|
Author |
Message |
|
TAGS:
|
|
|
Intern
Joined: 14 Nov 2011
Posts: 6
Followers: 0
Kudos [?]:
0
[0], given: 0
|
If x and y are positive, what is the value of x? [#permalink]
 09 Mar 2012, 21:22
Question Stats:
53% (02:07) correct
46% (01:12) wrong based on 28 sessions
If x and y are positive, what is the value of x? (1) 200% of x equals to 400% of y. (2) xy is the square of a positive integer.
Last edited by Bunuel on 09 Mar 2012, 23:39, edited 2 times in total.
Edited the question
|
|
|
|
|
|
|
Intern
Joined: 14 Nov 2011
Posts: 6
Followers: 0
Kudos [?]:
0
[0], given: 0
|
Re: if x and y are positive , what is the value of x?plz explain [#permalink]
09 Mar 2012, 21:33
bunual help on this question. Posted from my mobile device 
|
|
|
|
|
|
SVP
Joined: 16 Nov 2010
Posts: 1719
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 26
Kudos [?]:
229
[0], given: 35
|
Re: if x and y are positive , what is the value of x?plz explain [#permalink]
09 Mar 2012, 23:17
(1) 200/100 * x = 400/100 * y 2x = 4y X = 2y => X is even (2) Xy = 1,4,9,16,… Not Sufficient. (1) + (2) Suppose: 2y^2 = 16 Y = 2root(2) X = 4root(2) Or 2y^2 = 4 Y = root(2) X = 2root(2) Not Sufficient. So Answer is E.
_________________
Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 12116
Followers: 1879
Kudos [?]:
10131
[1] , given: 965
|
Re: If x and y are positive, what is the value of x? [#permalink]
09 Mar 2012, 23:38
1
This post received
KUDOS
If x and y are positive, what is the value of x?Notice that we are not told that x and y are integers only, we are just told that they are both positive. (1) 200% of x equals to 400% of y --> \frac{200}{100}*x=\frac{400}{100}*y --> x=2y. Not sufficient to get the single numerical value of x. (2) xy is the square of a positive integer --> xy=n^2, for some positive integer n. Not sufficient to get the single numerical value of x. (1)+(2) Since from (1) x=2y then from (2) x*\frac{x}{2}=n^2 --> x^2=2n^2 --> the value of x (x^2) is determined by the value of integer n, so we still cannot get the single numerical value of x. For example: if n=1 then x=\sqrt{2} but if n=2 then x=2\sqrt{2}. Not sufficient. Answer: E. Hope it's clear. subhashghosh wrote: (1)
200/100 * x = 400/100 * y
2x = 4y
X = 2y
=> X is even
Since we are not told that x and y are integers only, then from x=2y we cannot say whether x even: x will be even if y=integer; x will be odd if y=\frac{odd}{2}, for example if y=\frac{3}{2} then x=3=odd; x may not be an integer at all, for example if y=\frac{1}{3} then x=\frac{2}{3}\neq{integer}. In fact if we knew that x=even then x^2=2n^2, from (1)+(2), would have only one integer solution x=0 and n=0, but this would contradict the given fact that x is positive. Hope it's clear.
_________________
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
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!!! ,11 Mixed Questions NEW!!!, 12 Fresh Meat 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!!!, 11 New DS set. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
Intern
Joined: 06 Dec 2011
Posts: 3
Followers: 0
Kudos [?]:
0
[0], given: 0
|
Re: If x and y are positive, what is the value of x? [#permalink]
11 Mar 2012, 04:44
Bunuel wrote: If x and y are positive, what is the value of x?Notice that we are not told that x and y are integers only, we are just told that they are both positive. (1) 200% of x equals to 400% of y --> \frac{200}{100}*x=\frac{400}{100}*y --> x=2y. Not sufficient to get the single numerical value of x. (2) xy is the square of a positive integer --> xy=n^2, for some positive integer n. Not sufficient to get the single numerical value of x. (1)+(2) Since from (1) x=2y then from (2) x*\frac{x}{2}=n^2 --> x^2=2n^2 --> the value of x (x^2) is determined by the value of integer n, so we still cannot get the single numerical value of x. For example: if n=1 then x=\sqrt{2} but if n=2 then x=2\sqrt{2}. Not sufficient. Answer: E. Hope it's clear. subhashghosh wrote: (1)
200/100 * x = 400/100 * y
2x = 4y
X = 2y
=> X is even
Since we are not told that x and y are integers only, then from x=2y we cannot say whether x even: x will be even if y=integer; x will be odd if y=\frac{odd}{2}, for example if y=\frac{3}{2} then x=3=odd; x may not be an integer at all, for example if y=\frac{1}{3} then x=\frac{2}{3}\neq{integer}. In fact if we knew that x=even then x^2=2n^2, from (1)+(2), would have only one integer solution x=0 and n=0, but this would contradict the given fact that x is positive. Hope it's clear. Hello Bunuel, Thanks for this wonderful explanation! However I'm still not able to figure out the meaning of the following statement Quote: In fact if we knew that x=even then x^2=2n^2, from (1)+(2), would have only one integer solution x=0 and n=0, but this would contradict the given fact that x is positive. Can you please provide more clarity and let know which particular number property you are using to deduce the above statement?
