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Among the respondents of a survey, onefourth do not like to watch movies; and of those who do not like to watch movies, twothird do not like to read also. Can the number of respondents who do not like to read be 70?
(1) The number of respondents who like to read and also like to watch movies is 110
(2) The number of respondents of the survey is 480
Steps 1 & 2: Understand Question and Draw Inferences
Given: Let the total # of respondents be T
To find: Can number of people who don’t like to read be 70?
Step 3: Analyze Statement 1 independently
The number of respondents who like to read and also like to watch movies is 110
Since T is the number of students, it must be a positive integer.
Since Z = 70 doesn’t lead to a positive integer value of T, Z cannot be 70.
Step 4: Analyze Statement 2 independently
The number of respondents of the survey is 480
T = 480
So, the above table becomes:
Since there are 80 people who do not like reading, Z cannot be less than 80.
Therefore, Z cannot be 70
Step 5: Analyze Both Statements Together (if needed)
Since we’ve already arrived at a unique answer in each of Steps 3 and 4, this step is not required
Answer: Option D
If 30 percent of the students in an MBA program had read the work of Shakespeare, 35 percent had read the work of Peter Drucker and 5 percent had read the work of both Shakespeare and Peter Drucker, what percent of the students had read the work of neither Shakespeare nor Peter Drucker?
Given:
To find: % of students who had read neither Shakespeare nor Drucker
Approach:
Working Out:
Looking at the answer choices, we see that the correct answer is Option D
Of the 80 children in a group, 64 like chocolates. How many children do not like icecream?
(1) The number of children who like chocolates but do not like icecream is 10 more than the number of children who like icecream but do not like chocolate
(2) The number of children who like both icecream and chocolate is 38 more than the number of children who neither like icecream nor like chocolate
Steps 1 & 2: Understand Question and Draw Inferences
Given:
To find: Number of children who don’t like icecream
Step 3: Analyze Statement 1 independently
The number of children who like chocolates but do not like icecream is 10 more than the number of children who like icecream but do not like chocolate
Let the number of children who like icecream but do not like chocolate be Y
Let’s represent the given information in the table:
Thus, number of students who do not like icecream is 26.
Sufficient.
Step 4: Analyze Statement 2 independently
The number of children who like both icecream and chocolate is 38 more than the number of children who neither like icecream nor like chocolate
Let the number of children who neither like icecream nor like chocolate be X
Let’s represent the given information in the table:
Thus, number of students who do not like icecream is 26.
Sufficient.
Step 5: Analyze Both Statements Together (if needed)
Since we’ve already arrived at a unique answer in each of Steps 3 and 4, this step is not required
Answer: Option D
Out of the 60 employees of a startup, only 10 are nonengineers. How many employees of the startup are engineers with a MBA degree?
(1) Only 1 out of every 12 employees with a MBA degree is a nonengineer
(2) More than 55 percent of all employees have a MBA degree
Steps 1 & 2: Understand Question and Draw Inferences
Given: 60 employees classified on 2 attributes:
To find: Number of Engineers with MBA Degree
Step 3: Analyze Statement 1 independently
Statement 1 says that ‘Only 1 out of every 12 employees with a MBA degree is a nonengineer’
must be less than equal to the row total of 50
Step 4: Analyze Statement 2 independently
Statement 2 says that ‘More than 55 percent of all employees have a MBA degree’
However, this doesn’t answer the question about number of Engineers with MBA Degree
Not Sufficient.
Step 5: Analyze Both Statements Together (if needed)
Answer: Option E
In a certain town, 40 percent of the residents own a car. What percent of the residents own neither a house nor a car?
(1) Each resident who owns a house also owns a car but the viceversa is not true
(2) 30 percent of the residents own a house
Steps 1 & 2: Understand Question and Draw Inferences
The residents of the town are classified according to two attributes – housing and car ownership.
Let’s depict this fact, and the given information in a table.
Step 3: Analyze Statement 1 independently
So, the percentage of people who own a house but not own a car = 0%
Therefore, the percentage of people who neither own a house nor own a car = 60% – 0% = 60%
Therefore, St. 1 is sufficient to answer the question.
Step 4: Analyze Statement 2 independently
Statement 2 says that 30% of all residents own a house. Let’s represent this information in the table:
Not sufficient to determine a unique value of the unknown.
