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Absolute Values

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Source: — Data Sufficiency |
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by GMATGuruNY » Sun Sep 07, 2014 10:01 am
akhilsuhag wrote:If |x| = |2y| what is the value of x - 2y ?

(1) x + 2y = 6
(2) xy > 0
|x| = |2y|.
Case 1: x=2y
In this case, x-2y = 2y-2y = 0.
Case 2: x=-2y
In this case, x-2y = -2y-2y = -4y.

Statement 1: x+2y = 6
Case 1: x=2y
Substituting x=2y into x+2y = 6, we get:
2y + 2y = 6
4y = 6
y = 2/3.
Case 1 is possible.
In Case 1, x-2y = 0.

Case 2: x=-2y
Substituting x=-2y into x+2y = 6, we get:
-2y + 2y = 6
0 = 6.
Case 2 is not possible.

Since only Case 1 is possible, x-2y = 0.
SUFFICIENT.

Statement 2: xy > 0
In other words, x and y have the SAME SIGN.

Case 1: x=2y
If y=1, then x=2, satisfying the constraint that x and y have the same sign.
Thus, Case 1 is possible.
In Case 1, x-2y = 0.

Case 2: x=-2y
If y=1, then x=-2, violating the constraint that x and y have the same sign.
If y=-1, then x=2, violating the constraint that x and y have the same sign.
Implication:
Case 2 is not possible..

Since only Case 1 is possible, x-2y = 0.
SUFFICIENT.

The correct answer is D.
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by Brent@GMATPrepNow » Sun Sep 07, 2014 10:19 am
akhilsuhag wrote:If |x| = |2y| what is the value of x - 2y ?

(1) x + 2y = 6
(2) xy > 0

Target question: What is the value of x - 2y?

Given: |x| = |2y|
This means that EITHER x = 2y OR x = -2y
So, we need to consider these two possible CASES when examining each statement

Statement 1: x + 2y = 6
We'll examine the two possible CASES.
case a: x = 2y
So, we can replace 2y with x to get: x + x = 6
Solve, to get x = 3
This means that x = 3 and 2y = 3, so x - 2y = 0

case b: x = -2y
We can also say that -x = 2y
So, we can replace 2y with -x to get: x + (-x) = 6
Simplify to get: 0 = 6
Hmmmm, doesn't make any sense, so we can RULE OUT case b, which means only case a applies.
So, we can be certain that x - 2y = 0
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: xy > 0
This means that x and y are the same sign.
It ALSO means that x and 2y are the same sign
Let's check our two cases, and see what happens.

case a: x = 2y
This CONFORMS to our conclusion that x and 2y are the same sign
For case a, we already concluded that x - 2y = 0

case b: x = -2y
This DOES NOT conform to our conclusion that x and 2y are the same sign
So we can RULE OUT case b, which means only case a applies.
So, we can be certain that x - 2y = 0
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
SUFFICIENT

Answer = D

Cheers,
Brent
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by [email protected] » Sun Sep 07, 2014 11:29 am
Hi akhilsuhag,

This question can be solved by TESTing Values (there are some interesting Number Properties here too).

We're told that |X| = |2Y|. We're asked for the value of X - 2Y.

One of the Number Properties worth noting is that since we're dealing with absolute values, X and Y COULD have the SAME sign OR DIFFERENT signs.

eg. X = 2 or -2 when Y = 1 or -1

Fact 1: X + 2Y = 6

Since the result is +6, our options are limited. X and Y CAN'T both be negative (the sum would be negative). They also CAN'T be opposite signs (if they were, then X + 2Y would = 0 and we're told that the sum has to = 6).

We can only TEST positive values (and there's ONLY 1 positive option):
If X = 3, Y = 1.5, then the answer to the question is 3 - 2(1.5) = 0
Fact 1 is SUFFICIENT

Fact 2: XY > 0

This tells us that X and Y have the SAME sign (either both + or both - ).

If X = 2, Y = 1 and the answer to the question is 0
If X = -6, Y = -3 and the answer to the question is 0
The answer to the question will ALWAYS be 0
Fact 2 is SUFFICIENT

Final Answer: D

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