Question: Is √x and Integer?

Question REPHRASED: Is x square of an Integer?

Statement 1: x/6 is an odd integer.

i.e. x = 6*Odd
i.e .x can Never have 2^2 as factor
i.e. x will Definitely not be a perfect square
hence, √x will not be an integer

SUFFICIENT

Statement 2: x^2 is a multiple of 16.

Case 1: x^2 = 16, √x = 2 an Integer
Case 2: x^2 = 32, √x ≠ an Integer

NOT SUFFICIENT

Answer: Option A

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Question basically wants us to find whether x is a perfect square.

(1) x/6 is an odd integer.
So x=6*odd, which means x is multiple of 2 but not of 4.
Thus x is not a perfect square.
Sufficient

(2) \(x^2\) is a multiple of 16.
If \(x^2=16*81\)....yes
If \(x^2=16*3\)....no
Insufficient


A

However the value of x differs in both the statements, a situation that will not be seen in actual GMAT.
Statement I says it is multiple of just 2 because x/6 is odd, while statement II says x is a multiple of at least 4 because x^2 is a multiple of 16.
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Is √x an integer?

Stat1: x/6 is an odd integer.
x = 6, 18, 30, 42.....So, √x is not an integer. Sufficient.

Stat2: x^2 is a multiple of 16.
x^2 = 16, 32, 48,.....So, √x can be an integer or not. Not Sufficient.

So, I think A.

Plugged in values -

Is √x an integer?

(1) x/6 is an odd integer.

x=6 therefore 6/6=1. √6 is not an integer
x=18 therefore 18/6=3. √18 is not an integer
x=30 therefore 30/6=5. √30 is not an integer

Sufficient

(2) x^2 is a multiple of 16.
x=8 therefore 8^2. √8 is not an integer
x=12 therefore 12^2. √12 is not an integer
x=16 therefore 16^2. √16 IS an integer

Not sufficient

A

If x^2=16*9 is no also.
x^2=16*9 -> x=4*3 -> sqrt(12) is not an integer.

The example os "yes" would be:
x^2=16*81 -> x=4*9 -> sqrt(36) = 6

If x^2 = 16, x can be -4 as well right? Why are we not considering that case?