If x and y are both integers, which is larger, x^x or y^y?
1.x = y + 1
2.x^y > x and x is positive.
oa:c
Algebra ds
This topic has expert replies
GMAT/MBA Expert
- Anju@Gurome
- GMAT Instructor
- Posts: 511
- Joined: Wed Aug 11, 2010 9:47 am
- Location: Delhi, India
- Thanked: 344 times
- Followed by:86 members
Statement 1: Consider the the following two examples,srcc25anu wrote:If x and y are both integers, which is larger, x^x or y^y?
1.x = y + 1
2.x^y > x and x is positive.
- x = 2 and y = 1, x^x > y^y
x = -1 and y = -2, x^x < y^y
Statement 2: As x is a positive integer, x^y will be greater than x^x only if x > 1 and y > 1.
Consider the the following two examples,
- x = 2 and y = 3, x^x < y^y
x = 3 and y = 2, x^x > y^y
1 & 2 Together: Now, we know that both x and y are greater than 1 and x = y + 1
Hence, x^x = (y + 1)^(y + 1) > y^y
Sufficient
The correct answer is C.
Anju Agarwal
Quant Expert, Gurome
Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.
§ GMAT with Gurome § Admissions with Gurome § Career Advising with Gurome §
Quant Expert, Gurome
Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.
§ GMAT with Gurome § Admissions with Gurome § Career Advising with Gurome §
- hutch27
- Master | Next Rank: 500 Posts
- Posts: 141
- Joined: Fri Sep 07, 2012 10:25 pm
- Location: NY
- Thanked: 5 times
- Followed by:1 members
I had trouble with this one because I'm not that cultivated at recognizing properties of negative exponents. For example, I didn't realize that x^x < y^y when it's x=-1 and y=-2. Are there any good tips for that kind of stuff?