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# Is x% of x% of y equal to x% less than y ? (1) x(x + 100) =

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Is x% of x% of y equal to x% less than y ? (1) x(x + 100) = [#permalink]  30 Sep 2010, 00:43
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Is x% of x% of y equal to x% less than y ?

(1) x(x + 100) = 10,000
(2) y(y + 1) = 1
[Reveal] Spoiler: OA
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Re: DS question [#permalink]  30 Sep 2010, 00:49
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prashantbacchewar wrote:
Is x% of x% of y equal to x% less than y ?

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

Question: is $$\frac{x}{100}*\frac{x}{100}*y=y(1-\frac{x}{100})$$? --> is $$x^2y=100y(100-x)$$? --> is $$x^2y=y(10,000-100x)$$ --> is $$y(x^2+100x-10,000)=0$$?

Basically question is $$y=0$$ or/and $$x^2+100x-10,000=0$$?

(1) $$x(x + 100)=10,000$$ --> $$x^2+100x-10,000=0$$. Directly gives the answer. Sufficient.

(2) $$y(y+1)=1$$. Here it's clear that $$y\neq{0}$$, (substitute $$y=0$$ in this equation: $$0(0+1)=0\neq{1}$$). So we know that $$y\neq{0}$$, but don't know whether $$x^2+100x-10,000=0$$? Not sufficient.

Hope it's clear.
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Re: DS question [#permalink]  30 Sep 2010, 06:19
prashantbacchewar wrote:
Is x% of x% of y equal to x% less than y ?

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

LHS = (x/100)*(x/100)*y
RHS = (1-x/100) * y

LHS = RHS implies x^2/100 = (100-x) OR x^2+100x=10000

(1) This is exactly what we need to know. Sufficient

(2) The equality to be tested is independent of y. Insufficient

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Is x% of x% of y equal to x% less than y ? [#permalink]  25 Aug 2012, 22:26
Hello Guys,

I am new to GMAT preparation so need some help from you veterans .I cannot understand this question.As per my understanding x% of x% of any number is always less than x% of that number.For example, 10% of 10% of 100 : Since there is no bracket ,I can start from the left hand side .10% of 10% is 1% . 1% of 100 is 1. Now to the second part ...x% less than y,which means 10% less than y,which is nothing but 90.So 1 is always less than 90 .
Obvously I have got it all wrong ,but I cannot interpret it in any other manner .Please help .

Regards,
arijitb1980
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arijitb1980
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Re: Is x% of x% of y equal to x% less than y ? (1) x(x + 100) = [#permalink]  25 Aug 2012, 22:56
arijitb1980 wrote:
Hello Guys,

I am new to GMAT preparation so need some help from you veterans .I cannot understand this question.As per my understanding x% of x% of any number is always less than x% of that number.For example, 10% of 10% of 100 : Since there is no bracket ,I can start from the left hand side .10% of 10% is 1% . 1% of 100 is 1. Now to the second part ...x% less than y,which means 10% less than y,which is nothing but 90.So 1 is always less than 90 .
Obvously I have got it all wrong ,but I cannot interpret it in any other manner .Please help .

Regards,
arijitb1980

From your computations it is clear that $$x$$ cannot be 10. But it doesn't mean that there is no value of $$x$$ for which the equality holds.

Translating the question into an equation: is $$\frac{x}{100}*\frac{x}{100}y=(1-\frac{x}{100})y$$?

(1) If $$y=0,$$ then the equality certainly holds.
Dividing through by $$y,$$ the equation becomes $$x^2+x-10,000=0.$$
You can solve this quadratic and the positive root is approximately $$61.8.$$
So, here is the answer: for $$x=61.8$$, $$x%$$ of $$x%$$ of $$y$$ is $$x%$$ less than $$y.$$
Sufficient.

(2) We can deduce that $$y\neq0$$ but we don't know anything about $$x.$$
Not sufficient.

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Re: Is x% of x% of y equal to x% less than y ? (1) x(x + 100) = [#permalink]  10 Jun 2013, 02:53
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Re: Is x% of x% of y equal to x% less than y ? (1) x(x + 100) = [#permalink]  17 Jun 2014, 09:47
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Re: Is x% of x% of y equal to x% less than y ? (1) x(x + 100) =   [#permalink] 17 Jun 2014, 09:47
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