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08 Oct 2021, 10:09
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
46% (00:50) correct
54%
(00:54)
wrong
based on 250
sessions
History
Date
Time
Result
Not Attempted Yet
What is the value of \(x\), if \(x\) is even?
(1) \(x^2 = 2x \)
(2) \(x\) is non-negative
(1) \(x^2 = 2x \)
(2) \(x\) is non-negative
09 Oct 2021, 14:48
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GMATWhizTeam
(1) \(x^2 = 2x \)
=> x(x-2)=0 => x=0 or x=2, 2 values possible, so Not sufficient
(2) \(x\) is non-negative[/quote] => x can take values from 0,1,2,.... (and positive fractions too), Not Sufficient
Combining 1 and 2
Still x has 2 values, Not Sufficient
Hence E
11 Oct 2021, 05:01
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GMATWhizTeam
Solution:
We are given that \(x\) is an even number. This means the value of \(x\) can be \(-6, -4, -2, 0, 2, 4, 6\) and so on..
Statement 1: \(x^2 = 2x \)
One might be tempted to write \(x^2 = 2x \) as \(x = 2\). However, this is incorrect. We cannot divide both sides by x unless we know \(x≠0\).
A correct approach would be to write \(x^2 = 2x \) as \(x^2 - 2x = 0\)
\(⇒ x(x-2)=0\)
This tells us that the value of \(x\) can be \(0\) or \(2\). We do not get any specific value of \(x\) and thus statement 1 alone is not sufficient. We can eliminate options A and D.
Statement 2: \(x\) is non-negative
\(x\) is non-negative means the value of x can be \(0, 2, 4, 6, 8\) and so on.
We do not get any specific value of \(x\) and thus statement 2 alone is also not sufficient. We can eliminate option B.
Combinning:
From statement 1 we get: \(x=0\) or \(2\).
From statement 2 we get: \(x=0, 2, 4, 6\) and so on.
Upon combining, we get the value of \(x\) as \(0\) or \(2\).
We still do not get any specific value of \(x\).
Hence the right answer is Option E.
