Data Sufficiency- 1 Free MCQ Practice Test with Solutions

Test: Data Sufficiency- 1 - Question 1

Directions to Solve: In each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and mark the appreciate answer.

Question: In which year was Rahul born?
Statements:
I. Rahul at present is 25 years younger to his mother.
II. Rahul's brother, who was born in 1964, is 35 years younger to his mother.

A.
I alone is sufficient while II alone is not sufficient
B.
II alone is sufficient while I alone is not sufficient
C.
Either I or II is sufficient
D.
Neither I nor II is sufficient
E.
Both I and II are sufficient

Detailed Solution for Test: Data Sufficiency- 1 - Question 1

From Statement I:

Rahul = Mother - 25

From Statement II:

Rahul's brother born in 1964.

And, Rahul's Brother is 35 years younger to his mother.

So, his mother will be born on 1964 - 35 = 1929.

Now, After combining Statement I and II, we get:

Rahul was born on = 1929 + 25 = 1954.

So, Both Statement I and Statement II are sufficient.

Hence, the correct answer is "Option (E)".

Test: Data Sufficiency- 1 - Question 2

Directions to Solve: In each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and mark the appreciate answer.

Question: What will be the total weight of 10 poles, each of the same weight?
Statements:
I. One-fourth of the weight of each pole is 5 kg.
II. The total weight of three poles is 20 kilograms more than the total weight of two poles.

A.
I alone is sufficient while II alone is not sufficient
B.
II alone is sufficient while I alone is not sufficient
C.
Either I or II is sufficient
D.
Neither I nor II is sufficient
E.
Both I and II are sufficient

Detailed Solution for Test: Data Sufficiency- 1 - Question 2

From I, we conclude that weight of each pole = (4 x 5) kg = 20 kg.

So, total weight of 10 poles = (20 x 10) kg = 200 kg.

From II, we conclude that:

Weight of each pole = (weight of 3 poles) - (weight of 2 poles) = 20 kg.

So, total weight of 10 pojes = (20 x 10) kg = 200 kg.

So, Either of the statement is correct to give the answer.

So Option C is correct

Test: Data Sufficiency- 1 - Question 3

Directions to Solve: In each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and mark the appreciate answer.

Question: How many children does M have?
Statements:
I. H is the only daughter of X who is wife of M.
II. K and J are brothers of M.

A.
II alone is sufficient while I alone is not sufficient
B.
Neither I nor II is sufficient
C.
Either I or II is sufficient
D.
I alone is sufficient while II alone is not sufficient
E.
Both I and II are sufficient

Detailed Solution for Test: Data Sufficiency- 1 - Question 3

Statement I: H is the only daughter of X, who is the wife of M. This means M has at least one child (H, the daughter). Therefore, this statement alone is sufficient to answer that M has one child.
Statement II: K and J are brothers of M. This information provides no direct insight into how many children M has, as it talks about M's brothers, not M's children. Therefore, this statement alone is not sufficient to answer the question.

Hence, Statement I alone is sufficient, while Statement II alone is not sufficient to answer the question.

Test: Data Sufficiency- 1 - Question 4

Given below is a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements is sufficient to answer the question. You should use the given data and your knowledge of Mathematics to choose between the possible answers.

Question: Is a number T divisible by 144?

Statements:
I. T is a multiple of 216.

II. T is divisible by square of cube of 2.

A.
Choose this option if the Question can be answered by one of the Statements alone but not by the other.
B.
Choose this option if the Question can be answered by either Statement alone.
C.
Choose this option if the Question can be answered by using both Statements together, but cannot be answered by using either Statement alone.
D.
Choose this option if the Question cannot be answered even by using both Statements together.
E.
None of these

Detailed Solution for Test: Data Sufficiency- 1 - Question 4

From statement I:

If T is multiple of 216, then T can be 216 which is not divisible by 144 or T can be 432 which is divisible by 144. So, divisibility of T with 144 cannot be uniquely established.

∴ Statement I alone is not sufficient to answer the question.

From statement II:

T is divisible by square of cube of 2.

