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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   21 Jun 2010, 15:19
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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

Show SpoilerDoubt
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.

The correct answer is A.

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

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

what am i missing? please help
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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, 01:49
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Is x% of x% of y equal to x% less than y ?

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 \(y(x^2+100x-10,000)=0\)?

Essential the question asks: 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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Is x% of x% of y equal to x% less than y ? (1) x(x + 100) = [#permalink] New post   21 Jun 2010, 17:06
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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.

The correct answer is A.

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

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

what am i missing? please help


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 \(y\neq{0}\).

Answer: A.

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Re: DS question [#permalink] New post   30 Sep 2010, 07:19
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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Re: MGMAT test 4: X Percent of X Percent [#permalink] New post   07 Jul 2012, 04:22
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.

The correct answer is A.

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

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

what am i missing? please help


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 \(y\neq{0}\).

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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Re: MGMAT test 4: X Percent of X Percent [#permalink] New post   07 Jul 2012, 04:27
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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.

The correct answer is A.

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

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

what am i missing? please help


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 \(y\neq{0}\).

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

Hope it's clear.
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Is x% of x% of y equal to x% less than y ? [#permalink] New post   25 Aug 2012, 23:26
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, 23:56
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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 . :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   08 Dec 2012, 12:48
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

Please help. thanks in advance.
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Re: Is x% of x% of y equal to x% less than y ? (1) x(x + 100) = [#permalink] New post   09 Dec 2012, 07:09
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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

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 \(x^2+100x-10,000=0\)?

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] New post   07 Jul 2015, 15:19
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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

Answer: Option 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   07 Jul 2015, 15:24
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] New post   07 Jul 2015, 15:33
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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] New post   26 Jul 2015, 10:57
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.

Answer: A.

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] New post   26 Jul 2015, 11:17
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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.

Answer: A.

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] New post   04 Aug 2017, 07:54
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Hey Bunuel can you please help me here?
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] New post   25 Aug 2018, 18:34
mehrotrayashraj wrote:
Hey Bunuel can you please help me here?
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.
Thus the answer is 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   26 Aug 2018, 03:38
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mehrotrayashraj wrote:
Hey Bunuel can you please help me here?
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.
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Re: Is x% of x% of y equal to x% less than y ? (1) x(x + 100) = [#permalink] New post   29 Aug 2023, 03:10
Hi Bunuel,

Can you please explain in detail how you go from x^2y=y(10,000−100x) to y(x2+100x−10,000)=0.

What did you exactly do with the first equation to get the second equation aka what kind of operation did you perform on the first equation to get the second equation? that part i can't figure it out.

Thanks in advance!
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Re: Is x% of x% of y equal to x% less than y ? (1) x(x + 100) = [#permalink] New post   29 Aug 2023, 06:31
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Rebaz wrote:
Hi Bunuel,

Can you please explain in detail how you go from x^2y=y(10,000−100x) to y(x2+100x−10,000)=0.

What did you exactly do with the first equation to get the second equation aka what kind of operation did you perform on the first equation to get the second equation? that part i can't figure it out.

Thanks in advance!


\(x^2y=y(10,000-100x)\)

Rearrange the above to get:

\(x^2y-y(10,000-100x)=0\)

Factor out y to get:

\(y(x^2-10,000+100x)=0\).

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]
29 Aug 2023, 06:31
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