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Source: — Data Sufficiency |
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by GMATinsight » Wed Jul 23, 2014 3:23 am
abhasjha wrote:Image
Given : s = (x+y)^2 and t = (x-y)^2

Question : (2^s)/(2^t)?

Question Rephrased : 2^(s-t)= ?
Question Rephrased : (s-t)= ?
Using Given information
Question Rephrased : (s-t)= (x+y)^2 - (x-y)^2 =?
Question Rephrased : (x^2+y^2+2xy) - (x^2+y^2-2xy) =?
Question Rephrased : x^2+y^2+2xy - x^2-y^2+2xy =?
Question Rephrased : (4xy) =?

Statement 1) xy=12
SUFFICIENT

Statement 1) x/y=3
i.e. Case 1: x=3, y=1
i.e. Case 2: x=6, y=2
Multiple Solution

INSUFFICIENT

Answer: Option A
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by [email protected] » Wed Jul 23, 2014 12:09 pm
Hi abhasjha,

Sometimes the way to deal with a "crazy looking" DS question is just to try to reasonably prove that a pattern exists (by TESTing VALUES).

Here, we're given....
S = (X+Y)^2
T = (X-Y)^2

We're asked for the value of (2^S)/(2^T). This can be rewritten as 2^(S-T). So the question is really asking for the value of S-T.

Fact 1: XY = 12

Let's TEST VALUES
If....
X = 12, Y = 1
S = 13^2 = 169
T = 11^2 = 121
S-T = 48

If....
X =6, Y = 2
S = 8^2 = 64
T = 4^2 = 16
S-T = 48.....interesting. That's the same answer we got before.....

If...
X = 3, Y = 4
S = 7^2 = 49
T = (-1)^2 = 1
S-T = 48....With 3 separate Test Cases, the answer is ALWAYS 48. This is not an accident; this is clearly a pattern.
Fact 1 is SUFFICIENT

Fact 2: X/Y = 3

If X = 3, Y = 1
S = 4^2 = 16
T = 2^2 = 4
S - T = 12

If X = 6, Y = 2
S = 8^2 = 64
T = 4^2 = 16
S - T = 48

These are different answers.
Fact 2 is INSUFFICIENT

Final Answer: A

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by perwinsharma » Sun Jul 27, 2014 3:11 am
The question wants us to solve for 2^s/2^t = 2^(s - t)

=> If we can calculate s - t, we will get the answer.

First, let's simply the question stem:
s = (x + y)^2 = x^2 + y^2 + 2xy
t = (x - y)^2 = x^2 + y^2 - 2xy

=> s - t = ( x^2 + y^2 + 2xy ) - ( x^2 + y^2 - 2xy ) = 4xy

Considering Statement (1) alone:

xy = 12
=> 4xy = 48
SUFFICIENT

Considering statement (2) alone:

x/y = 3
There's no way we can find out the value of xy.
INSUFFICIENT

The answer is (A).
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