Square of cube of 2 = (2 × 2 × 2)² = 64

⇒ T is a multiple of 64.

So, T can be 192 which is not divisible by 144 or T can be 576 which is divisible by 144. So, divisibility of T with 144 cannot be uniquely established.

∴ Statement II alone is not sufficient to answer the question.

From statements I and II together:

T is divisible by square of cube of 2.

Square of cube of 2 = (2 × 2 × 2)² = 64

⇒ T is a multiple of 64.

Also, T is a multiple of 216.

⇒ T will be a multiple of LCM(216, 64).

⇒ T will be a multiple of 1728.

We know, 1728 = 144 x 12.

If T is divisible by 1728, it would be divisible by all its factors.

∴ T will be divisible by 144.

∴ Using both the statements together, we can answer the given question.

Test: Data Sufficiency- 1 - Question 5

Directions to Solve: In each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and mark the appreciate answer.

Question: How much was the total sale of the company?
Statements:
I. The company sold 8000 units of product A each costing Rs. 25.
II. This company has no other product line.

A.
I alone is sufficient while II alone is not sufficient
B.
II alone is sufficient while I alone is not sufficient
C.
Both I and II are needed to answer the question
D.
Neither I nor II is sufficient
E.
Either I or II is sufficient

Detailed Solution for Test: Data Sufficiency- 1 - Question 5

From I, total sale of product A = Rs. (8000 x 25) = Rs. 200000.

From II, we know that the company deals only in product A.

This implies that sale of product A is the total sale of the company, which is Rs. 200000.

So Option C is correct

Test: Data Sufficiency- 1 - Question 6

Directions to Solve: In each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and mark the appreciate answer.

Question: The last Sunday of March, 2006 fell on which date?
Statements:
I. The first Sunday of that month fell on 5th.
II. The last day of that month was Friday.

A.
I alone is sufficient while II alone is not sufficient
B.
II alone is sufficient while I alone is not sufficient
C.
Either I or II is sufficient
D.
Neither I nor II is sufficient
E.
Both I and II are sufficient

Detailed Solution for Test: Data Sufficiency- 1 - Question 6

From I, we conclude that 5th, 12th, 19th and 26th of March, 2006 were Sundays.

So, the last Sunday fell on 26th.

From II, we conclude that 31st March, 2006 was Friday. Thus, 26th March, 2006 was the last Sunday of the month.

So Option C is correct

Test: Data Sufficiency- 1 - Question 7

Directions to Solve: In each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and mark the appreciate answer.

Question: How many children are there between P and Q in a row of children?
Statements:
I. P is fifteenth from the left in the row.
II. Q is exactly in the middle and there are ten children towards his right.

A.
I alone is sufficient while II alone is not sufficient
B.
II alone is sufficient while I alone is not sufficient
C.
Either I or II is sufficient
D.
Neither I nor II is sufficient
E.
Both I and II are sufficient

Detailed Solution for Test: Data Sufficiency- 1 - Question 7

Correct option is E
From II, Q being in the middle, there are 10 children to his right as well as to his left. So, Q is 11th from the left.
From I, P is 15th from the left.
Thus, from both I and II, we conclude that there are 3 children between P and Q

Test: Data Sufficiency- 1 - Question 8

Directions to Solve: In each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and mark the appreciate answer.

Question: How is J related to P?
Statements:
I. M is brother of P and T is sister of P.
II. P's mother is married to J's husband who has one son and two daughters.

A.
I alone is sufficient while II alone is not sufficient
B.
II alone is sufficient while I alone is not sufficient
C.
Either I or II is sufficient
D.
Neither I nor II is sufficient
E.
Both I and II are sufficient

Detailed Solution for Test: Data Sufficiency- 1 - Question 8

According to the question, if we see that the statements as given below:
Statement I, M is the brother of P and T is the sister of P.
From I, the relation between J and P cannot be determined.
From statement II, we know that P's mother is married to J's husband, which means that J is P's mother.
Hence, If the data in statement I alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question is the correct answer.
So Option B is correct

Test: Data Sufficiency- 1 - Question 9

Directions to Solve: In each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and mark the appreciate answer.

