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Algebra ds

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Source: — Data Sufficiency |

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by Anju@Gurome » Fri Apr 19, 2013 9:28 pm
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.
Statement 1: Consider the the following two examples,
  • x = 2 and y = 1, x^x > y^y
    x = -1 and y = -2, x^x < y^y
Not sufficient.

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
Not sufficient.

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.
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by hutch27 » Sat Apr 20, 2013 6:44 am
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?
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