What is the value of X?
1. X^4 = X
2. X^2 > X
OA: C
I was confused about the 2 statements because I thought they contradict each other
Source: another GMAT site
DS
This topic has expert replies

 Master  Next Rank: 500 Posts
 Posts: 218
 Joined: 23 Nov 2011
 Thanked: 26 times
 Followed by:4 members
1. X is {1, 0, 1}ariz wrote:What is the value of X?
1. X^4 = X
2. X^2 > X
INSUFFICIENT
2. X < 0 or X > 1
INSUFFICIENT
1,2.
The intersection of the sets {1, 0, 1} and {... 4, 3, 2, 1, 2, 3, ...} is {1}
SUFFICIENT
Answer C BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
Last edited by chieftang on Tue Jan 10, 2012 10:55 am, edited 1 time in total.
 GMATGuruNY
 GMAT Instructor
 Posts: 15533
 Joined: 25 May 2010
 Location: New York, NY
 Thanked: 13060 times
 Followed by:1901 members
 GMAT Score:790
Statement 1: xâ�´ = x.ariz wrote:What is the value of X?
1. X^4 = X
2. X^2 > X
OA: C
I was confused about the 2 statements because I thought they contradict each other
Source: another GMAT site
Case 1: xâ�´ = x.
xâ�´  x = 0.
x(xÂ³  1) = 0.
x = 0 or x=1.
Case 2: xâ�´ = x.
xâ�´ + x = 0.
x(xÂ³ + 1) = 0.
x = 0 or x= 1.
Since it's possible that x=1, x=0, or x=1, INSUFFICIENT.
Statement 2: xÂ² > x.
xÂ²  x > 0.
x(x1) > 0.
The critical points are x=0 and x=1.
These are the only values where xÂ² = x.
When x is any other value, xÂ² > x or xÂ² < x.
Thus, there are 3 ranges to consider: x<0, 0<x<1, and x>1.
To determine the range of x, test one value to the left and right of each critical point.
When x = 1, xÂ² > x. Thus, x<0 is part of the range.
When x = 1/2, xÂ² < x. Thus, 0<x<1 is not part of the range.
When x = 2, xÂ² > x. Thus, x>1 is part of the range.
Thus, two ranges satisfy statement 2:
x<0 or x>1.
INSUFFICIENT.
Statements 1 and 2 combined:
Of the three values that satisfy statement 1, only x=1 is included in the ranges that satisfy statement 2 (x<0 or x>1).
Thus, x=1.
SUFFICIENT.
The correct answer is C.
Mitch Hunt
Private Tutor for the GMAT and GRE
[email protected]
If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.
Available for tutoring in NYC and longdistance.
For more information, please email me at [email protected].
Student Review #1
Student Review #2
Student Review #3
Private Tutor for the GMAT and GRE
[email protected]
If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.
Available for tutoring in NYC and longdistance.
For more information, please email me at [email protected].
Student Review #1
Student Review #2
Student Review #3

 Master  Next Rank: 500 Posts
 Posts: 218
 Joined: 23 Nov 2011
 Thanked: 26 times
 Followed by:4 members
Oh, ya, I missed X > 1 for statement 2 and luckily still got the correct solution. Haste makes waste! Updated my work. Answer unchanged.GMATGuruNY wrote:Statement 1: xâ�´ = x.ariz wrote:What is the value of X?
1. X^4 = X
2. X^2 > X
OA: C
I was confused about the 2 statements because I thought they contradict each other
Source: another GMAT site
Case 1: xâ�´ = x.
xâ�´  x = 0.
x(xÂ³  1) = 0.
x = 0 or x=1.
Case 2: xâ�´ = x.
xâ�´ + x = 0.
x(xÂ³ + 1) = 0.
x = 0 or x= 1.
Since it's possible that x=1, x=0, or x=1, INSUFFICIENT.
Statement 2: xÂ² > x.
xÂ²  x > 0.
x(x1) > 0.
The critical points are x=0 and x=1.
These are the only values where xÂ² = x.
When x is any other value, xÂ² > x or xÂ² < x.
Thus, there are 3 ranges to consider: x<0, 0<x<1, and x>1.
To determine the range of x, test one value to the left and right of each critical point.
When x = 1, xÂ² > x. Thus, x<0 is part of the range.
When x = 1/2, xÂ² < x. Thus, 0<x<1 is not part of the range.
When x = 2, xÂ² > x. Thus, x>1 is part of the range.
Thus, two ranges satisfy statement 2:
x<0 or x>1.
INSUFFICIENT.
Statements 1 and 2 combined:
Of the three values that satisfy statement 1, only x=1 is included in the ranges that satisfy statement 2 (x<0 or x>1).
Thus, x=1.
SUFFICIENT.
The correct answer is C.