If x<y<0, x<0 and y<0.
(1) Can be written as (x - y) = 5 / (x+y). This indicates that since 5 / (x+y) has no one unique value for x<y<0, then statement I is NS
(2)
Keep in my x and y are both negative. This means the ONLY possible combinations such that xy=6 and x<y<0 are as follows:
If x=-3 y=-2, then x - y = -1
If x=-6 y=-1, then x - y = -5
TOGETHER
Use the data from both statements together.
If x=-3 y=-2, then x - y = -1 ; does (x - y) = 5/(x+y)? Does -1=5/(-5). Yes. We now know that x-y can equal -1.
If x=-6 y=-1, then x - y = -5 ; does (x - y) = 5/(x+y)? Does -5=5/(-7). No. This cannot be a solution.
Only one solution is possible and unique, so the answer should be C.
Inequality prob
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Consider (1) alone first.
If (x+y)(x-y) = 5, then since x and y are integers, (x+y) = -1 and (x-y) = -5 is one possibility and (x+y) = -5 and (x-y) = -1 is the other possibility.
Now (x+y) = -1 is not possible because both x and y are negative integers.
So (x+y) = -5 and (x-y) = -1 is a valid possibility which is giving x = -3 and y = -2.
So (1) alone is sufficient.
Next consider (2) alone.
xy = 6 implies that possible pairs of x and y are (-1,-6), (-6,-1), (-2,-3), (-3,-2).
Since we do not get a unique answer (2) alone is not sufficient.
The correct answer is hence (A).
If (x+y)(x-y) = 5, then since x and y are integers, (x+y) = -1 and (x-y) = -5 is one possibility and (x+y) = -5 and (x-y) = -1 is the other possibility.
Now (x+y) = -1 is not possible because both x and y are negative integers.
So (x+y) = -5 and (x-y) = -1 is a valid possibility which is giving x = -3 and y = -2.
So (1) alone is sufficient.
Next consider (2) alone.
xy = 6 implies that possible pairs of x and y are (-1,-6), (-6,-1), (-2,-3), (-3,-2).
Since we do not get a unique answer (2) alone is not sufficient.
The correct answer is hence (A).
Last edited by Rahul@gurome on Sun Jul 11, 2010 8:23 pm, edited 1 time in total.
Rahul Lakhani
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Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
