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# Are x and y both positive? (1) 2x -2y = 1 (2) \frac{x}{y}

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Manager
Joined: 09 Jul 2008
Posts: 111

Kudos [?]: 44 [0], given: 1

Location: Dallas, TX
Schools: McCombs 2011
Are x and y both positive? (1) 2x -2y = 1 (2) \frac{x}{y} [#permalink]

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11 Feb 2009, 15:47
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Are x and y both positive?

(1) $$2x -2y = 1$$

(2) $$\frac{x}{y} > 1$$

Kudos [?]: 44 [0], given: 1

Senior Manager
Joined: 30 Nov 2008
Posts: 483

Kudos [?]: 376 [0], given: 15

Schools: Fuqua

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11 Feb 2009, 20:18
IMO E.

From clue 1, 2(x - y) = 1==> x - y = 1/2.

For (x,y) being (1,1/2) satisfying clue 1, x and y are positive.
For (x,y) = (-1/2,-1) satisfying clue 1, x and y are negative.

Two different ans and hence Insufficient.

From clue 2,
x/y > 1 ==> x > y. ==> x-y > 0.
For (x,y) being (3,1) satisfying clue 1, x and y are positive.
For (x,y) = (-1,-3) satisfying clue 1, x and y are negative.

Two different ans and hence Insufficient.

Combining both the clues.

x-y = 1/2 and x - y > 0. Does not provide any addiitonal information. Hence insufficient.

Kudos [?]: 376 [0], given: 15

Director
Joined: 29 Aug 2005
Posts: 855

Kudos [?]: 519 [0], given: 7

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12 Feb 2009, 03:48
C.
Replace Stmt1 in Stmt2.

Kudos [?]: 519 [0], given: 7

Intern
Joined: 12 Feb 2009
Posts: 1

Kudos [?]: [0], given: 0

Schools: MIT

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12 Feb 2009, 04:36

From clue 1, 2(x - y) = 1==> x - y = 1/2.

For (x,y) being (1,1/2) satisfying clue 1, x and y are positive.
For (x,y) = (-1/2,-1) satisfying clue 1, x and y are negative.

Two different ans and hence Insufficient.

From clue 2,
x/y > 1 ==> x > y. ==> x-y > 0. (if y is positive)
For (x,y) being (3,1) satisfying clue 1, x and y are positive.

x/y > 1 ==> x < y. ==> x-y < 0. (if y is negative)
For (x,y) = (-3,-1) satisfying clue 1, x and y are negative.

Combining both the equation we have x should be positive because if x is negative then x
should be less than y as proved in second condition which is not the case in condition 1.

Combining both the clues.

x-y = 1/2 and x - y > 0. Does not provide any addiitonal information. Hence insufficient.

Kudos [?]: [0], given: 0

Re: DS: Inequality   [#permalink] 12 Feb 2009, 04:36
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