Question: How is T related to K?
Statements:
I. R's sister J has married T's brother L, who is the only son of his parents.
II. K is the only daughter of L and J.

A.
I alone is sufficient while II alone is not sufficient
B.
II alone is sufficient while I alone is not sufficient
C.
Both I and II are sufficient
D.
Neither I nor II is sufficient
E.
Either I or II is sufficient

Detailed Solution for Test: Data Sufficiency- 1 - Question 9

From I, we know that L is T's brother and J's husband. Since L is the only son of his parents, T is L's sister.

From II, we know that K is L's daughter.

Thus, from I and II, we conclude that T is the sister of K's father i.e. T is K's aunt.

So Option C is correct

Test: Data Sufficiency- 1 - Question 10

Directions to Solve: In each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and mark the appreciate answer.

Question: How is X related to Y?
Statements:
I. Y and Z are children of D who is wife of X.
II. R's sister X is married to Y's father.

A.
I alone is sufficient while II alone is not sufficient
B.
II alone is sufficient while I alone is not sufficient
C.
Either I or II is sufficient
D.
Neither I nor II is sufficient
E.
Both I and II are sufficient

Detailed Solution for Test: Data Sufficiency- 1 - Question 10

From I, we conclude that Y is the child of D who is wife of X i.e. X is Y's father.

From II, X is married to Y's father. This implies that X is Y's mother.

So Option C is correct

Test: Data Sufficiency- 1 - Question 11

Directions to Solve: In each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and mark the appreciate answer.

Question: Who is to the immediate right of P among five persons P, Q, R, S and T facing North?
Statements:
I. R is third to the left of Q and P is second to the right of R.
II. Q is to the immediate left of T who is second to the right of P.

A.
I alone is sufficient while II alone is not sufficient
B.
II alone is sufficient while I alone is not sufficient
C.
Either I or II is sufficient
D.
Neither I nor II is sufficient
E.
Both I and II are sufficient

Detailed Solution for Test: Data Sufficiency- 1 - Question 11

Statement I: R is third to the left of Q and P is second to the right of R.

Case 1:

Case 2:

In both the cases, Q is to the immediate right of P.

Statement II: Q is the immediate left of T who is second to the right of P

Case 1:

Case 2:

Case 3:

In all three cases, Q is to the immediate right of P.

Therefore, the data either in (I) or (II) are sufficient to answer the question

Hence, option C is the correct answer.

Test: Data Sufficiency- 1 - Question 12

Directions to Solve: In each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and mark the appreciate answer.

Question: On which date of the month was Anjali born in February 2004?
Statements:
I. Anjali was born on an even date of the month.
II. Anjali's birth date was a prime number.

A.
I alone is sufficient while II alone is not sufficient
B.
II alone is sufficient while I alone is not sufficient
C.
Both I and II are sufficient
D.
Neither I nor II is sufficient
E.
Either I or II is sufficient

Detailed Solution for Test: Data Sufficiency- 1 - Question 12

From I and II, we conclude that Anjali was born in February 2004 on a date which is an even prime number. Since the only even prime number is 2, so Anjali was born on 2nd February, 2004.

So Option C is correct

Test: Data Sufficiency- 1 - Question 13

Directions to Solve: In each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and mark the appreciate answer.

Question: How is F related to P?
Statements:
I. P has two sisters M and N.
II. F's mother is sister of M's father.

A.
I alone is sufficient while II alone is not sufficient
B.
II alone is sufficient while I alone is not sufficient
C.
Either I or II is sufficient
D.
Both I and II are sufficient
E.
Neither I nor II is sufficient

Detailed Solution for Test: Data Sufficiency- 1 - Question 13

From I and II, we conclude that P is M's brother and so M's father is P's father. So, F is the child of the sister of P's father i.e. F's mother is P's aunt or F is P's cousin.

So Option D is correct

Test: Data Sufficiency- 1 - Question 14

Directions to Solve: In each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and mark the appreciate answer.

Question: How is X related to Y?
Statements:
I. Y says, "I have only one brother".
II. X says, "I have only one sister".

