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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, 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.

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
[Reveal] Spoiler: OA
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Re: MGMAT test 4: X Percent of X Percent [#permalink] New post 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.

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.
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Re: MGMAT test 4: X Percent of X Percent [#permalink] New post 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] New post 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.

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, 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.

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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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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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, 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

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, 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?

Hope it's clear.
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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Is x% of x% of y equal to x% less than y ? [#permalink] New post 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
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Re: Is x% of x% of y equal to x% less than y ? [#permalink] New post 17 Oct 2013, 05:02
adg142000 wrote:
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] New post 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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Re: Is x% of x% of y equal to x% less than y ? [#permalink] New post 17 Oct 2013, 06:56
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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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