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# x and y are both positive? (1) 2x-2y = 1 (2) x/y > 1

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x and y are both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

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15 Feb 2009, 02:23
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x and y are both positive?

(1) 2x-2y = 1
(2) x/y > 1

Seems easy but I chose E which is incorrect, pls help to explain.

Thanks.

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15 Feb 2009, 03:50
x and y are both positive?

(1) 2x-2y = 1
(2) x/y > 1

Statement 1 simplifies to x - y = 1/2

x and y could both be positive (eg. 2 and 1.5), YES
x and y could both be negative(eg. -1.5 and -2), NO. Therefore insufficient.

Statement 2 simplifies to |x|>|y|, with both x and y being either positive or negative. Insufficient.

Both statements together, you know that x is more than y by half, and that |x| > |y|. This only happens when both x and y are positive. Sufficient.

Choose C.

-BM-

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15 Feb 2009, 05:51
thank you for your explanation bluementor.

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15 Feb 2009, 09:59
bluementor wrote:
x and y are both positive?

(1) 2x-2y = 1
(2) x/y > 1

Statement 1 simplifies to x - y = 1/2

x and y could both be positive (eg. 2 and 1.5), YES
x and y could both be negative(eg. -1.5 and -2), NO. Therefore insufficient.

Statement 2 simplifies to |x|>|y|, with both x and y being either positive or negative. Insufficient.

Both statements together, you know that x is more than y by half, and that |x| > |y|. This only happens when both x and y are positive. Sufficient.

Choose C.

-BM-

I see you explanation. Now, I do not get modx>mod y from statement 2.
If we just take x/y>1
x=y+1/2
y=-2
and x=-1.5
x/y is not greater than 1. So, I guess I do not need to assume modx>mody.

Thus, the only way for both to be true together is if x and y are both positive.
_________________

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tusharvk

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16 Feb 2009, 05:47
tusharvk wrote:

I see you explanation. Now, I do not get modx>mod y from statement 2.
If we just take x/y>1
x=y+1/2
y=-2
and x=-1.5
x/y is not greater than 1. So, I guess I do not need to assume modx>mody.

Thus, the only way for both to be true together is if x and y are both positive.

tusharvk, you are right. |x|>|y| is not needed. But thats the info you get from statement 2. It is only when you combine it with statement 1 that you can get a definite answer, as you have pointed out by plugging numbers.

-BM-

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16 Feb 2009, 21:16
Attachment:

inequality.JPG [ 10.94 KiB | Viewed 811 times ]

C. ( as marked by intersection of line x-y =1/2 with area x/y>1

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Re: DS   [#permalink] 16 Feb 2009, 21:16
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