Step 5: Analyze Both Statements Together (if needed)
Since we arrived at an answer in Step 3, this step is not required.
Answer: A
In a class of 120 students, 80 enrolled for a Mathematics seminar, 60 enrolled for Business Basics seminar, while 12 did not enroll for either of the 2 seminars. How many students enrolled for both the seminars?
Given: A class of 120 students who are classified on their enrollment for 2 seminars:
Representing the given information visually:
TO find: Number of students who enrolled for both seminars
Approach:
Working Out
Answer: Option B
List A ={1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
The integers from list A are used to form two distinct sets P and Q each consisting of distinct integers only. If all the integers from list A are used at least once and none of the integers are used more than twice, how many integers from list A are used more than once?
1) The numbers of integers in sets P and Q are, respectively, 2 and 3 less than the number of integers in list A.
2) The difference between the sum of the integers in sets P and Q and the sum of the integers in list A is 15.
Steps 1 & 2: Understand Question and Draw Inferences
Given:
To Find: Number of integers used more than once
So to determine the number of integers used more than once, we will have to find value of (x+y).
Step 3: Analyze Statement 1 independently
The numbers of integers in sets P and Q are, respectively, 2 and 3 less than the number of integers in list A.
Since we know the value of x+y, we will find the answer.
Sufficient to answer.
Step 4: Analyze Statement 2 independently
The difference between the sum of the integers in sets P and Q and the sum of the integers in list A is 15.
Since we do not know the exct number of repeated integers, we will not be able to determine the value of x &y
Insufficient to answer
Step 5: Analyze Both Statements Together (if needed)
As we have a unique answer from step3, this step is not required.
Answer: A
At a certain university, 120 students were asked to take a surprise quiz to check their awareness of history and civil rights. The score distribution of the students is tabulated below:
If 70 students scored greater than 30% in both tests, what was the number of students who scored less than 30% in both the history and the civil rights sections of the quiz?
Given:
To find: Number of students who scored <30% in History and <30% in Civil Rights
Approach:
Working Out:
Note that from the table given in the question, we know that the total number of students who scored less than 30% in Civil Rights is 36, and the total number of students who scored less than 30% in History is 20
Step 2: The number of students who scored < 30% in History and ≥ 30% in Civil Rights
Step 3: The number of students who scored < 30% in History and in Civil Rights
Looking at the answer choices, we see that the correct answer is Option A
200 students in an MBA program voted for 2 electives A and B to be included in their curriculum. A student could vote for either one or both or none of the electives. If 30% of the students voted for elective A, how many students voted for both the electives?
1) The sum of the number of students who voted for none of the electives and those who voted for only elective A is 50% more than the number of students who voted for only elective B.
2) 60% of the students did not vote for elective B.
Steps 1 & 2: Understand Question and Draw Inferences
Given:
To Find: Value of b
Step 3: Analyze Statement 1 independently
The sum of the number of students who voted for none of the electives and those who voted for only elective A is 50% more than the number of students who voted for only elective B.
Insufficient to answer.
Step 4: Analyze Statement 2 independently
60% of the students did not vote for elective B.
Insufficient to answer
Step 5: Analyze Both Statements Together (if needed)
Now we have 4 equations and 4 unknowns, so we will be able to determine a unique value of b.
Sufficient to answer
Answer: C
Out of the 14 people in a group, 3 like to play Badminton, Soccer and Volleyball. If there are 7 people in the group who like to play Volleyball and 5 who like to play Badminton and Soccer, what is the number of people who do not like to play any of the 3 games?
Given: 14 people classified for their liking for games as follows:
To find: (Number of people who Do not Like Volleyball and who do not Like Badmintion and Soccer = Number of people who Do Not Like Volleyball – Number of people who Like Badminton and Soccer)
Approach:
Working Out
2. Now, let’s focus at the last column (‘Total’) of the table
‘Do Not Like Volleyball’ Total number = 14 – 7 = 7
3. Finally, let’s focus on the ‘Do not Like Volleyball’ row of the table:
‘Do not Like Volleyball – Like Badminton and Soccer’ Number = 7 – 2 = 5
This is our required number
Answer: Option B
Set A contains n distinct positive integers, all greater than 1. If the number of even integers in the set is 5 and the set also contains 4 odd prime numbers, what is the value of n?
