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If x>y>0, is y<2?

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Math Revolution GMAT Instructor
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If x>y>0, is y<2?  [#permalink]

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New post 16 Jan 2018, 02:28
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A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

44% (02:05) correct 56% (02:11) wrong based on 52 sessions

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[GMAT math practice question]

If \(x>y>0\), is \(y<2\)?

\(1) \frac{1}{x} = \frac{1}{2}\)
\(2) (\frac{1}{x})+(\frac{1}{y}) =1\)

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Re: If x>y>0, is y<2?  [#permalink]

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New post 16 Jan 2018, 02:45
1
1) if 1/x = 1/2
then x=2
then 0<y<2 --> SUFF

since 1 is suff -> A or D

2)
-don't make the mistake to assume x and y are integers
if you do then the only solution for 1/x + 1/y = 1 would be for x=y=2 <-- this goes against the given information.

-we know both x and y are positive(>0) so 1/x and 1/y will also be positive
-this means that neither will be bigger than 1 otherwise 2) has no solution
--> suff
(example solution is: x=4, y=4/3 --> 1/4 + 1/(4/3) = 1 --> 1/4 + 3/4 = 1)

--> D: each statement alone is suff
Math Revolution GMAT Instructor
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Re: If x>y>0, is y<2?  [#permalink]

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New post 18 Jan 2018, 01:39
=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 2 variables (\(x\) and \(y\)) and 1 equation ( \(x > y\)), D is most likely to be the answer.

Condition 1)
\(\frac{1}{x} = \frac{1}{2}\) implies that \(x = 2\). Since \(x > y\), we must have \(y < 2.\)
Condition 1) is sufficient.

Condition 2)
The original condition \(x > y > 0\) implies that \(\frac{1}{x} < \frac{1}{y}\).
Using \(\frac{1}{x} + \frac{1}{y} = 1\) and \(\frac{1}{x} < \frac{1}{y}\) together, we can see that \(\frac{1}{y} > \frac{1}{2}\).
Thus, \(0 < y < 2\).
Condition 2) is sufficient.

Therefore, the answer is D.
Note: The VA approach tells us that the answer is most likely to be D, since this is a CMT(Common Mistake Type) 4B question.
Condition 1) is easy to check, but condition 2) is more difficult to work with. If you can’t figure out condition 2), you should choose D as the answer.
Answer: D
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Re: If x>y>0, is y<2? &nbs [#permalink] 18 Jan 2018, 01:39
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