If x and y are positive integers, what is the value of x ?
(1) x, y, and xy are distinct perfect squares less than 100.
(2) x<5
OA is C
Perfect Squares
This topic has expert replies
- hja379
- Master | Next Rank: 500 Posts
- Posts: 208
- Joined: Thu Aug 26, 2010 3:10 pm
- Thanked: 20 times
- Followed by:2 members
Last edited by hja379 on Mon Mar 21, 2011 8:02 am, edited 1 time in total.
Google "GMAT Pill"<--really helpful, worth checking out--especially for RC passages.
e-gmat SC: Never thought it would be fun learning SC.
India School Fund: Education through Innovation - A HBS start-up.
e-gmat SC: Never thought it would be fun learning SC.
India School Fund: Education through Innovation - A HBS start-up.
- gig92
- Senior | Next Rank: 100 Posts
- Posts: 78
- Joined: Fri Jul 23, 2010 2:22 am
- Thanked: 2 times
- Followed by:1 members
hja379 wrote:If x and y are positive integers, what is the value of x ?
(1) x, y, and xy are distinct perfect squares less than 100.
(2) x<5
OA after discussion.
Given x & y > 0
Stmnt 2 : x < 5 -- Insuff
Stmnt 1 : x, y, and xy perfect square less than 100
as such there can be many values of x and y
x y
1 9
4 9
4 16
16 4 Thus Insuff
From Stmnt 1 and 2
x < 5
xy < 100
Now, only possible values of x, y:
x y
1 4
4 4
1 1
so Ans, IMO:
E
gig92
- kmittal82
- Master | Next Rank: 500 Posts
- Posts: 324
- Joined: Mon Jul 05, 2010 6:44 am
- Location: London
- Thanked: 70 times
- Followed by:3 members
(E) in my opinion, here's why:
(1)
Perfect square between 0 and 100 = 1,4,9,16,25,36,49,64,81
If we set either x or y as 1, then the other could be either value and satisfy the "xy" is a perfect square argument
If we set either as 4, then the other number can be 1,9, or16, since no other combination would satisfy the "xy" requirement
So, insufficient
(2) x < 5 could mean x = 1,2,3 or 4, not sufficient in itself
Combine (1) and (2)
The possible value for x could be 1 or 4, so still not sufficient.
(1)
Perfect square between 0 and 100 = 1,4,9,16,25,36,49,64,81
If we set either x or y as 1, then the other could be either value and satisfy the "xy" is a perfect square argument
If we set either as 4, then the other number can be 1,9, or16, since no other combination would satisfy the "xy" requirement
So, insufficient
(2) x < 5 could mean x = 1,2,3 or 4, not sufficient in itself
Combine (1) and (2)
The possible value for x could be 1 or 4, so still not sufficient.
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
hja379 wrote:If x and y are positive integers, what is the value of x ?
(1) x, y, and xy are distinct perfect squares less than 100.
(2) x<5
OA after discussion.
Statement 1: x, y and xy are distinct perfect squares less than 100.
x=1 is not possible because then xy = y, which does not satisfy the condition that y and xy be different values.
y=1 is not possible because then xy = x, which does not satisfy the condition that x and xy be different values.
The following combinations work:
x=4, y=9, xy = 4*9 = 36.
x=9, y=4, xy = 9*4 = 36.
Since x=4 and x=9 each satisfy statement 1, insufficient.
Statement 2: x<5.
x could be any integer between 0 and 5.
Insufficient.
Statements 1 and 2 together:
Since x=1 does not satisfy statement 1, and x=4 is the only other perfect square less than 5, we know that x=4.
Sufficient.
The correct answer is C.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
- kmittal82
- Master | Next Rank: 500 Posts
- Posts: 324
- Joined: Mon Jul 05, 2010 6:44 am
- Location: London
- Thanked: 70 times
- Followed by:3 members
>x=1 is not possible because then xy = y, which does not satisfy the condition that y and xy be different values.GMATGuruNY wrote:hja379 wrote:If x and y are positive integers, what is the value of x ?
(1) x, y, and xy are distinct perfect squares less than 100.
(2) x<5
OA after discussion.
Statement 1: x, y and xy are distinct perfect squares less than 100.
x=1 is not possible because then xy = y, which does not satisfy the condition that y and xy be different values.
y=1 is not possible because then xy = x, which does not satisfy the condition that x and xy be different values.
The following combinations work:
x=4, y=9, xy = 4*9 = 36.
x=9, y=4, xy = 9*4 = 36.
Since x=4 and x=9 each satisfy statement 1, insufficient.
Statement 2: x<5.
x could be any integer between 0 and 5.
Insufficient.
Statements 1 and 2 together:
Since x=1 does not satisfy statement 1, and x=4 is the only other perfect square less than 5, we know that x=4.
Sufficient.
The correct answer is C.
y=1 is not possible because then xy = x, which does not satisfy the condition that x and xy be different values.
D'oh!! completely missed that point... good question
- hja379
- Master | Next Rank: 500 Posts
- Posts: 208
- Joined: Thu Aug 26, 2010 3:10 pm
- Thanked: 20 times
- Followed by:2 members
Tricky one. I updated the OA.
@Mitch- Thanks for the response.
@Mitch- Thanks for the response.
Google "GMAT Pill"<--really helpful, worth checking out--especially for RC passages.
e-gmat SC: Never thought it would be fun learning SC.
