gmat focus DS -4
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- GMATinsight
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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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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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich
- perwinsharma
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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).
=> 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).