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x2y = 10,000y – 100xy [multiplying by the common denominator 10,000] x2y + 100xy – 10,000y = 0 [everything to one side, because it’s quadratic] y(x2 + 100x – 10,000) = 0 [factoring] Therefore, the answer to the prompt question is affirmative if either x2 + 100x – 10,000 = 0 or y = 0.

(1) SUFFICIENT: This statement rearranges to give = 0.

(2) INSUFFICIENT: y cannot be 0, but no information is provided about x, making it impossible to determine whether x2 + 100x – 10,000 = 0.

Re: MGMAT test 4: X Percent of X Percent [#permalink]
21 Jun 2010, 16:06

Expert's post

zisis wrote:

Is x% of x% of y equal to x% less than y ?

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

OA: A

x2y = 10,000y – 100xy [multiplying by the common denominator 10,000] x2y + 100xy – 10,000y = 0 [everything to one side, because it’s quadratic] y(x2 + 100x – 10,000) = 0 [factoring] Therefore, the answer to the prompt question is affirmative if either x2 + 100x – 10,000 = 0 or y = 0.

(1) SUFFICIENT: This statement rearranges to give = 0.

(2) INSUFFICIENT: y cannot be 0, but no information is provided about x, making it impossible to determine whether x2 + 100x – 10,000 = 0.

(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.

To elaborate more: the problem with your solution is that you solved incorrectly y(y+1)=1. y(y+1)=1 --> y^2+y-1=0 --> solving for y: y=\frac{-1-\sqrt{5}}{2} or y=\frac{-1+\sqrt{5}}{2}, so y\neq{0}.

Re: MGMAT test 4: X Percent of X Percent [#permalink]
07 Jul 2012, 03:22

Bunuel wrote:

zisis wrote:

Is x% of x% of y equal to x% less than y ?

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

OA: A

x2y = 10,000y – 100xy [multiplying by the common denominator 10,000] x2y + 100xy – 10,000y = 0 [everything to one side, because it’s quadratic] y(x2 + 100x – 10,000) = 0 [factoring] Therefore, the answer to the prompt question is affirmative if either x2 + 100x – 10,000 = 0 or y = 0.

(1) SUFFICIENT: This statement rearranges to give = 0.

(2) INSUFFICIENT: y cannot be 0, but no information is provided about x, making it impossible to determine whether x2 + 100x – 10,000 = 0.

(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.

To elaborate more: the problem with your solution is that you solved incorrectly y(y+1)=1. y(y+1)=1 --> y^2+y-1=0 --> solving for y: y=\frac{-1-\sqrt{5}}{2} or y=\frac{-1+\sqrt{5}}{2}, so y\neq{0}.

Answer: A.

Hope it's clear.

Can you explain this part \frac{x}{100}*\frac{x}{100}*y=y(1-\frac{x}{100})? --> my R.H.S of equation is coming as y-x/100 kindly correct me if i am wrong
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_______________________________________________________________________________________________________________________________ If you like my solution kindly reward me with Kudos.

Re: MGMAT test 4: X Percent of X Percent [#permalink]
07 Jul 2012, 03:27

1

This post received KUDOS

Expert's post

riteshgupta wrote:

Bunuel wrote:

zisis wrote:

Is x% of x% of y equal to x% less than y ?

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

OA: A

x2y = 10,000y – 100xy [multiplying by the common denominator 10,000] x2y + 100xy – 10,000y = 0 [everything to one side, because it’s quadratic] y(x2 + 100x – 10,000) = 0 [factoring] Therefore, the answer to the prompt question is affirmative if either x2 + 100x – 10,000 = 0 or y = 0.

(1) SUFFICIENT: This statement rearranges to give = 0.

(2) INSUFFICIENT: y cannot be 0, but no information is provided about x, making it impossible to determine whether x2 + 100x – 10,000 = 0.

(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.

To elaborate more: the problem with your solution is that you solved incorrectly y(y+1)=1. y(y+1)=1 --> y^2+y-1=0 --> solving for y: y=\frac{-1-\sqrt{5}}{2} or y=\frac{-1+\sqrt{5}}{2}, so y\neq{0}.

Answer: A.

Hope it's clear.

Can you explain this part \frac{x}{100}*\frac{x}{100}*y=y(1-\frac{x}{100})? --> my R.H.S of equation is coming as y-x/100 kindly correct me if i am wrong

Consider this: 10% less than y is y*(1-\frac{10}{100})=y*0.9, the same way "x% less than y": is y(1-\frac{x}{100}).

Re: Is x% of x% of y equal to x% less than y ? (1) x(x + 100) = [#permalink]
09 Dec 2012, 06:09

Expert's post

morfin wrote:

I do not understand the question. Why did you rephrase the question FROM "Is x% of x% of y equal to x% less than y ?" TO Is y = 0 ?

When I read the question, I wrote down (x%((x%)y)) = x%<y

Please help. thanks in advance.

"Is x% of x% of y equal to x% less than y?" means is \frac{x}{100}*\frac{x}{100}*y=y(1-\frac{x}{100})?

If you manipulate with this expression as shown above the questions becomes: is y(x^2+100x-10,000)=0? So, the question basically asks whether y=0 or/and x^2+100x-10,000=0?

Re: Is x% of x% of y equal to x% less than y ? [#permalink]
17 Oct 2013, 05:31

Expert's post

adg142000 wrote:

my approach for the above was i reduced the word statement to equation with statement 1 as :

xy/(x+100)=y(1-x/100)? ,,and took the values x=10 and y =10 for which 100/110< 9

but for x=10 and y=-10

-100/110 is not less than -9.

I got this problem wrong for this reason. Do for percentage problems -ve sign has to be ignored???

Plugging-in is not the correct approach for this question, as because the values of x and y are fixed by the fact statements.

We have to prove whether \frac{x}{100}*\frac{x}{100}*y = y*(1-\frac{x}{100}) or not --> \frac{x}{100}*y[\frac{x}{100}*+1] = y\toAfter re-arranging we get

x*(x+100)*y = 10000y \to Is y*[x*(x+100)-10000]=0?

From F.S 1, we know that x*(x+100) = 10000, thus Sufficient.

From F.S 2, we know only the value of y, and nothing about x. Insufficient

A.

I believe negative percentage makes sense when there is a decrease . So it will not be wrong to say for example that the decrease in the value was 5% or the percentage change was -5%.
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