India School Fund: Education through Innovation - A HBS start-up.
e-gmat SC: Never thought it would be fun learning SC.
India School Fund: Education through Innovation - A HBS start-up.
- gig92
- Senior | Next Rank: 100 Posts
- Posts: 78
- Joined: Fri Jul 23, 2010 2:22 am
- Thanked: 2 times
- Followed by:1 members
GMATGuruNY wrote:hja379 wrote:If x and y are positive integers, what is the value of x ?
(1) x, y, and xy are distinct perfect squares less than 100.
(2) x<5
OA after discussion.
Statement 1: x, y and xy are distinct perfect squares less than 100.
x=1 is not possible because then xy = y, which does not satisfy the condition that y and xy be different values.
y=1 is not possible because then xy = x, which does not satisfy the condition that x and xy be different values.
The following combinations work:
x=4, y=9, xy = 4*9 = 36.
x=9, y=4, xy = 9*4 = 36.
Since x=4 and x=9 each satisfy statement 1, insufficient.
Statement 2: x<5.
x could be any integer between 0 and 5.
Insufficient.
Statements 1 and 2 together:
Since x=1 does not satisfy statement 1, and x=4 is the only other perfect square less than 5, we know that x=4.
Sufficient.
The correct answer is C.
@Mitch
It seems that 1 is a perfect square:
https://www.tutorvista.com/math/is-1-a-perfect-square
https://www.math.com/school/subject1/les ... 1L9DP.html
https://www.mathsisfun.com/square-root.html
What did I miss..?
gig92
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
The smallest perfect square is 1.gig92 wrote:GMATGuruNY wrote:hja379 wrote:If x and y are positive integers, what is the value of x ?
(1) x, y, and xy are distinct perfect squares less than 100.
(2) x<5
OA after discussion.
Statement 1: x, y and xy are distinct perfect squares less than 100.
x=1 is not possible because then xy = y, which does not satisfy the condition that y and xy be different values.
y=1 is not possible because then xy = x, which does not satisfy the condition that x and xy be different values.
The following combinations work:
x=4, y=9, xy = 4*9 = 36.
x=9, y=4, xy = 9*4 = 36.
Since x=4 and x=9 each satisfy statement 1, insufficient.
Statement 2: x<5.
x could be any integer between 0 and 5.
Insufficient.
Statements 1 and 2 together:
Since x=1 does not satisfy statement 1, and x=4 is the only other perfect square less than 5, we know that x=4.
Sufficient.
The correct answer is C.
@Mitch
It seems that 1 is a perfect square:
https://www.tutorvista.com/math/is-1-a-perfect-square
https://www.math.com/school/subject1/les ... 1L9DP.html
https://www.mathsisfun.com/square-root.html
What did I miss..?
But statement 1 states that x, y and xy are distinct (meaning different) perfect squares. In order for xy to be distinct from x and y, neither x=1 nor y=1 can be used. To illustrate:
If x=1 and y=4, then xy = 1*4 = 4.
Since y and xy are the same value, the combination above does not satisfy the condition that x, y and xy be distinct perfect squares.
If y=1 and x=4, then xy = 4*1 = 4.
Since x and xy are the same value, the combination above does not satisfy the condition that x, y and xy be distinct perfect squares.
Hope the explanation above clarifies why x=1 cannot be used in statement 1.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
- gig92
- Senior | Next Rank: 100 Posts
- Posts: 78
- Joined: Fri Jul 23, 2010 2:22 am
- Thanked: 2 times
- Followed by:1 members
Thanks for your time and yes it's GREAT ... I missed that "distinct"...GMATGuruNY wrote:The smallest perfect square is 1.gig92 wrote:GMATGuruNY wrote:hja379 wrote:If x and y are positive integers, what is the value of x ?
(1) x, y, and xy are distinct perfect squares less than 100.
(2) x<5
OA after discussion.
Statement 1: x, y and xy are distinct perfect squares less than 100.
x=1 is not possible because then xy = y, which does not satisfy the condition that y and xy be different values.
y=1 is not possible because then xy = x, which does not satisfy the condition that x and xy be different values.
The following combinations work:
x=4, y=9, xy = 4*9 = 36.
x=9, y=4, xy = 9*4 = 36.
Since x=4 and x=9 each satisfy statement 1, insufficient.
Statement 2: x<5.
x could be any integer between 0 and 5.
Insufficient.
Statements 1 and 2 together:
Since x=1 does not satisfy statement 1, and x=4 is the only other perfect square less than 5, we know that x=4.
Sufficient.
The correct answer is C.
@Mitch
It seems that 1 is a perfect square:
https://www.tutorvista.com/math/is-1-a-perfect-square
https://www.math.com/school/subject1/les ... 1L9DP.html
https://www.mathsisfun.com/square-root.html
What did I miss..?
But statement 1 states that x, y and xy are distinct (meaning different) perfect squares. In order for xy to be distinct from x and y, neither x=1 nor y=1 can be used. To illustrate:
If x=1 and y=4, then xy = 1*4 = 4.
Since y and xy are the same value, the combination above does not satisfy the condition that x, y and xy be distinct perfect squares.
If y=1 and x=4, then xy = 4*1 = 4.
Since x and xy are the same value, the combination above does not satisfy the condition that x, y and xy be distinct perfect squares.
Hope the explanation above clarifies why x=1 cannot be used in statement 1.
gig92