A.
I alone is sufficient while II alone is not sufficient
B.
II alone is sufficient while I alone is not sufficient
C.
Either I or II is sufficient
D.
Neither I nor II is sufficient
E.
Both I and II are sufficient

Detailed Solution for Test: Data Sufficiency- 1 - Question 14

Statement I: Y says, "I have only one brother."

This statement alone does not provide any information about the relationship between X and Y. We do not know who Y's brother is, nor do we know if X is related to Y.

Statement II: X says, "I have only one sister."

This statement alone does not provide any information about the relationship between X and Y. We do not know who X's sister is, nor do we know if Y is related to X.

Combining Statements I and II:

Even when combining both statements, we do not have enough information to determine the relationship between X and Y. We need more information about the family structure or a direct statement about how X and Y are related.

Therefore, the data given in both statements I and II together are not sufficient to answer the question.

Answer: D Neither I nor II is sufficient

Test: Data Sufficiency- 1 - Question 15

Directions to Solve: In each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and mark the appreciate answer.

Question: B is the brother of A. How is A related to B?
Statements:
I. A is the sister of C.
II. E is the husband of A.

A.
I alone is sufficient while II alone is not sufficient
B.
II alone is sufficient while I alone is not sufficient
C.
Either I or II is sufficient
D.
Neither I nor II is sufficient
E.
Both I and II are sufficient

Detailed Solution for Test: Data Sufficiency- 1 - Question 15

B is A's brother means A is either brother or sister of B. Now, each one of I and II individually indicates that A is a female, which means that A is B's sister.

So Option C is correct

Test: Data Sufficiency- 1 - Question 16

Directions to Solve: In each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and mark the appreciate answer.

Question: How many children are there in the row of children facing North?
Statements:
I. Vishakha who is fifth from the left end is eighth to the left of Ashish who is twelfth from the right end.
II. Rohit is fifth to the left of Nisha who is seventh from the right end and eighteenth from the left end.

A.
I alone is sufficient while II alone is not sufficient
B.
II alone is sufficient while I alone is not sufficient
C.
Either I or II is sufficient
D.
Neither I nor II is sufficient
E.
Both I and II are sufficient

Detailed Solution for Test: Data Sufficiency- 1 - Question 16

Since 8th to the left of 12th from the right is 20th from the right, so from I, we know that Vishakha is 5th from left and 20th from right i.e. there are 4 children to the left and 19 to the right of Vishakha. So, there are (4 + 1 + 19) i.e. 24 children in the row.

From II, Nisha is 7th from right and 18th from left end of the row.

So, there are (6 + 1 + 17) = 24 children in the row.

So Option C is correct

Test: Data Sufficiency- 1 - Question 17

Directions to Solve: In each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and mark the appreciate answer.

Question: How many doctors are practising in this town?
Statements:
I. There is one doctor per seven hundred residents.
II. There are 16 wards with each ward having as many doctors as the number of wards.

A.
I alone is sufficient while II alone is not sufficient
B.
II alone is sufficient while I alone is not sufficient
C.
Either I or II is sufficient
D.
Neither I nor II is sufficient
E.
Both I and II are sufficient

Detailed Solution for Test: Data Sufficiency- 1 - Question 17

From I, total number of doctors in town = (1/700 x N), where N = total number of residents in town. But, the value of N is not known.

From II, total number of doctors in town

= (Number of wards in town) x (Number of doctors in each ward)

= 16 x 16 = 256.

So Option B is correct

Test: Data Sufficiency- 1 - Question 18

Directions to Solve: In each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and mark the appreciate answer.

Question: On which day of the week was birthday of Sahil?
Statements:
I. Sahil celebrated his birthday the very next day on which Arun celebrated his birthday.
II. The sister of Sahil was born on the third day of the week and two days after Sahil was born.

A.
I alone is sufficient while II alone is not sufficient
B.
II alone is sufficient while I alone is not sufficient
C.
Either I or II is sufficient
D.
Neither I nor II is sufficient
E.
Both I and II are sufficient

Detailed Solution for Test: Data Sufficiency- 1 - Question 18

I does not mention the day of the week on the birthday of either Arun or Sahil.

