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MGMAT question on percents...not clear on what question is

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Source: — Data Sufficiency |

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by Anurag@Gurome » Mon Apr 18, 2011 10:44 pm
alltimeacheiver wrote:Is x% of x% of y equal to x% less than y ?

(1) x(x + 100) = 10,000
(2) y(y + 1) = 1
(1) x% of x% of y = x% less than y means (x/100)(x/100)y = y - y(x/100)
x²y/10000 = y - xy/100
x²/10000 = 1 - x/100
x²/10000 + x/100 = 1
x² + 100x = 10000
x(x + 100) = 10000, same as statement 1.

So, (1) is SUFFICIENT.

(2) y² + y - 1 = 0, which is a quadratic equation.
From the steps done in statement 1, it can be easily seen that we may or may not obtain the above quadratic from x% of x% of y equal to x% less than y.
So, (2) is NOT SUFFICIENT.

The correct answer is A.
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by GMATGuruNY » Fri Apr 22, 2011 6:20 am
alltimeacheiver wrote:Is x% of x% of y equal to x% less than y ?

(1) x(x + 100) = 10,000
(2) y(y + 1) = 1
Plug in y=100.

Rephrase the question:
Is x% of x% of 100 equal to 100 decreased by x% of 100?

Translate into math:
x/100 * x/100 * 100 = 100 - (x/100)*100
x²/100 = 100 - x
x² = 10,000 - 100x
x² + 100x = 10,000.

Question rephrased:
Does x² + 100x = 10,000?

Statement 1: x(x + 100) = 10,000
x² + 100x = 10,000.
Sufficient.

Statement 2: y(y + 1) = 1.
No information about x.
Insufficient.

The correct answer is A.
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