(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

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

MathRevolution Could you please help me with the response in the Variable Approach here. Thanks!

MathRevolution could you please help solving this question using the Variable Approach?

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
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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.
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chetan2u

Regarding the part where you said "x could be a fraction" for statement 1 :

Isn't it ALWAYS true that The square root of any positive integer is either an integer or an irrational number, never a fraction?
Can you please clarify?
Thanks in advance!

(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.
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