Is x an integer? (1) x^2 is an integer. (2) x/2 is not an integer.

Question

Is x an integer?

(1) x^2 is an integer.
(2) x/2 is not an integer.

DS73402.01

Mo2men · Accepted Answer

(1) x^2 is an integer.

Let x= \sqrt{2} ...............Answer is No
Let x=1...............Answer is Yes

Insufficient

(2)x/2 is not an integer

Let x= \sqrt{2} ...............Answer is No
Let x=1...............Answer is Yes

Insufficient

Combine 1 & 2

Use same examples above.....so Insufficient

Answer: E

chetan2u · Answer

Is x an integer?

(1) x^2 is an integer.
x could be a fraction, integer or square root..
x=2..YES
x= \sqrt{2} ..NO
Insuff

(2) x/2 is not an integer.
x could be 3....yes
x= \sqrt{2} ..NO
Insuff

Combined..
x=3...yes
x= \sqrt{2} ..NO
Insuff

E

BrentGMATPrepNow · Answer

Target question :    Is x an integer?

Statement 1 : x² is an integer.  
Let's TEST some values.
There are several values of x that satisfy statement 1. Here are two: 
 Case a : x = 1. In this case, the answer to the target question is  YES, x IS an integer 
 Case b : x = √2. In this case, the answer to the target question is  NO, x is NOT an integer 
Since we cannot answer the  target question  with certainty, statement 1 is NOT SUFFICIENT

Statement 2 : x/2 is not an integer. 
NOTE: Notice that we can re-use the same counterexamples from statement 1. 
 Case a : x = 1. In this case, the answer to the target question is  YES, x IS an integer 
 Case b : x = √2. In this case, the answer to the target question is  NO, x is NOT an integer 
Since we cannot answer the  target question  with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined    
IMPORTANT: Since I was able to use the  same counter-examples  to show that each statement ALONE is not sufficient, the same counter-examples will satisfy the two statements COMBINED. 
So, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent

QuantMadeEasy · Answer

To find whether x is an integer or not

(1) x can be 3 or \sqrt{3}. Insufficient

(2) Still x can be 3 or \sqrt{3}. Insufficient

(1)+(2) With above values, the question cannot be answer. insufficient

E is correct.

Basshead · Answer

(1) If  x^2 = 5 ; x is not an integer. If  x^2 = 16 , x is an integer. INSUFFICIENT

(2) We can't conclude anything here. INSUFFICIENT.

(1&2) Together, we still can't conclude anything. INSUFFICIENT.

Answer is E.

MBAHOUSE · Answer

Classic question for plug in numbers

bumpbot · Answer

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Is x an integer? (1) x^2 is an integer. (2) x/2 is not an integer.

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GMAT Data Sufficiency (DS) Questions

Is x an integer? (1) x^2 is an integer. (2) x/2 is not an integer.

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