From statement [1]
x > 0, now y can be positive or negative,
assume y is positive, then (x-y) < (x+y) ==> (x-y)/(x+y) < 1
assume y is negative, then (x-y) > (x+y) ==> (x-y)/(x+y) > 1
Hence statement [1] alone is not sufficient.
From statement[2]
Following the above logic for y, we get the 2 different results and hence statement [2] alone is not sufficient.
Considering statement [1] and [2] together, we get a unique answer, so statement [1] and [2] together are sufficient to solve the problem
Whats the OA?
Thanks
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Source: Beat The GMAT — Data Sufficiency |
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givemeanid
- Master | Next Rank: 500 Posts
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(x-y)/(x+y) > 1?
(1) x>0
(2) y<0
x = 1/4
y = -1/2
x-y = 1/4 - (-1/2) = 3/4
x+y = 1/4 - 1/2 = -1/2
(x-y)/(x+y) = 3/4 / -1/2 = -3/2 (<1)
x = 4
y = -2
x-y = 6
x+y = 2
6/2 = 3 (>1)
NOT SUFFICIENT. Hence E.
(1) x>0
(2) y<0
x = 1/4
y = -1/2
x-y = 1/4 - (-1/2) = 3/4
x+y = 1/4 - 1/2 = -1/2
(x-y)/(x+y) = 3/4 / -1/2 = -3/2 (<1)
x = 4
y = -2
x-y = 6
x+y = 2
6/2 = 3 (>1)
NOT SUFFICIENT. Hence E.
So It Goes
I don't understand, the answer should be (B). Here is my thinking:givemeanid wrote:(x-y)/(x+y) > 1?
(1) x>0
(2) y<0
x = 1/4
y = -1/2
x-y = 1/4 - (-1/2) = 3/4
x+y = 1/4 - 1/2 = -1/2
(x-y)/(x+y) = 3/4 / -1/2 = -3/2 (<1)
x = 4
y = -2
x-y = 6
x+y = 2
6/2 = 3 (>1)
NOT SUFFICIENT. Hence E.
x-y/x+y > 1 ?
... x-y > x+y ?
... x-x > y+y ?
... 2y < 0 ?
... y < 0 ? must be answered, for the original question to be answered.
Choice (1) doesn't answer this, (2) does. Hence (B). \
Correct me if I am wrong, please.
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givemeanid
- Master | Next Rank: 500 Posts
- Posts: 277
- Location: New York, NY
- Thanked: 6 times
If m/n > 1, it does not mean m > n. You DO NOT know whether n is +ve or -ve.x-y/x+y > 1 ?
... x-y > x+y ?
Remember, if you multiply (or divide) both sides of the inequality by a negative number, the sign of inequality reverses.
In this case. you do not know whether x+y is +ve or -ve. So, you cannot multiply both sides by (x+y).
So It Goes
Oops, my bad... I guess I better brush up my inequalities...givemeanid wrote:If m/n > 1, it does not mean m > n. You DO NOT know whether n is +ve or -ve.x-y/x+y > 1 ?
... x-y > x+y ?
Remember, if you multiply (or divide) both sides of the inequality by a negative number, the sign of inequality reverses.
In this case. you do not know whether x+y is +ve or -ve. So, you cannot multiply both sides by (x+y).
Thanks a lot givemeanid...
How about this?
x-y/x+y > 1 = x-y/x+y -1 > 0 = -2y/x+y > 0
so the question would be
is -2y/x+y > 0
1. x > 0
we don't know anything about y so NS
2. y < 0
we don't know anything about x , so NS
1 & 2 . if y is -ve, -2y will be +ve, however x+y can be +ve or -ve depending on the values of x and y. hence NS
Ans is E
x-y/x+y > 1 = x-y/x+y -1 > 0 = -2y/x+y > 0
so the question would be
is -2y/x+y > 0
1. x > 0
we don't know anything about y so NS
2. y < 0
we don't know anything about x , so NS
1 & 2 . if y is -ve, -2y will be +ve, however x+y can be +ve or -ve depending on the values of x and y. hence NS
Ans is E
