example:x = 24. It is divisible by 8. It is divisible by 12 as well.
Knowing that x is divisible by 8 is not enough to answer the question.
Statement 2 ALONE is NOT sufficient.
Eliminate choice B. Choices narrow down to C or E.
Evaluate Statements (1) & (2) Together: x is divisible by 6 & x is divisible by 8
From statement 1, if x is divisible by 6, it is definitely divisible by 3.
From statement 2, if x is divisible by 8, it is definitely divisible by 4.
So, by combining the two statements, we can conclude that x is divisible by 3 and by 4.
Or that x is divisible by 12.
Eliminate choice B. Choices narrow down to C or E.
Evaluate Statements (1) & (2) Together: x is divisible by 6 & x is divisible by 8
From statement 1, if x is divisible by 6, it is definitely divisible by 3.
From statement 2, if x is divisible by 8, it is definitely divisible by 4.
So, by combining the two statements, we can conclude that x is divisible by 3 and by 4.
Or that x is divisible by 12.
Numbers
All numbers used are real numbers.
Figures
A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).
Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.
You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.
All figures lie in a plane unless otherwise indicated.
Q.How is Bill related to Betty?
1. Cindy, the wife of Bill's only brother Chris does not have any siblings.
2. Betty is Cindy's brother in law's wife.- a)Statement (1 ) ALONE is sufficient, but statement (2 ) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed
Correct answer is option 'C'. Can you explain this answer?
Numbers
All numbers used are real numbers.
Figures
A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).
Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.
You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.
All figures lie in a plane unless otherwise indicated.
Q.
All numbers used are real numbers.
Figures
A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).
Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.
You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.
All figures lie in a plane unless otherwise indicated.
Q.
How is Bill related to Betty?
1. Cindy, the wife of Bill's only brother Chris does not have any siblings.
2. Betty is Cindy's brother in law's wife.
1. Cindy, the wife of Bill's only brother Chris does not have any siblings.
2. Betty is Cindy's brother in law's wife.
a)
Statement (1 ) ALONE is sufficient, but statement (2 ) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed
|
|
Palak Saha answered |
We combine the two statements, we know that Bill and Cindy are related to each other through Chris, who is the only brother of Bill and that Cindy is Betty's brother in law's wife.
Cindy does not have any siblings and hence her brother in law has to necessarily be her husband's sibling. As Chris is the only brother of Bill, Cindy's brother in law has to be Bill and Betty is his wife.
Statements TOGETHER are SUFFICIENT.
Choice C is the answer.
Numbers
All numbers used are real numbers.
Figures
A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).
Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.
You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.
All figures lie in a plane unless otherwise indicated.
Q.When Y is divided by 2, is the remainder 1?
1. (-1) (Y+2) = -1
2. Y is prime.- a)Statement (1 ) ALONE is sufficient, but statement (2 ) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed
Correct answer is option 'A'. Can you explain this answer?
Numbers
All numbers used are real numbers.
Figures
A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).
Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.
You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.
All figures lie in a plane unless otherwise indicated.
Q.
All numbers used are real numbers.
Figures
A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).
Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.
You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.
All figures lie in a plane unless otherwise indicated.
Q.
When Y is divided by 2, is the remainder 1?
1. (-1) (Y+2) = -1
2. Y is prime.
1. (-1) (Y+2) = -1
2. Y is prime.
a)
Statement (1 ) ALONE is sufficient, but statement (2 ) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed
|
|
Palak Saha answered |
STATEMENT 1:
(-1)ODD NUMBER = -1
Therefore, Y + 2 is an odd number.
Hence, Y has to be an odd number.
So, when Y is divided by 2, the remainder is 1.
Statement 1 ALONE is SUFFICIENT.
Eliminate choices B, C, and E. Answer choices narrow down to A or D.
STATEMENT 2:
Y could be '2' which is an even number.
So, if Y is 2, when Y is divided by 2, the remainder is '0'.
All other prime numbers are odd numbers.
So, if Y is one of the other prime numbers, when Y is divided by 2, the remainder is '1'.
We donot have enough data in the question stem or statement 2 to conclude whether Y is 2 or one of the other prime numbers.
As we are not able to conclude whether Y is an even number using statement 2, it is not sufficient.
Therefore, Y + 2 is an odd number.
Hence, Y has to be an odd number.
So, when Y is divided by 2, the remainder is 1.
Statement 1 ALONE is SUFFICIENT.
Eliminate choices B, C, and E. Answer choices narrow down to A or D.
STATEMENT 2:
Y could be '2' which is an even number.
So, if Y is 2, when Y is divided by 2, the remainder is '0'.
All other prime numbers are odd numbers.
So, if Y is one of the other prime numbers, when Y is divided by 2, the remainder is '1'.
We donot have enough data in the question stem or statement 2 to conclude whether Y is 2 or one of the other prime numbers.
As we are not able to conclude whether Y is an even number using statement 2, it is not sufficient.
Statement 2 ALONE is NOT sufficient.
Choice A is the correct answer.
Choice A is the correct answer.
Numbers
All numbers used are real numbers.
Figures
A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).
Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.
You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.
