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Difficulty:
45%
(medium)
Question Stats:
70% (01:57) correct
30%
(01:50)
wrong
based on 688
sessions
History
Date
Time
Result
Not Attempted Yet
19 Feb 2012, 11:30
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Is x > y?
(1) x^2 > y. Clearly insufficient: if x=2 and y=3 then the answer is NO but if x=2 and y=1 then the answer is YES.
(2) √x < y. Also insufficient: if x=4 and y=5 then the answer is NO but if x=4 and y=3 then the answer is YES. Notice that since x is under the square root sign then it must be true that \(x\geq{0}\).
(1)+(2) \(\sqrt{x}<y<x^2\) --> both \(x\) and \(y\) are between \(\sqrt{x}\) and \(x^2\), but we can not say which one is greater. Not sufficient. For example: if \(x=y=4\) (\(\sqrt{4}<4<4^2\)) then the answer is NO but if \(x=4\) and \(y=3\) (\(\sqrt{4}<3<4^2\)) then the answer is YES. Not sufficient.
Answer: E.
Hope it's clear.
(1) x^2 > y. Clearly insufficient: if x=2 and y=3 then the answer is NO but if x=2 and y=1 then the answer is YES.
(2) √x < y. Also insufficient: if x=4 and y=5 then the answer is NO but if x=4 and y=3 then the answer is YES. Notice that since x is under the square root sign then it must be true that \(x\geq{0}\).
(1)+(2) \(\sqrt{x}<y<x^2\) --> both \(x\) and \(y\) are between \(\sqrt{x}\) and \(x^2\), but we can not say which one is greater. Not sufficient. For example: if \(x=y=4\) (\(\sqrt{4}<4<4^2\)) then the answer is NO but if \(x=4\) and \(y=3\) (\(\sqrt{4}<3<4^2\)) then the answer is YES. Not sufficient.
Answer: E.
Hope it's clear.
20 Feb 2012, 00:18
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GMATPASSION
First of all: on DS questions when plugging numbers, goal is to prove that the statement is not sufficient. So we should try to get a YES answer with one chosen number(s) and a NO with another.
Now, number picking strategy can vary for different problems. Generally it's good to test negative/positive/zero as well as integer/fraction to get a YES and a NO answers. If you deal with two variables it's also helpful to test x<y and x>y in addition to the former.
As for this question: you don't really need to test the numbers for it, I just used them to demonstrate that the statements are not sufficient.
From (1)+(2): we have that \(\sqrt{x}<y<x^2\). Both \(x\) and \(y\) are between \(\sqrt{x}\) and \(x^2\) (\(x\) is between them because \(\sqrt{x}<x^2\), which means that \(x>1\)):
\(\sqrt{x}\)------\(x\)------\(x^2\), now \(y\) can be in the green range (answer YES) as well in the red range (answer NO). So, we can not say whether x>y.
Hope it's clear.
