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Is x < y ? (1) y/x > x/y (2) y > 100

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Senior Manager
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Is x < y ? (1) y/x > x/y (2) y > 100  [#permalink]

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New post 18 Apr 2014, 09:04
2
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A
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C
D
E

Difficulty:

  55% (hard)

Question Stats:

57% (02:03) correct 43% (01:45) wrong based on 129 sessions

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Is x < y ?

(1) y/x > x/y
(2) y > 100
Magoosh GMAT Instructor
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Re: Is x < y ? (1) y/x > x/y (2) y > 100  [#permalink]

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New post 18 Apr 2014, 09:41
2
1
goodyear2013 wrote:
Is x < y ?

(1) y/x > x/y
(2) y > 100

Dear goodyear2013
I'm happy to help. :-)

This is a very tricky one. You may find this blog on arithmetic with inequalities helpful:
http://magoosh.com/gmat/2013/gmat-quant ... qualities/

Statement #1: y/x > x/y
If x & y are both positive, then we can simply cross multiply, (y^2) > (x^2), and take a square root, y > x.
But, of course, the catch is --- we don't know whether x or y is positive. Suppose y = -5 and x = -2. Then Statement #1 is true, but x > y This is that tricky idea that a negative number with a smaller absolute value is larger than a negative number with a larger absolute value. It's better to have $500 in your checking account than $100, but it's better to have $100 in debt on your credit card than $500.
We can't answer the prompt with this alone. This statement, alone and by itself, is insufficient.

Statement #2: y > 100
Well, this one simply gives us no constraints on x at all, so x could be anything. We don't know. This statement, alone and by itself, is insufficient.

Combined statements
Think of this way
Case One: x is negative --- then, since we know y is positive, any positive number is greater than any negative number. Therefore, it must be true that y > x.

Case Two: x is positive. Then, as in statement #1 above, we can cross-multiply in the inequality, take a square-root, and get y > x.

Thus, regardless of where x falls, y must be greater than x. Combined the statements are sufficient. OA = (C)

Does all this make sense?
Mike :-)
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Re: Is x < y ? (1) y/x > x/y (2) y > 100  [#permalink]

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New post 18 Apr 2014, 09:50
Is x < y ?

(1) y/x > x/y. If \(y=2\) and \(x=1\), then \(x<y\) but if \(y=-2\) and \(x=-1\), then \(x>y\). Not sufficient.

Notice that we cannot cross-multiply given inequality because we don't know the signs of x and y.

(2) y > 100. We know nothing about x. Not sufficient.

(1)+(2)

If x is a negative number then obviously: \((y=positive)>(x=negative)\);

If x is a positive number (so if both x and y are positive) then we can cross-multiply (1) and get: \(y^2>x^2\) --> take the square root: \(|y|>|x|\) --> \(y>x\).

Sufficient.

Answer: C.
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Re: Is x < y ? (1) y/x > x/y (2) y > 100  [#permalink]

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