All figures lie in a plane unless otherwise indicated.
Q.Is x3 > x2 ?
1. x > 0
2. x < 1- a)Statement (1 ) ALONE is sufficient, but statement (2 ) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed
Correct answer is option 'B'. Can you explain this answer?
Numbers
All numbers used are real numbers.
Figures
A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).
Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.
You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.
All figures lie in a plane unless otherwise indicated.
Q.
All numbers used are real numbers.
Figures
A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).
Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.
You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.
All figures lie in a plane unless otherwise indicated.
Q.
Is x3 > x2 ?
1. x > 0
2. x < 1
1. x > 0
2. x < 1
a)
Statement (1 ) ALONE is sufficient, but statement (2 ) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed
|
|
Palak Saha answered |
Statement 1: x > 0
We know that x is a positive number.
Interval 1: If 0 < x < 1, then x3 < x2.
For example, (0.5)3 = 0.125, which is lesser than (0.5)2 = 0.25
The answer to the question is NO.
Interval 2: If x > 1, then x3 > x2
For example, 23 = 8 which is greater than 22 = 4
The answer to the question is YES.
We do NOT have a DEFINITE answer using statement 1.
Statement 1 ALONE is NOT sufficient.
Eliminate choices A and D. Choices narrow down to B, C or E.
We know that x is a positive number.
Interval 1: If 0 < x < 1, then x3 < x2.
For example, (0.5)3 = 0.125, which is lesser than (0.5)2 = 0.25
The answer to the question is NO.
Interval 2: If x > 1, then x3 > x2
For example, 23 = 8 which is greater than 22 = 4
The answer to the question is YES.
We do NOT have a DEFINITE answer using statement 1.
Statement 1 ALONE is NOT sufficient.
Eliminate choices A and D. Choices narrow down to B, C or E.
Evaluate Statement (2) ALONE
Statement 2: x < 1
Interval 1: For positive values of x, i.e., 0 < x < 1, we know x3 < x2.
The answer to the question is NO.
Statement 2: x < 1
Interval 1: For positive values of x, i.e., 0 < x < 1, we know x3 < x2.
The answer to the question is NO.
Interval 2:For negative values of x, x3 will be a negative number and x2 will be a positive number.
Hence, x3 < x2
The answer to the question is NO.
Hence, x3 < x2
The answer to the question is NO.
Lastly, what is the answer if x = 0?
When x = 0, x3 = x2.
The answer to the question is NO.
When x = 0, x3 = x2.
The answer to the question is NO.
Hence, if we know that x < 1, we can conclude that x3 is NOT GREATER THAN x2.
We have a DEFINITE answer, even if it is NO.
We have a DEFINITE answer, even if it is NO.
Statement 2 ALONE is sufficient. Eliminate choices C and E.
Choice B is the answer.
NumbersAll numbers used are real numbers.
FiguresA figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.All figures lie in a plane unless otherwise indicated.
Question: What is the value of b?
1) a = 3
2) (a-3)(b+2)=0- a)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- b)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
- c)EACH statement ALONE is sufficient to answer the question asked.
- d)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
- e)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
Correct answer is option 'D'. Can you explain this answer?
Numbers
All numbers used are real numbers.
Figures
Figures
A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).
Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.
You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.
All figures lie in a plane unless otherwise indicated.
Question: What is the value of b?
1) a = 3
2) (a-3)(b+2)=0
Question: What is the value of b?
1) a = 3
2) (a-3)(b+2)=0
a)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
b)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
c)
EACH statement ALONE is sufficient to answer the question asked.
d)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
e)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
|
Rahul Kapoor answered |
The correct answer is E. i.e., Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Explanatory Answer
Statement 1: It is obvious that statement 1 is not sufficient. Data given does not provide any information about the value of b. So, we can eliminate choices A and D. So we are down to choices B, C or E.
Statement 1: It is obvious that statement 1 is not sufficient. Data given does not provide any information about the value of b. So, we can eliminate choices A and D. So we are down to choices B, C or E.
Statement 2: An equation with two variables ‘a’ and ‘b’. Hence, the information provided is not sufficient.
Note do not make the mistake of solving the equation as either (a – 3) = 0 or (b + 2) = 0 and decide that b = -2. What if only (a – 3) = 0 and (b + 2) was not ‘0’.
Combining the two statements, we know a = 3, so, (a – 3) = 0. But that leaves the question of what (b + 2) or what ‘b’ is unanswered.
Hence, choice D is the correct answer.
Numbers
All numbers used are real numbers.
Figures
A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).
Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.
You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.
All figures lie in a plane unless otherwise indicated.
Q.If a salesman received a commission of 3% of the sales that he has booked in a month, what was the sales booked by the salesman in the month of November 2003?
1. The sales booked by the salesman in the month of November 2003 minus salesman's commission was $245,000
2. The selling price of the sales booked by the salesman in the month of November 2003 were 125 percent of the original purchase price of $225,000.- a)Statement (1 ) ALONE is sufficient, but statement (2 ) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed
Correct answer is option 'D'. Can you explain this answer?
Numbers
All numbers used are real numbers.
