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A
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62%
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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
(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
Updated on: 15 Jun 2022, 15:59
Originally posted by BrentGMATPrepNow on 15 Jun 2022, 10:57.
Last edited by BrentGMATPrepNow on 15 Jun 2022, 15:59, edited 1 time in total.
Last edited by BrentGMATPrepNow on 15 Jun 2022, 15:59, edited 1 time in total.
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Bunuel
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
15 Jun 2022, 14:23
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BrentGMATPrepNow
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
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