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28 Aug 2017, 03:27
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E
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42% (02:16) correct
58%
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Fresh GMAT Club Tests' Challenge Question:
If x ≠ 0, what is the value of x?
(1) The distance between x and -x on the number line is equal to the distance between x^2 and -x^2
(2) x ? |x| = 0, where ? represents one of the three operations addition, subtraction, or multiplication
M36-38
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18 Oct 2021, 09:52
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Bunuel
Official Solution:
If \(x ≠ 0\), what is the value of \(x\)?
(1) The distance between \(x\) and \(-x\) on the number line is equal to the distance between \(x^2\) and \(-x^2\)
The distance between \(a\) and \(b\) on the number line is \(|a - b|\). Thus, the statement above means \(|x - (-x)| = |x^2 - (-x^2)|\)
\(|2x| = |2x^2|\)
\(|2x| = |2x|*|x|\)
Reduce by \(|2x|\) (note here that we can safely do that since \(|2x|\neq 0\). We are told \(x ≠ 0\), thus \(|2x|\neq 0\)):
\(1 = |x|\)
\(x\) can be 1 or -1. Not sufficient.
(2) \(x ? |x| = 0\), where \(?\) represents one of the three operations addition, subtraction, or multiplication
If \(?\) is addition we'd have \(x + |x| = 0\), which is true for all non-positive values of \(x\).
If \(?\) is subtraction we'd have \(x - |x| = 0\), which is true for all non-negative values of \(x\).
If \(?\) is multiplication we'd have \(x*|x| = 0\), which is true when \(x=0\) but since we are told that \(x ≠ 0\), then \(?\) cannot be multiplication.
Not sufficient.
(1)+(2) If \(?\) is subtraction then \(x=1\) (from (1)) but if \(?\) is addition then \(x=-1\) (from (1)). Not sufficient.
Answer: E
General Discussion
Luckisnoexcuse
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28 Aug 2017, 03:35
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Bunuel
(1) x can take 0 or 1 or -1
in all the cases the distance between x and -x on the number line is equal to the distance between x^2 and -x^2
not sufficient
(2) if x = 0 then ? represents any one of the operations
if x=-1 then ? represents addition
if x=1 then ? represent subtraction
not sufficient
on combining also not sufficient
E
