CAT 1995 | Question: 94

Question

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

What is value of x, if x and y are consecutive positive even integers?

a. if the questions can be answered with the help of both the statements but not with the help of either statement itself.

b. if the question can not be answered even with the help of both the statements.

c. if the question can be answered with the help 0 statement II alone

d. if the question can be answered with the help of statement I alone

I. $(x - y)^{2} = 4$.

II. $(x + y)^{2} < 100$

Answer 1

Statement 1:

(x−y)^2=4. $\Rightarrow$ (x - y) = 2...........(1)

which is anyways true since x and y are consecutive positive even integers.

Two unknown one equation

Therefore Statement 1) alone cannot determine x and y.

 Statement 2:

(x + y)^2 < 100

(x + y) < 10...........(2)

Let x = 2b

From (1) , put value of x in (1)

2b - y = 2

y = 2b - 2

Put the value of y in (2)

2b + 2b - 2  < 10

4b < 12

 b < 3

This again does not uniquely finds x since 'a' can be either 1 or 2.

Since Statement 1) does not provide any additional information while Statement 2) cannot answer the question

therefore both statements cannot answer the question. 

Option B is the Correct Answer.