According to II, Sahil's sister was born on Wednesday and Sahil was born two days before Wednesday i.e. on Monday.

So Option B is correct

Test: Data Sufficiency- 1 - Question 19

Directions to Solve: In each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and mark the appreciate answer.

Question: How many pages of book X did Robert read on Sunday?
Statements:
I. The book has 300 pages out of which two-thirds were read by him before Sunday.
II. Robert read the last 40 pages of the book on the morning of Monday.

A.
I alone is sufficient while II alone is not sufficient
B.
Both I and II are sufficient
C.
Either I or II is sufficient
D.
Neither I nor II is sufficient
E.
II alone is sufficient while I alone is not sufficient

Detailed Solution for Test: Data Sufficiency- 1 - Question 19

From I and II, we find that Robert read (300 x 2/3) i.e. 200 pages before Sunday and the last 40 pages on Monday.

This means that he read [300 - (200 + 40)] i.e. 60 pages on Sunday.

So Option B is correct

Test: Data Sufficiency- 1 - Question 20

Directions to Solve: In each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and mark the appreciate answer.

Question: How is Tanya(girl) related to the man in the photograph?
Statements:
I. Man in the photograph is the only son of Tanya's grandfather.
II. The man in the photograph has no brothers or sisters and his father is Tanya's grandfather.

A.
I alone is sufficient while II alone is not sufficient
B.
Either I or II is sufficient
C.
II alone is sufficient while I alone is not sufficient
D.
Neither I nor II is sufficient
E.
Both I and II are sufficient

Detailed Solution for Test: Data Sufficiency- 1 - Question 20

From I, we conclude that the man is the only son of Tanya's grandfather i.e. he is Tanya's father or Tanya is the man's daughter.
From II, we conclude that the man's father is Tanya's grandfather. Since the man has no brothers or sisters, so he is Tanya's father or Tanya is the man's daughter.

Test: Data Sufficiency- 1 - Question 21

Directions to Solve: In each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and mark the appreciate answer.

Question: Among T, V, B, E and C, who is the third from the top when arranged in the descending order of their weights?
Statements:
I. B is heavier than T and C and is less heavier than V who is not the heaviest.
II. C is heavier than only T.

A.
I alone is sufficient while II alone is not sufficient
B.
II alone is sufficient while I alone is not sufficient
C.
Either I or II is sufficient
D.
Neither I nor II is sufficient
E.
Both I and II are sufficient

Detailed Solution for Test: Data Sufficiency- 1 - Question 21

From I, we have: B > T, B > C, V > B. Thus, V is heavier than each one of B, T and C. But V is not the heaviest. So, E is the heaviest.

Thus, we have the order. E > V > B > T > C or E > V > B > C > T. Clearly, B is third from the top.

So Option A is correct

Test: Data Sufficiency- 1 - Question 22

Directions to Solve: In each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and mark the appreciate answer.

Question: Which word in the code language means 'flower'?
Statements:
I. 'de fu la pane' means 'rose flower is beautiful' and 'la quiz' means 'beautiful tree'.
II. 'de la chin' means 'red rose flower' and 'pa chin' means 'red tea'.

A.
I alone is sufficient while II alone is not sufficient
B.
Neither I nor II is sufficient
C.
Either I or II is sufficient
D.
II alone is sufficient while I alone is not sufficient
E.
Both I and II are sufficient

Detailed Solution for Test: Data Sufficiency- 1 - Question 22

To determine which word in the code language means 'flower,' let's analyze the statements.

Statements

Statement I:
'de fu la pane' means 'rose flower is beautiful'
'la quiz' means 'beautiful tree'

Statement II:
'de la chin' means 'red rose flower'
'pa chin' means 'red tea'

Analysis

Statement I Analysis:

From 'de fu la pane' = 'rose flower is beautiful', we can identify the words for 'rose', 'flower', 'is', and 'beautiful'.
From 'la quiz' = 'beautiful tree', we can identify the words for 'beautiful' and 'tree'.
Thus, we have the common word 'la' which appears in both statements, indicating it could be 'beautiful'.

