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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]  21 Jun 2010, 14:19
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61% (02:18) correct 39% (01:47) wrong based on 102 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: Doubt
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.

--------------------------------------------------------------

But, I believe D:
A sufficient
B: y=1 or y+1=1 therefore y=0 therefore B sufficient...

[Reveal] Spoiler: OA
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Re: MGMAT test 4: X Percent of X Percent [#permalink]  21 Jun 2010, 16:06
Expert's post
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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.

--------------------------------------------------------------

But, I believe D:
A sufficient
B: y=1 or y+1=1 therefore y=0 therefore B sufficient...

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 does $$y=0$$ 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.

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 $$y\neq{0}$$.

Hope it's clear.
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Re: MGMAT test 4: X Percent of X Percent [#permalink]  22 Jun 2010, 12:55
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yeh...makes a bit more sense now.......thanks
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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.

--------------------------------------------------------------

But, I believe D:
A sufficient
B: y=1 or y+1=1 therefore y=0 therefore B sufficient...

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 does $$y=0$$ 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.

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 $$y\neq{0}$$.

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

--------------------------------------------------------------

But, I believe D:
A sufficient
B: y=1 or y+1=1 therefore y=0 therefore B sufficient...

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 does $$y=0$$ 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.

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 $$y\neq{0}$$.

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 $$y(1-\frac{x}{100})$$.

Hope it's clear.
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Re: Is x% of x% of y equal to x% less than y ? (1) x(x + 100) = [#permalink]  08 Dec 2012, 11:48
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

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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

"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 $$x^2+100x-10,000=0$$?

Hope it's clear.
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Is x% of x% of y equal to x% less than y ? [#permalink]  17 Oct 2013, 04:53
Is x% of x% of y equal to x% less than y ?

(1) x(x + 100) = 10,000
(2) y(y + 1) = 1
Current Student
Joined: 07 Jan 2013
Posts: 46
Location: India
Concentration: Finance, Strategy
GMAT 1: 570 Q46 V23
GMAT 2: 710 Q49 V38
GPA: 2.9
WE: Information Technology (Computer Software)
Followers: 1

Kudos [?]: 14 [0], given: 23

Re: Is x% of x% of y equal to x% less than y ? [#permalink]  17 Oct 2013, 05:02
Is x% of x% of y equal to x% less than y ?

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

what I wanted to know about the above question is that while plugging in values can we use -ve values for Y.

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???
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Re: Is x% of x% of y equal to x% less than y ? [#permalink]  17 Oct 2013, 05:31
Expert's post
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 --> $$\frac{x}{100}*y[\frac{x}{100}*+1] = y$$ $$\to$$After 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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Re: Is x% of x% of y equal to x% less than y ? [#permalink]  17 Oct 2013, 06:56
Expert's post
Is x% of x% of y equal to x% less than y ?

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

Merging similar topics. Please refer to the solutions above.
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Re: Is x% of x% of y equal to x% less than y ?   [#permalink] 17 Oct 2013, 06:56
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