|
|
|
|
|
|
SVP
Joined: 16 Nov 2010
Posts: 1719
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 26
Kudos [?]:
229
[0], given: 35
|
Re: If x and y are positive, what is the value of x? [#permalink]
11 Mar 2012, 04:49
raul2011 wrote: Bunuel wrote: If x and y are positive, what is the value of x?Notice that we are not told that x and y are integers only, we are just told that they are both positive. (1) 200% of x equals to 400% of y --> \frac{200}{100}*x=\frac{400}{100}*y --> x=2y. Not sufficient to get the single numerical value of x. (2) xy is the square of a positive integer --> xy=n^2, for some positive integer n. Not sufficient to get the single numerical value of x. (1)+(2) Since from (1) x=2y then from (2) x*\frac{x}{2}=n^2 --> x^2=2n^2 --> the value of x (x^2) is determined by the value of integer n, so we still cannot get the single numerical value of x. For example: if n=1 then x=\sqrt{2} but if n=2 then x=2\sqrt{2}. Not sufficient. Answer: E. Hope it's clear. subhashghosh wrote: (1)
200/100 * x = 400/100 * y
2x = 4y
X = 2y
=> X is even
Since we are not told that x and y are integers only, then from x=2y we cannot say whether x even: x will be even if y=integer; x will be odd if y=\frac{odd}{2}, for example if y=\frac{3}{2} then x=3=odd; x may not be an integer at all, for example if y=\frac{1}{3} then x=\frac{2}{3}\neq{integer}. In fact if we knew that x=even then x^2=2n^2, from (1)+(2), would have only one integer solution x=0 and n=0, but this would contradict the given fact that x is positive. Hope it's clear. Hello Bunuel, Thanks for this wonderful explanation! However I'm still not able to figure out the meaning of the following statement Quote: In fact if we knew that x=even then x^2=2n^2, from (1)+(2), would have only one integer solution x=0 and n=0, but this would contradict the given fact that x is positive. Can you please provide more clarity and let know which particular number property you are using to deduce the above statement? _________________
Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 12116
Followers: 1879
Kudos [?]:
10131
[0], given: 965
|
Re: If x and y are positive, what is the value of x? [#permalink]
11 Mar 2012, 04:59
raul2011 wrote: Hello Bunuel, Thanks for this wonderful explanation! However I'm still not able to figure out the meaning of the following statement Quote: In fact if we knew that x=even then x^2=2n^2, from (1)+(2), would have only one integer solution x=0 and n=0, but this would contradict the given fact that x is positive. Can you please provide more clarity and let know which particular number property you are using to deduce the above statement? Sure. We know that n is a positive integer. Now, if x is an even integer, then x^2=2n^2 should be true for some integers n and x, but it's true only for one integer solution x=n=0, which cannot be valid, since we are given that x is a positive number (0 is neither positive nor negative). Hope it's clear.
