GMAT PREP INEQUALITY ??

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GMAT PREP INEQUALITY ??

by dferm » Mon Apr 28, 2008 6:57 am
PLEASE HELP...
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by akshatsingh » Fri May 02, 2008 2:16 am
My answer is C.

Is that correct ?

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by amitansu » Fri May 02, 2008 4:11 am
I just have a small confusion !!

The q says : Are x and y both positive ?
1. 2x-2y=1
2. x/y>1

In statement 2 we have x/y >1 => x > y
then pluggin some valus of x and y we can have results like :

x=3; y=2 so x/y >1 (both are positive)
x=-3; y=-2 so x/y >1( but x is smaller than y, which contradicts the inequality condition !!)
x=1/2 and y=1/3then x/y >1 (both are positive and x>y)
x=-1/2 and y= -1/3 then x/y >1 (x is smaller than y here)

So for me seems like , it can be concluded both are positive under this condition !!

Can anybody throw some light !!

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by amitansu » Fri May 02, 2008 8:35 pm
Any expert's solution for this confusion....


I request Stuart/Ron can you please help !!


regards,
Amit

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by Stuart@KaplanGMAT » Sat May 03, 2008 10:43 am
amitansu wrote:I just have a small confusion !!

In statement 2 we have x/y >1 => x > y

Can anybody throw some light !!
Your problem stems from your manipulation of this inequality.

We have to be VERY careful when we manipulate inequalities. Remember, if you multiple or divide both sides by a negative, you need to reverse the inequality.

So:

x/y > 1

To get to "x > y", you actually multiply both sides by "y". So, we get two solutions:

if y > 0, then x > y

However, if y < 0, we actually get x < y.

So, we are allowed to pick x = -3 and y = -2, since:

-3/-2 = 1.5 > 1
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by aditikedia » Sat Aug 09, 2008 7:10 pm
Hey Stuart,

In this question, aren't there 2 situations?

1) x and y - Both positive
2) x and y - Both negative

x/y > 1

Now, if y is positive, then x>y, however, if y is negative, then, x<y.

Therefore how is the answer c?

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by Stuart@KaplanGMAT » Sat Aug 09, 2008 7:43 pm
aditikedia wrote:Hey Stuart,

In this question, aren't there 2 situations?

1) x and y - Both positive
2) x and y - Both negative

x/y > 1

Now, if y is positive, then x>y, however, if y is negative, then, x<y.

Therefore how is the answer c?
My previous post didn't even address the whole question, I was just responding the manipulation of statement (2).

Looking at the statements together, we know that:

(1) x - y = 1/2

and

(2) if y is negative, y > x; and
if y is positive, then x > y.

We can rewrite (1) as:

x - y = 1/2
x = y + 1/2

If x = y + 1/2, then x MUST be greater than y, which means it's no longer possible for x and y to both be negative (since when that happens, y > x).

Therefore, if both statements are true, x and y must both be positive.
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by aditikedia » Sat Aug 09, 2008 7:52 pm
Thanks Stuart!

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by II » Sat Aug 23, 2008 12:42 pm
what level question would you say this is ?
Also are there any other approaches to solve this one ?

Thanks.

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by aj5105 » Thu Nov 13, 2008 10:18 pm
from statement 1----x/y - 1 = 0.5 * 1/y (divide by y both sides)

from statement 2----x/y>1

Combine both--- x/y -1 must be positive number.This implies RHS must be positive.This further implies 1/y must be positive.

therefore x & y must be positive.