Combining this, we can deduce:

'de' might be 'rose' or 'flower'
'fu' might be 'rose' or 'flower'
'pane' might be 'is' or 'beautiful'
'quiz' means 'tree'
'la' means 'beautiful'

From these deductions, 'flower' can be identified if we compare it with 'de' or 'fu'. But we do not have enough information to exactly determine which one is 'flower'.

Statement II Analysis:

From 'de la chin' = 'red rose flower', we have:
- 'de' = 'red'
- 'la' = 'rose' (by elimination, because 'chin' has to be 'flower')
From 'pa chin' = 'red tea':
- 'pa' = 'tea'
- 'chin' = 'red'

Here, 'chin' seems to be 'red', and 'de' is 'flower' which is consistent with the given data.

Since 'chin' = 'red' and 'de' = 'flower', we have clearly identified 'de' as 'flower'.

Conclusion:

Statement II alone is sufficient to determine that 'de' means 'flower'.

Statement I alone does not provide sufficient information to identify the word for 'flower' precisely.

Thus, the correct answer is:

(D) If the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.

Test: Data Sufficiency- 1 - Question 23

Given below is a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements is sufficient to answer the question. You should use the given data and your knowledge of Mathematics to choose between the possible answers.

Question: X, Y and Z are integers. Is X an odd number?

Statements:

I. An odd number is obtained when X is divided by 5.

II. X + Y is an odd number.

A.
Choose this option if the Question can be answered by one of the Statements alone but not by the other.
B.
Choose this option if the Question can be answered by either Statement alone.
C.
Choose this option if the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.
D.
Choose this option if the Question cannot be answered even by using both Statements together.
E.
None of these

Detailed Solution for Test: Data Sufficiency- 1 - Question 23

X, Y and Z are integers.

From statement I:

An odd number is obtained when X is divided by 5.

⇒ X/5 = odd number

We know, 5 is an odd number

Thus, X = 5 × (odd number)

We know that, whenever any odd number is multiplied by any other odd number, it gives an odd number.

Hence, X is an odd number
∴ the data in statement I alone is sufficient to answer the question

From statement II:

(X + Y) is an odd number.

Here, the following cases arise which can make (X + Y) odd:

X : even and Y: odd

Or

X : odd and Y : even

Thus, we cannot determine if X is an odd number or not; hence statement II alone is not sufficient to answer the question.

∴ The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.

Test: Data Sufficiency- 1 - Question 24

Directions to Solve: In each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and mark the appreciate answer.

Question: How many students in a class play football?
Statements:
I. Only boys play football.
II. There are forty boys and thirty girls in the class.

A.
I alone is sufficient while II alone is not sufficient
B.
II alone is sufficient while I alone is not sufficient
C.
Either I or II is sufficient
D.
Neither I nor II is sufficient
E.
Both I and II are sufficient

Detailed Solution for Test: Data Sufficiency- 1 - Question 24

It is not mentioned whether all the boys or a proportion of them play football.

So Option D is correct

Test: Data Sufficiency- 1 - Question 25

Directions to Solve: In each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and mark the appreciate answer.

Question: On a T.V. channel, four serials A, B, C, and D were screened, one on eacn days, on four consecutive days but not necessarily in that order. On which day was serial C screened?
Statements:
I. The first serial was screened on 23rd, Tuesday and was followed by serial D.
II. Serial A was not screened on 25th and one serial was screened between serials A and B.

A.
I alone is sufficient while II alone is not sufficient
B.
II alone is sufficient while I alone is not sufficient
C.
Both I and II are sufficient
D.
Neither I nor II is sufficient
E.
Either I or II is sufficient

Detailed Solution for Test: Data Sufficiency- 1 - Question 25

From I, we know that the serials were screened on 23rd, 24th, 25th and 26th.

Clearly, D was screened second i.e. on 24th, Wednesday.

From II, we know that one serial was screened between A and B.

So, A and B were screened first and third, i.e. on 23rd and 25th. But, A was not screened on 25th.

So, A was screened on 23rd and B on 25th. Thus, C was screened on 26th, Friday.

So Option C is correct

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