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06 Mar 2009, 10:21
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Guys, just for fun.. this question used to be a popular hazing question in my college. I have adapted it to PS format.
===
if x and y are integers such that x not equal to y, atleast how many solutions exist for following equation:
x^y + y^x = n such that n is an integer variable belonging to [1000, 1099]
A) 100
B) 200
C) 250
D) 350
E) 450
Hope there are members from my college who would recognize this one
===
if x and y are integers such that x not equal to y, atleast how many solutions exist for following equation:
x^y + y^x = n such that n is an integer variable belonging to [1000, 1099]
A) 100
B) 200
C) 250
D) 350
E) 450
Hope there are members from my college who would recognize this one
Archived Topic
Hi there,
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06 Mar 2009, 14:05
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xyz21
Since x and y are integers and x is not equal to y, the only values for x and y that satisfy the given equation is: either x = 1 and y = 1000 or x = 1000 and y = 1.
If one value (x/y) is 2, the other value (y/x) ranges from 9.82 to 9.97.
Similarly, if one value is 2, the other value ranges arround 6.10.
Are the answer choices correct?
06 Mar 2009, 22:41
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xyz21
Of course, with those answer choices, A must be correct (if this is a GMAT question). Even if you find there are 940 solutions, then certainly there are 'at least 100'.
But as GMATTiger pointed out above, we have the solution x = 1, y = 1000. We actually have solutions x = 1, and y = 999, 1000, 1001, 1002, ... 1098, giving us a hundred solutions. The equation is symmetric in x and y, so if you consider the solutions y = 1, x = 999, 1000, 1001... 1098 to be different from the first set of solutions, we then get up to 200. If my mental arithmetic was right, there aren't any other solutions, though I checked that very quickly.
