Data Sufficiency Questions for CAT

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Data Sufficiency Questions for CAT
Data Sufficiency Questions for CAT

Data Sufficiency Questions for CAT:

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Instructions:

Directions for the following four questions:
Each question is followed by two statements, A and B. Answer each question using the following instructions:

Question 1:

In a particular school, sixty students were athletes. Ten among them were also among the top academic performers. How many top academic performers were in the school?
A. Sixty per cent of the top academic performers were not athletes.
B. All the top academic performers were not necessarily athletes.

a) The question can be answered by using the statement A alone but not by using the statement B alone.
b) The question can be answered by using the statement B alone but not by using the statement A alone.
c) The question can be answered by using either of the statements alone
d) The question can be answered by using both the statements together but not by either of the statements alone.
e)The question cannot be answered on the basis of the two statements.

Question 2:

Five students Atul, Bala, Chetan, Dev and Ernesto were the only ones who participated in a quiz contest. They were ranked based on their scores in the contest. Dev got a higher rank as compared to Ernesto, while Bala got a higher rank as compared to Chetan. Chetan’s rank was lower than the median. Who among the five got the highest rank?
A. Atul was the last rank holder.
B. Bala was not among the top two rank holders.

a) The question can be answered by using the statement A alone but not by using the statement B alone.
b) The question can be answered by using the statement B alone but not by using the statement A alone.
c) The question can be answered by using either of the statements alone.
d) The question can be answered by using both the statements together but not by either of the statements alone.
e)The question cannot be answered on the basis of the two statements.

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Question 3:

Thirty per cent of the employees of a call centre are males. Ten per cent of the female employees have an engineering background. What is the percentage of male employees with engineering background?
A. Twenty five per cent of the employees have engineering background.
B. Number of male employees having an engineering background is 20% more than the number of female employees having an engineering background

a) The question can be answered by using the statement A alone but not by using the statement B alone.
b) The question can be answered by using the statement B alone but not by using the statement A alone.
c) The question can be answered by using either of the statements alone.
d) The question can be answered by using both the statements together but not by either of the statements alone.
e)The question cannot be answered on the basis of the two statements.

Question 4:

In a football match, at the half-time, Mahindra and Mahindra Club was trailing by three goals. Did it win the match?
A. In the second-half Mahindra and Mahindra Club scored four goals.
B. The opponent scored four goals in the match.

a) The question can be answered by using the statement A alone but not by using the statement B alone.
b) The question can be answered by using the statement B alone but not by using the statement A alone.
c) The question can be answered by using either of the statements alone.
d) The question can be answered by using both the statements together but not by either of the statements alone.
e)The question cannot be answered on the basis of the two statements.

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Answers and Explanations for Data Sufficiency Questions for CAT:

Solutions:

1) Answer (A)

No. of athletes which are top academic performers: 10
According to statement a) Sixty per cent of the top academic performers were not athletes so 40% of top academic performers are athletes which we know is 10. So total no. of top academic performers are 25.
Hence statement a is alone to answer the question.
while we cant deduce anything from statement b .

2) Answer (D)

From the information given in the question, D has a better rank than E and B has a better rank than C. Also, C = 4 or 5.
From statement A, A = 5 => C = 4. But we do not know if D or B is number 1.
From statement B, B = 3 or 4. Again, we cannot determine the number 1 rank precisely.
By using both the statements together, we know C = 4, A = 5, B = 3 and D has a better rank than E.
So, D = 1 and E = 2. Therefore, the question can be answered by using both the statements together.
Hence, option D.

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3) Answer (C)

Let the total number of employees be 100k.
Number of males = 30k. Number of females = 70k.
Number of female engineers = 7k.
From statement A, number of male engineers = 25k – 7k = 18k.
From statement B, number of male engineers = (6/5)*7k.
Therefore, percentage of male engineers can be calculated.
So, the question can be answered by either statement alone.

4) Answer (E)

From statement A, we know that the club scored four goals in the second half but we do not know the number of goals scored by the opposition. So, we cannot answer the question.
From statement B, we know that the opposition scored 4 goals in the match but we do not know the number of goals scored by Mahindra and Mahindra club. So, we cannot answer the question.
Using both the statements, we know that the opposition scored 4 goals in the match and Mahindra and Mahindra scored 4 goals in the second half. But, we do not know if the score was 3-0 or 4-1 at the end of first half. If it was 4-1, then Mahindra and Mahindra would win the match after the second half. But if the score was 3-0 at the end of first half, the match would end in a draw after the second half.
Therefore, the question cannot be answered even by using both the statements together.

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