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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] New post 30 Sep 2010, 00:43
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56% (02:37) correct 44% (02:11) wrong based on 196 sessions
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] New post 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.

Answer: A.

Hope it's clear.
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Re: DS question [#permalink] New post 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

Answer is (a)
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Is x% of x% of y equal to x% less than y ? [#permalink] New post 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 . :roll:

Regards,
arijitb1980
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Re: Is x% of x% of y equal to x% less than y ? (1) x(x + 100) = [#permalink] New post 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 . :roll:

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.

Answer A
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Re: Is x% of x% of y equal to x% less than y ? (1) x(x + 100) = [#permalink] New post 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] New post 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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