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# Is 0 < (x−y)/(x−2y) < 1?

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Math Expert
Joined: 02 Sep 2009
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Is 0 < (x−y)/(x−2y) < 1?  [#permalink]

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13 Feb 2015, 07:45
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Difficulty:

75% (hard)

Question Stats:

54% (02:23) correct 46% (01:54) wrong based on 147 sessions

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Is 0 < (x−y)/(x−2y) < 1?

(1) x > y
(2) x > 2y

Kudos for a correct solution.

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Re: Is 0 < (x−y)/(x−2y) < 1?  [#permalink]

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13 Feb 2015, 10:10
1
1
Both statements are insufficient (even when combined).
The answer depends on whether the numbers are positive or negative.

If x = 5 and y = 2, then $$(5-2) / (5-4) = 3$$ which is greater than 1.
If x = 5 and y = -2, then $$(5-(-2)) / (5-(-4)) = 7/9$$ which is less than 1.

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Re: Is 0 < (x−y)/(x−2y) < 1?  [#permalink]

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14 Feb 2015, 08:14
1
I say E as well.

rephrase the equation:

0(x-2y)<x-y<1(x-2y)
0<x-y<x-2y
y<x<x-y

1) x>y
2>1 ----- (1)<(2)<(2-1) ---- 1<2<1 DOESN'T WORK
2>-1 ---- (-1)<(2)<(2- (-1)) ---- -1<2<3 WORKS
NS - depends on values chosen

2) X>2Y can use same numbers as above
2>-2
NS - depends on values chosen

Same information provided for each statement. Together NS

Ans - E
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Re: Is 0 < (x−y)/(x−2y) < 1?  [#permalink]

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16 Feb 2015, 00:53
Ans - E
Rephrasing the Question, we get
x-2y > x-y >0
-2y > -y > -x
Is x> y > 2y

1) Not suff
2) Not Suff

When combining, we dont know the relation between y & 2y - The results can vary if we quickly plug in +ve, -ve integers or decimals

Hence E
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Re: Is 0 < (x−y)/(x−2y) < 1?  [#permalink]

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16 Feb 2015, 01:41
1
I think it is E.

Statement 1 is not sufficient as there are many numbers possible.
Statement 2 is also not sufficient. Similar to statement 1.

Math Expert
Joined: 02 Sep 2009
Posts: 52303
Re: Is 0 < (x−y)/(x−2y) < 1?  [#permalink]

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16 Feb 2015, 05:31
Bunuel wrote:
Is 0 < (x−y)/(x−2y) < 1?

(1) x > y
(2) x > 2y

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION

Explanation: In order to answer the question, we will need to determine whether the numerator is greater than the denominator.

This tells us only that the numerator is positive.
This tells us only that the denominator is positive.
Together, we know that the numerator and denominator are positive, but we don't know which is larger. For example, if x and y are 1 and -1, the answer to the question stem is YES, because plugging in those values give us 2/3 , which is between 0 and 1. But, if x and y are 5 and 2, the answer to the question stem is NO, because we get 3, which is not between 0 and 1. Insufficient.
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Re: Is 0 < (x−y)/(x−2y) < 1?  [#permalink]

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05 Jan 2016, 18:27
i solved it in ~ 2mins by picking numbers.

x-y/x-2y will be between 0 and 1 if both expressions are of the same sign, and the second one will be greater than the first one.

1. x>y. not sufficient.
x=6, y=-5 -> yes.
x=6, y=2 -> no.
A and D - eliminated.

2. x>2y.
x=6, y=1 -> no
x=6, y=-5 -> yes.

2 outcomes, not sufficient, B out.

1+2
x=6 and y=-5 -> yes
x=6, and y=1 -> no.

eliminate C, and pick E.
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Posts: 7212
Re: Is 0 < (x−y)/(x−2y) < 1?  [#permalink]

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05 Jan 2016, 21:24
2
Bunuel wrote:
Is 0 < (x−y)/(x−2y) < 1?

(1) x > y
(2) x > 2y

Kudos for a correct solution.

what does the Q stem tell us about x and y..
two things are required for the ans to be yes or no...
1) $$\frac{(x−y)}{(x−2y)}$$ should be positive..
so both num and denominator have to be of same sign...

2) for $$\frac{(x−y)}{(x−2y)}$$ to be between 0 and 1, num has to be smaller than denominator..
x-y<x-2y..
or y<0..

We can have any data given but we have to look for the above condition..
so what we should look for..
a) either both are correct then ans is YES
b) if we prove even one incorrect, the answer is NO..

lets see the statements...
(1) x > y.... y need not be -ive. and nothing can be said about signs of num and denominator...insuff
(2) x > 2y... we can say both num and deno are positive, but cannot say about the sign of y..insuff.

combined nothing new.. insuff
E
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: Is 0 < (x−y)/(x−2y) < 1?  [#permalink]

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17 Apr 2018, 19:56
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Re: Is 0 < (x−y)/(x−2y) < 1? &nbs [#permalink] 17 Apr 2018, 19:56
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