(1) The set contains 2 odd composite numbers.
(2) The set contains 6 composite numbers
Steps 1 & 2: Understand Question and Draw Inferences
Given: A set of n distinct positive integers, all greater than 1,is classified based on 2 attributes:
To find: n = ?
Step 3: Analyze Statement 1 independently
Statement 1 says that ‘The set contains 2 odd composite numbers’
Step 4: Analyze Statement 2 independently
Statement 2 says that ‘The set contains 6 composite numbers’
Completing the table, we see that we still do not get the value of n
So, Statement 2 alone is not sufficient
Step 5: Analyze Both Statements Together (if needed)
Since we’ve already arrived at a unique answer in Step 3, this step is not required
Answer: Option A
From a list of integers, all the multiples of 5 are sorted into Set A and all the even integers are sorted into Set B. If 60% of the integers in Set A and 50% of the integers in Set B are not divisible by 10, which of the following statements must be true?
I. The number of integers in Set A is less than the number of integers in Set B
II. The number of integers in Set B that are divisible by 10 is greater than the corresponding number in Set A
III. The number of odd multiples of 5 in Set A is greater than the number of integers in Set B that are not divisible by 10.
Given:
To find: Which of the 3 statements must be true?
Approach:
Working Out:
Looking at the answer choices, we see that the correct answer is Option C
A class in a certain school consists of boys and girls in the ratio of 2:1 . In a mathematics test, 60% of the class passed the test. If 40% of the boys failed the test, what percentage of the class are girls who passed the test?
Given
To Find:
Approach
Working Out
So, the number of girls who passed the test are equal to 20% of the total class strength.
Answer: B
A survey was conducted among a group of 83 American travel enthusiasts to determine the countries that the group members had visited. The data collected in the survey is summarized as below:
What is the number of surveyed travel enthusiasts who had visited all the three countries?
Given:
To find: The number of surveyed people who visited all 3 countries.
Approach:
Working Out:
Looking at the answer choices, we see that the correct answer is Option D
The table above shows the result of a survey done on 45 people in a residential area. 25 people in the survey had a television and 10 people had neither a television nor a cell phone.. If the number of people who did not have a television was equal to the number of people who had a television but did not have a cell phone, what was the ratio of the number of people who did not have a cell phone and the number of people who did not have a television?
Given
To Find:
Approach
Working Out
Answer: D
The table above shows the research data gathered from a group of rural and urban residents. What is the number of rural residents who own a car?
(1) The number of rural residents in the group is 60% of the number of urban residents in the group.
(2) The difference between the number of urban residents who own a car and the number of rural residents who own a car is onefifth of the number of rural and urban residents in the group.
Steps 1 & 2: Understand Question and Draw Inferences
Given: Data on two parameters are:
To find: Number of rural residents who own a car
The table can be filled in terms of P and Q as follows:
Step 3: Analyze Statement 1 independently
*(Number of urban residents)
Step 4: Analyze Statement 2 independently
Case 1: Q < 15
Case 2: Q > 15
2 values of Q. Not sufficient.
Step 5: Analyze Both Statements Together (if needed)
Case 1 : Q = 7
Case 2: Q = 27
Since the number of people cannot be in fractions, Case 2 can be rejected
So, Q = 7.
Answer: Option C
Of the 48 students in a class, 16 like to study History. What percentage of the girls in the class do not like to study History?
(1) Onethird of the boys in the class like to study History
(2) The number of girls who like History is 50 percent of the number of girls who do not like History
Steps 1 & 2: Understand Question and Draw Inferences
Given:
Step 3: Analyze Statement 1 independently
Onethird of the boys in the class like to study History
Sufficient
Step 4: Analyze Statement 2 independently
The number of girls who like History is 50 percent of the number of girls who do not like History
Sufficient
Step 5: Analyze Both Statements Together (if needed)
Since we’ve already arrived at a unique answer in Step 3 and Step 4, this step is not required
Answer: Option D
All the employees of Company X were appraised at the year end. 40% of the employees got a promotion, 50% of the employees got a salary hike and 30% of the employees neither got a promotion nor got a salary hike. If there were 40 employees who got both the promotion and the salary hike, what was the number of employees in the company?
