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Percent of percent DS

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Source: — Data Sufficiency |

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by Anurag@Gurome » Mon Dec 26, 2011 3:40 am
karthikpandian19 wrote:Is X percent of Y more than Z percent of W?

(1) X percent of Z is one half of Y percent of W.

(2) X=Y and 2·Z=W
Is X% of Y > Z% of W? or is XY > ZW?

(1) X% of Z = (1/2)Y% of W
XZ/100 = YW/200
2XZ = YW; NOT sufficient.

(2) X = Y and 2Z = W
X² > 2Z²; NOT sufficient.

Combining (1) and (2), 2XZ = YW or X = Y and W = 2X does not imply anything new; NOT sufficient.

The correct answer is E.
Last edited by Anurag@Gurome on Tue Dec 27, 2011 1:51 am, edited 1 time in total.
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by karthikpandian19 » Mon Dec 26, 2011 5:18 am
@Anurag...

I found this from Master GMAT preparation question and it states the answer as E

Explanation:

"MASTER GMAT:
Correct.Solving this question by any method other than Plugging In would be suicidal.Plug in for statement (1) x=10, z=50, y=10, w=100 to get a "No" answer. Ask yourself if it is always "No". Try different numbers. For instance, x=30, z=20, y=30, w=40. The answer is now "Yes". Therefore, (1) Maybe->Insufficient->BCE.Plug in for statement (2). Try to use the same numbers if you can, to save time and careless errors. There is no definite answer, therefore (2) Maybe->Insufficient->CE.Combining the statements does not make any difference, as the numbers prove. Therefore, (1)+(2) Maybe-> Insufficient->E."
Anurag@Gurome wrote:
karthikpandian19 wrote:Is X percent of Y more than Z percent of W?

(1) X percent of Z is one half of Y percent of W.

(2) X=Y and 2·Z=W
Is X% of Y > Z% of W? or is XY > ZW?

(1) X% of Z = (1/2)Y% of W
XZ/100 = YW/200
2XZ = YW; NOT sufficient.

(2) X = Y and 2Z = W
X² > 2Z²; NOT sufficient.

Combining (1) and (2), 2X² = 2XZ or X = Z = Y and W = 2X implies X² > 2X², which is not true. So, the answer to the main question is "No"; SUFFICIENT.

The correct answer is C.
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by karthikpandian19 » Mon Dec 26, 2011 11:43 pm
Can anyone explain which the explanations above is correct???
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by rijul007 » Mon Dec 26, 2011 11:58 pm
karthikpandian19 wrote:Is X percent of Y more than Z percent of W?

(1) X percent of Z is one half of Y percent of W.

(2) X=Y and 2·Z=W
Rephrase the ques as
Is XY/100 > WZ/100?
or

Is XY > WZ?


(1) X percent of Z is one half of Y percent of W.

XZ/100 = YW/200
XZ = YW/2

Lets check by plugging numbers
case 1:
X = 2
Y = 1
Z = 50
W = 100

case 2:
X = 50
Y = 100
W = 1
Z = 2



Not sufficient


(2) X=Y and 2·Z=W

XY = Y^2 = X^2
WZ = 4Z^2 = W^2 / 4

Not sufficient

Combining (1) and (2)
Substitute X=Y and 2.Z = W in XZ = YW/2

1/2 = 1/2

Not sufficient


Option E
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by rijul007 » Tue Dec 27, 2011 12:05 am
Anurag@Gurome wrote:
karthikpandian19 wrote:Is X percent of Y more than Z percent of W?

(1) X percent of Z is one half of Y percent of W.

(2) X=Y and 2·Z=W
Is X% of Y > Z% of W? or is XY > ZW?

(1) X% of Z = (1/2)Y% of W
XZ/100 = YW/200
2XZ = YW; NOT sufficient.

(2) X = Y and 2Z = W
X² > 2Z²; NOT sufficient.

Combining (1) and (2), 2X² = 2XZ or X = Z = Y and W = 2X implies X² > 2X², which is not true. So, the answer to the main question is "No"; SUFFICIENT.

The correct answer is C.
2XZ = YW
=> 2XZ = 2XZ

Z is not equal to X
So the conversion 2XZ to 2X² would be wrong.
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by Anurag@Gurome » Tue Dec 27, 2011 1:53 am
rijul007 wrote:
2XZ = YW
=> 2XZ = 2XZ

Z is not equal to X
So the conversion 2XZ to 2X² would be wrong.
That's right, i have edited the previous post. Thanks for pointing the same!
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by ArunangsuSahu » Tue Jan 03, 2012 10:08 pm
Question: XY >ZW?

Statement 1:

2XZ = YW

No Conclusion....INSUFFICIENT

Statement 2:

X=Y, 2Z =W.

No Correlation...INSUFFICIENT

Combining (1) and (2) Y^2 > 2Z^2...NO CONCLUSION

So (E) is the answer
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