My answer is C.
Is that correct ?
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GMAT PREP INEQUALITY ??
Source: Beat The GMAT — Data Sufficiency |
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 !!
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 !!
Any expert's solution for this confusion....
I request Stuart/Ron can you please help !!
regards,
Amit
I request Stuart/Ron can you please help !!
regards,
Amit
-
Stuart@KaplanGMAT
- GMAT Instructor
- Posts: 3225
- Location: Toronto
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Your problem stems from your manipulation of this inequality.amitansu wrote:I just have a small confusion !!
In statement 2 we have x/y >1 => x > y
Can anybody throw some light !!
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
Stuart Kovinsky | Kaplan GMAT Faculty | Toronto
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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?
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?
-
Stuart@KaplanGMAT
- GMAT Instructor
- Posts: 3225
- Location: Toronto
- Thanked: 1710 times
- GMAT Score:800
My previous post didn't even address the whole question, I was just responding the manipulation of statement (2).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?
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.
Stuart Kovinsky | Kaplan GMAT Faculty | Toronto
Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course
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.
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.
