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Is x% of x% of y equal to x% less than y ? (1) x(x + 100) = [#permalink]
 21 Jun 2010, 15:19
Question Stats:
63% (02:29) correct
36% (02:43) wrong based on 1 sessions
Is x% of x% of y equal to x% less than y ? (1) x(x + 100) = 10,000 (2) y(y + 1) = 1 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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Re: MGMAT test 4: X Percent of X Percent [#permalink]
21 Jun 2010, 17:06
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]
22 Jun 2010, 13:55
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, 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]
07 Jul 2012, 04:27
1
This post received
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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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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
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. NEW!!!
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. NEW!!!
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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, 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]
09 Dec 2012, 07:09
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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, 07:09
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