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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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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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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
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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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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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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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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]  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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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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Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Percent and Interest Problems: math-number-theory-percents-91708.html

All DS Percent and Interest Problems to practice: search.php?search_id=tag&tag_id=33
All PS Percent and Interest Problems to practice: search.php?search_id=tag&tag_id=54

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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 ? (1) x(x + 100) = [#permalink]  07 Jul 2015, 14:19
Expert's post
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 (x/100)*(x/100)*y = y - (x/100)*y
Question : Is (x/100)*(x/100)*y = y[1 - (x/100)]
Question : Is (x/100)^2 = (100 - x)/100
Question : Is (x)^2 = (100 - x)*100?
Question : Is x^2 +100x = 10,000?

Question : Is x(x +100) = 10,000?

Statement 1: x(x + 100) = 10,000
SUFFICIENT

Statement 2: y(y + 1) = 1
NOT SUFFICIENT

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Re: Is x% of x% of y equal to x% less than y ? (1) x(x + 100) = [#permalink]  07 Jul 2015, 14:24
How did rhs become y(1-x/100)? Please explain i am unable to understand...
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Re: Is x% of x% of y equal to x% less than y ? (1) x(x + 100) = [#permalink]  07 Jul 2015, 14:33
Expert's post
Shreks1190 wrote:
How did rhs become y(1-x/100)? Please explain i am unable to understand...

x% less than y means "y - (x% of y)"
which is same as y - (x/100)*y
Take y common
the expression becomes y[1 - (x/100)]

I hope it helps!
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Re: Is x% of x% of y equal to x% less than y ? (1) x(x + 100) = [#permalink]  26 Jul 2015, 09:57
Bunuel wrote:
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.

Hello Bunuel, I could not understand one thing that why did you not eliminate y from $$x^2y=100y(100-x)$$ and kept till the end ?. As far as I know percentages dont have sign.
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Re: Is x% of x% of y equal to x% less than y ? (1) x(x + 100) = [#permalink]  26 Jul 2015, 10:17
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Expert's post
anurag356 wrote:
Bunuel wrote:
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.

Hello Bunuel, I could not understand one thing that why did you not eliminate y from $$x^2y=100y(100-x)$$ and kept till the end ?. As far as I know percentages dont have sign.

1. We are concerned about the sign when we are dealing with inequalities, not equations.
2. Have you read the highlighted part??? y = 0 also satisfies the equation hence we cannot reduce by it because division by 0 is not allowed.
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Re: Is x% of x% of y equal to x% less than y ? (1) x(x + 100) =   [#permalink] 26 Jul 2015, 10:17
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