Figures
A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).
Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.
You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.
All figures lie in a plane unless otherwise indicated.
Q.
All numbers used are real numbers.
Figures
A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).
Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.
You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.
All figures lie in a plane unless otherwise indicated.
Q.
If a salesman received a commission of 3% of the sales that he has booked in a month, what was the sales booked by the salesman in the month of November 2003?
1. The sales booked by the salesman in the month of November 2003 minus salesman's commission was $245,000
2. The selling price of the sales booked by the salesman in the month of November 2003 were 125 percent of the original purchase price of $225,000.
1. The sales booked by the salesman in the month of November 2003 minus salesman's commission was $245,000
2. The selling price of the sales booked by the salesman in the month of November 2003 were 125 percent of the original purchase price of $225,000.
a)
Statement (1 ) ALONE is sufficient, but statement (2 ) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed
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Kiran Nambiar answered |
From statement 1, we know the sales value after the salesman's commission is subtracted.
From the question stem, we know his commission is 3% of the sales booked. Then value of sales after subtracting his commission is 100 - 3 = 97% of the sales booked.
Putting the two together, we can deduce that 97% of sales booked = $245,000. So we can find out the sales booked.
Caveat: Do not waste time computing the value. All we need to know is whether the answer will be unique. We know the answer is unique.
Statement 1 ALONE is SUFFICIENT.
Eliminate choices B, C and E.
====
====
From statement 2, we know that the original purchase of the products is $225,000.
We can compute the sales booked as 125% of 225,000 = 1.25 * 225,000.
Caveat: Do not waste time computing the value. All we need to know is whether the answer will be unique. We know the answer is unique.
Statement 2 ALONE is SUFFICIENT.
Each statement is INDEPENDENTLY sufficient. So, choice D is the correct answer to this data sufficiency question.
Numbers
All numbers used are real numbers.
Figures
A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).
Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.
You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.
All figures lie in a plane unless otherwise indicated.
Q.Is x/y a terminating decimal?
1. x is a multiple of 2
2. y is a multiple of 3- a)Statement (1 ) ALONE is sufficient, but statement (2 ) alone is not sufficient to answer the question asked.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
- d)EACH statement ALONE is sufficient to answer the question asked.
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed
Correct answer is option 'E'. Can you explain this answer?
Numbers
All numbers used are real numbers.
Figures
A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).
Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.
You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.
All figures lie in a plane unless otherwise indicated.
Q.
All numbers used are real numbers.
Figures
A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).
Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.
You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.
All figures lie in a plane unless otherwise indicated.
Q.
Is x/y a terminating decimal?
1. x is a multiple of 2
2. y is a multiple of 3
1. x is a multiple of 2
2. y is a multiple of 3
a)
Statement (1 ) ALONE is sufficient, but statement (2 ) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed
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Gauri Iyer answered |
Evaluate Statement (1) ALONE
Statement (1) : x is a multiple of 2
Statement (1) : x is a multiple of 2
No information about y has been provided.
Approach: Let us look for a counter example.
Approach: Let us look for a counter example.
Example: When x = 2 and y = 3, x/y is non-terminating.
The answer to the question is NO.
The answer to the question is NO.
Counter Example: When x = 2 and y = 4, x/y is terminating.
The answer to the question is YES.
The answer to the question is YES.
We have found a counter example. Therefore, statement 1 does not provide a DEFINITE answer.
Statement 1 ALONE is NOT sufficient.
Eliminate choices A and D. Choices narrow down to B, C or E.
Statement 1 ALONE is NOT sufficient.
Eliminate choices A and D. Choices narrow down to B, C or E.
Evaluate Statement (2) ALONE
Statement (2) : y is a multiple of 3
Statement (2) : y is a multiple of 3
No information about x has been provided.
Approach: Let us look for a counter example.
Approach: Let us look for a counter example.
Example:When x = 3 and y = 3, xyxy is terminating.
The answer to the question is YES.
The answer to the question is YES.
Counter Example: When x = 2 and y = 3, xyxy is non-terminating.
The answer to the question is NO.
The answer to the question is NO.
We have found a counter example. Therefore, statement 2 does not provide a DEFINITE answer.
Statement 2 ALONE is NOT sufficient.
Eliminate choice B. Choices narrow down to C or E.
Evaluate Statements (1) & (2) Together
Statements Together : x is a multiple of 2 & y is a multiple of 3
Approach: Let us look for a counter example.
Statement 2 ALONE is NOT sufficient.
Eliminate choice B. Choices narrow down to C or E.
Evaluate Statements (1) & (2) Together
Statements Together : x is a multiple of 2 & y is a multiple of 3
Approach: Let us look for a counter example.
Example:When x = 6 and y = 6, x/y is terminating.
The answer to the question is YES.
The answer to the question is YES.
Counter Example: When x = 2 and y = 3, x/y is non-terminating.
The answer to the question is NO.
The answer to the question is NO.
We have found a counter example. Despite combining the information in the statements we are not able to find a DEFINITE answer.
Statements TOGETHER are NOT SUFFICIENT. Choice E is the answer.
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Logical Knowledge for Super TET
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