Is x an even integer?

Question

Is  x  an even integer?
 
(1)  \sqrt{x}  is a multiple of 2.

(2)  x^2  is a multiple of 4.

Are You Up For the Challenge: 700 Level Questions

BrentGMATPrepNow · Answer

Target question :    Is x an even integer?

Statement 1 :  \sqrt{x}  is a multiple of 2  
In other words,  \sqrt{x} = 2k  for some integer  k 
Now square both sides to get:  x = 4k^2 . 
This means  x  is a multiple of  4 , which means   x  is definitely an even integer 
Since we can answer the  target question  with certainty, statement 1 is SUFFICIENT

Statement 2 :  x^2  is a multiple of 4 
There are several values of x that satisfy statement 2. Here are two: 
 Case a : x = √12. Here, x² = (√12)² = 12, and 12 is a multiple of 4. In this case, the answer to the target question is  NO, x is not an even integer 
 Case b : x = 2. Here, x² = 2² = 4, and 4 is a multiple of 4. In this case, the answer to the target question is  YES, x is an even integer 
Since we can’t answer the  target question  with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Avish11 · Answer

Hey, I reckon, based on your explanation, you have mistaken the first statement as x(squared) is a multiple of 2, instead of sqrt(x) is a multiple of 2

My answer is A

Sqrt (x) is a multiple of 2 so if sqrt(x) is anything 0,2,4,6,8,10, its square will also be divisible by 2 hence an even integer

Statement 2 is insufficient
X(squared) can be 4 (divisible by 4) which means x is 2 and YES EVEN
But if x squared is 12 (divisible by 4), x is sqrt(12), not an even number

Posted from my mobile device

BrentGMATPrepNow · Answer

You're absolutely right! 
I somehow misread statement 1 as " x^2  is a multiple of 2"

I have edited my response accordingly. 
Kudos for you!!!

SaquibHGMATWhiz · Answer

I thought I can add some value here in terms of building a process to solve such questions.

TBH, These types of questions can often catch someone off guard. So how do we make sure that we do not commit any mistakes?

We always suggest that you form equations and then infer from the same.

Statement 1: 
  \sqrt{x}  is a multiple of 2.
So we write them as,  \sqrt{x}  = 2K
Hence, x = 4 k^2

It is very easy to infer from this that x must be a multiple of 2(actually a multiple of 4). We eliminate options B, C, and E.

Statement 2 
  x^2  is a multiple of 4
So we write,  x^2 =4p
Or, x =2 \sqrt{p}  or -2 \sqrt{p}

So it will be an even integer when p is a perfect square and if p is not then it will be an irrational number. 
So this is not sufficient and we eliminate option D.

The answer is A

Shikhar22 · Answer

Hello experts. Just one question, can zero not satisfy both the statements above?

Posted from my mobile device

EducationAisle · Answer

Yes, and x =  \sqrt{8}  (for example) also satisfies (2). So based on (2) we cannot say for sure whether x is an even integer. Hence, (2) is insufficient.

MBAHOUSE · Answer

This is the kind of Data Sufficiency that you need to decide if you go for algebra or plug in numbers.
I decided for both.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Is x an even integer?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards