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02 Oct 2017, 04:42
Kudos
Bookmarks
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
38% (02:07) correct
62%
(01:43)
wrong
based on 55
sessions
History
Date
Time
Result
Not Attempted Yet
If x is an integer, is \(\sqrt{3x - y} = \sqrt{2x - 2y}\) ?
(1) x^2 = y
(2) x^3 = y
(1) x^2 = y
(2) x^3 = y
Bunuel
\(\sqrt{3x - y} = \sqrt{2x - 2y}\), square both sides to get
\(3x-y=2x-2y\) or the question becomes Is \(x=-y\) ?
Statement 1: implies that \(x=\sqrt{y}\) or \(-\sqrt{y}\). \(x\) can be equal to \(-y\) in one situation; if \(y=1\) and \(x=-\sqrt{y}\) but if \(y\) has any other value then \(x\) will not be equal to \(-y\). hence no unique value. Insufficient
Statement 2: \(x=y^\frac{1}{3}\).
If \(x=1, y=1\), then \(x\) is not equal to \(-y\)
but if \(x=0, y=0\), then \(x=-y\) Hence. Sufficient
Combining 1 & 2, there is no unique answer. Hence Insufficient
IMO E
05 Oct 2017, 05:22
Kudos
Bookmarks
Bunuel
Question : is \(\sqrt{3x - y} = \sqrt{2x - 2y}\) ?
Squaring both sides
Question : is 3x - y = 2x - 2y?
Question : x = -y ?
Statement 1: x^2 = y
@x = 1, y = 1 Answer to the question is NO
@x = -1, y = 1 Answer to the question is YES
NOT SUFFICIENT
Statement 2: x^3 = y
@x = 1, y = 1 Answer to the question is NO
@x = 0, y = 0 Answer to the question is YES i.e. x = -y
NOT SUFFICIENT
Combining the two statements
@x = 1, y = 1 Answer to the question is NO
@x = 0, y = 0 Answer to the question is YES i.e. x = -y
NOT SUFFICIENT
Answer: Option E
