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CAT 1991 — QA Question 51

Data SufficiencyEasy
Passage / Data

Answer the following questions based on the information given below:

There were a hundred schools in a town. Of these, the number of schools having a play – ground was 30, and these schools had neither a library nor a laboratory. The number of schools having a laboratory alone was twice the number of those having a library only. The number of schools having a laboratory as  well as a library was one fourth the number of those having a laboratory alone. The number of schools  having either a laboratory or a library or both was 35.

Each of these items has a question followed by two statements. As the answer,

Type 1, If the question can be answered with the help of statement I alone,
Type 2, If the question can be answered with the help of statement II alone,
Type 3, If both the statement I and statement II are needed to answer the question, and
Type 4, If the question cannot be answered even with the help of both the statements.

What is the value of prime number x?

  1. x2 + x is a two digit number greater than 50.
  2. x3 is a three digit number.

Answer & solution

  • 1

  • B

    2

  • C

    3

  • D

    4

Solution

From statement I : x2 + x > 50 and x2 + x < 100

⇒ x(x + 1) > 50

Only prime number 7 satisfies the above equation. 

So the question can be answered from statement 1 alone.

From statement II : x can be 5 or 7.

Hence, 1.

CAT 1991 QA Q51: Each of these items has a question followed by two statements. As the answer, Type 1, If the question can be a — Solution | TheCATExam