_________________
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
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!!! ,11 Mixed Questions NEW!!!, 12 Fresh Meat 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!!!, 11 New DS set. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
Senior Manager
Joined: 24 Aug 2009
Posts: 312
Schools: Harvard, Columbia, Stern, Booth, LSB,
Followers: 2
Kudos [?]:
159
[0], given: 229
|
Re: If x and y are positive, what is the value of x? [#permalink]
11 Sep 2012, 05:45
Bunuel wrote: If x and y are positive, what is the value of x?Notice that we are not told that x and y are integers only, we are just told that they are both positive. (1) 200% of x equals to 400% of y --> \frac{200}{100}*x=\frac{400}{100}*y --> x=2y. Not sufficient to get the single numerical value of x. (2) xy is the square of a positive integer --> xy=n^2, for some positive integer n. Not sufficient to get the single numerical value of x. (1)+(2) Since from (1) x=2y then from (2) x*\frac{x}{2}=n^2 --> x^2=2n^2 --> the value of x (x^2) is determined by the value of integer n, so we still cannot get the single numerical value of x. For example: if n=1 then x=\sqrt{2} but if n=2 then x=2\sqrt{2}. Not sufficient. Answer: E. Hope it's clear. subhashghosh wrote: (1)
200/100 * x = 400/100 * y
2x = 4y
X = 2y
=> X is even
Since we are not told that x and y are integers only, then from x=2y we cannot say whether x even: x will be even if y=integer; x will be odd if y=\frac{odd}{2}, for example if y=\frac{3}{2} then x=3=odd; x may not be an integer at all, for example if y=\frac{1}{3} then x=\frac{2}{3}\neq{integer}. In fact if we knew that x=even then x^2=2n^2, from (1)+(2), would have only one integer solution x=0 and n=0, but this would contradict the given fact that x is positive. Hope it's clear. Hi Bunuel, Thanks for the nice explanation . I would like to modify the question a bit & would like to present a twist to the same question. If the new statement reads "If x and y are positive integers, what is the value of x" rather than "If x and y are positive, what is the value of x" Now what will be the answer. As per me the answer should be C because i believe no such value will exist. Kindly enlighten us all.
_________________
If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS.
Kudos always maximizes GMATCLUB worth -Game Theory
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 12116
Followers: 1879
Kudos [?]:
10131
[0], given: 965
|
Re: If x and y are positive, what is the value of x? [#permalink]
11 Sep 2012, 06:03
fameatop wrote: Bunuel wrote: If x and y are positive, what is the value of x?Notice that we are not told that x and y are integers only, we are just told that they are both positive. (1) 200% of x equals to 400% of y --> \frac{200}{100}*x=\frac{400}{100}*y --> x=2y. Not sufficient to get the single numerical value of x. (2) xy is the square of a positive integer --> xy=n^2, for some positive integer n. Not sufficient to get the single numerical value of x. (1)+(2) Since from (1) x=2y then from (2) x*\frac{x}{2}=n^2 --> x^2=2n^2 --> the value of x (x^2) is determined by the value of integer n, so we still cannot get the single numerical value of x. For example: if n=1 then x=\sqrt{2} but if n=2 then x=2\sqrt{2}. Not sufficient. Answer: E. Hope it's clear. subhashghosh wrote: (1)
200/100 * x = 400/100 * y
2x = 4y
X = 2y
=> X is even
Since we are not told that x and y are integers only, then from x=2y we cannot say whether x even: x will be even if y=integer; x will be odd if y=\frac{odd}{2}, for example if y=\frac{3}{2} then x=3=odd; x may not be an integer at all, for example if y=\frac{1}{3} then x=\frac{2}{3}\neq{integer}. In fact if we knew that x=even then x^2=2n^2, from (1)+(2), would have only one integer solution x=0 and n=0, but this would contradict the given fact that x is positive. Hope it's clear. Hi Bunuel, Thanks for the nice explanation . I would like to modify the question a bit & would like to present a twist to the same question. If the new statement reads "If x and y are positive integers, what is the value of x" rather than "If x and y are positive, what is the value of x" Now what will be the answer. As per me the answer should be C because i believe no such value will exist. Kindly enlighten us all. In this case, for (1)+(2) we would have the same equation: x=2n^2, which has only one integer solution for x and n: x=n=0 but since we are told that x is a positive integer then this solution is no good. But we won't see such question on the real test where no value can satisfy the statements. So, the question in this case would be flawed.
_________________
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
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!!! ,11 Mixed Questions NEW!!!, 12 Fresh Meat 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!!!, 11 New DS set. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
|
Re: If x and y are positive, what is the value of x?
[#permalink]
11 Sep 2012, 06:03
|
|
|
|
|
|
|
|
|
Similar topics |
Author |
Replies |
Last post |
|
Similar
Topics:
|
 |
|
|
If x and y are positive integers, what is the value of x +
|
japped187 |
2 |
30 Apr 2008, 01:55 |
|
|
4
|
|
If x and y are positive, what is the value of x y? (1) (x^2
|
carlson2010 |
3 |
10 Jun 2008, 13:33 |
|
|
|
|
If x and y are positive integers, what is the value of x?
|
linau1982 |
5 |
16 Oct 2008, 07:58 |
|
|
|
|
If x and y are positive integers, what is the value of x +
|
tharunv |
5 |
30 Oct 2008, 18:34 |
|
|
|
 |
If x and y are positive, what is the value of x-y?
|
eybrj2 |
2 |
05 Apr 2012, 13:25 |
|
|
|
|
|
|
close