Given
To Find: Number of employees in the company?
Approach
Total employees in the company = Employees who got only salary hike + Employees who got only promotion + Employees who got salary hike and promotion + Employees who got neither salary hike nor promotion
Working Out
Hence, the total number of employees in the company = 200
Answer: D
The human resources manager of a company compiled the data that the company had on the academic qualifications of its 100 employees. He observed that employees who had an Engineering and an MBA degree were the most in number and employees who had neither an Engineering nor an MBA degree were the least in number. If there were 20 employees who had an Engineering degree, but not an MBA degree, which of the following cannot be the number of employees who had an MBA degree?
Given
To Find: Among the options, which of them cannot be the number of employees who had an MBA degree?
Approach
2. We need to find the possible range of values of employees who had an MBA degree = b + c
3. As we know that total number of employees is 100 and d is minimum number of employees possible, we will use this information to find out the range of values of b + c
Working Out
Answer: A
A survey was conducted to find out the number of languages spoken by the 210 employees of a company. It was found that 60 employees did not speak English, 150 employees did not speak German and 170 employees did not speak French. If there were 20 employees who did not speak German or English and 20 employees who did not speak French or English, what was the maximum number of employees who spoke only English? Assume that each of the employees spoke at least one language and no employee spoke any language other than English, French and German.
Given
To Find: Maximum number of employees who spoke only English
Approach
Working Out
Answer: C
In a certain group of women, 70 percent of the women were employed and 25 percent did not have a graduate degree. Which of the following statements cannot be true?
Given:
To find: Which of the 3 statements cannot be true?
Approach:
Working Out:
Remember that the question is asking if a Statement is definitely false (that is, false for all possible values of Y)
The maximum possible value of Z is 25%. In this case, the table will look as under:
Looking at the answer choices, we see that the correct answer is Option A
A group of friends went to an icecream parlour and ordered only two types of icecream  chocolate and strawberry. Of the people in the group, at least one person ate only one type icecream, some people ate both types of icecream and at least one person did not eat any type of icecream. Did more people eat chocolate icecream than strawberry icecream?
1) The ratio of the number of people who ate chocolate icecream and people who ate strawberry icecream was greater than the ratio of the total number of people who went to icecream parlour and the number of people who did not eat any type of icecream.
2) The number of people who ate only one type of icecream is greater than the number of people who ate strawberry icecream.
Steps 1 & 2: Understand Question and Draw Inferences
Given:
To Find: If a + b > c + b ?
Step 3: Analyze Statement 1 independently
The ratio of the numbers of people who ate chocolate icecream and people who ate strawberry icecream was greater than the ratio of the total number of people who went to icecream parlour and the number of people who did not eat any type of icecream.
Sufficient to answer
Step 4: Analyze Statement 2 independently
The number of people who ate only one type of icecream is greater than the number of people who ate strawberry icecream.
Insufficient to answer
Step 5: Analyze Both Statements Together (if needed)
As we have a unqiue answer from step3, this step is not required.
Answer: A
In College X in the United States, there are 200 students in a class, of which 80 are female. If 10% of the class consists of female nonAmerican students and 3/5^{th }of the class are American students, how many of the students in the class are male American students?
Given
To Find: Number of students who are male Americans?
Approach
1. To find the number of male americans, we will use the relation:
2. Now, Number of female students = Number of female American students + Number of female nonAmerican students
Working Out
So, there are 60 male American students.
Answer: C
In a locality, for every person, who owns only a car, there are 3 people who own only a bike. The number of people who own both a car and a bike is half the number of people who either own only a car or only a bike. If the number of people who neither own a car nor a bike is equal to the number of people who own a bike, which of the following can be the total number of people in the locality?
Given
To Find: Among the options, which can be the total people in the locality?
Approach
Working Out
Answer: C
In a certain class of 66 students, 30 students study Science, 40 students study Humanities and 40 students study Dance. If all the students studied at least one of the subjects, then what is the maximum possible number of students who study all the three subjects?
Given:
To find: X – N = ?
Approach:
Working Out:
Looking at the answer choices, we see that the correct answer is Option D
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