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

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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

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...

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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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Math Expert V
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Is x% of x% of y equal to x% less than y ? (1) x(x + 100) =  [#permalink]

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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 $$y\neq{0}$$.

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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

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]

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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]

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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]

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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]

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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]

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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]

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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 ?  [#permalink]

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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

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]

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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]

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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 (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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GMAT 1: 690 Q50 V33 Re: Is x% of x% of y equal to x% less than y ? (1) x(x + 100) =  [#permalink]

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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]

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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]

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

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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]

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I took the answer as C, because only when y is not equal to 0 is the first statement valid. As we do not yet know whether y is not equal to 0, we will need the second equation. I think we cannot take the first equation as there is no mention of y and it breaks when y=0.
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Re: Is x% of x% of y equal to x% less than y ? (1) x(x + 100) =  [#permalink]

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mehrotrayashraj wrote:
I took the answer as C, because only when y is not equal to 0 is the first statement valid. As we do not yet know whether y is not equal to 0, we will need the second equation. I think we cannot take the first equation as there is no mention of y and it breaks when y=0.

When we know $$a=0$$, we can conclude that $$a*b = 0$$

Statement 1 says $$x^2+100x−10,000=0$$, so $$(x^2+100x−10,000)*y=0$$ --> YES. Sufficient.
Statement 2 says $$y≠0$$
If $$x^2+100x−10,000=0$$, then $$(x^2+100x−10,000)*y=0$$ --> YES
If $$x^2+100x−10,000≠0$$, then $$(x^2+100x−10,000)*y≠0$$ --> NO
-> Statement 2 alone is not sufficient.
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Re: Is x% of x% of y equal to x% less than y ? (1) x(x + 100) =  [#permalink]

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mehrotrayashraj wrote:
I took the answer as C, because only when y is not equal to 0 is the first statement valid. As we do not yet know whether y is not equal to 0, we will need the second equation. I think we cannot take the first equation as there is no mention of y and it breaks when y=0.

The question asks: is $$y(x^2+100x-10,000)=0$$?

So, is is $$y=0$$ OR/AND $$x^2+100x-10,000=0$$? Notice that IF $$x^2+100x-10,000=0$$, then no matter what the value of y is, $$y(x^2+100x-10,000)=y*0=0$$.

(1) says that $$x^2+100x-10,000=0$$, thus $$y(x^2+100x-10,000)=y*0=0$$.

Hope it helps.
_________________ Re: Is x% of x% of y equal to x% less than y ? (1) x(x + 100) =   [#permalink] 26 Aug 2018, 03:38

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