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B
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Difficulty:
75%
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Question Stats:
42% (01:36) correct
58%
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Consider the expression \(\frac{(A!)}{((B!)^x * (C!)^y * (D!)^z))}\) where A,B,C,D,x,y,z are all positive integers >=1. Is this expression an integer ?
(1) B+C+D < A
(2) xB+yC+zD < A
(1) B+C+D < A
(2) xB+yC+zD < A
08 Sep 2010, 01:27
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The answer is B
This is one of those questions me and a friend of mine made up to test each other (both of us have GMATs coming up). So I have a solution with me, but it is rather unconventional :
It is easy to prove that (1) alone cant be the answer since there is no constraint on x,y,z and one can make these big enough to exceed the numerator. Eg 7! / (2!^40 * 3!^20 * 1!^1)
To show that (2) alone is sufficient :
Consider the question "How many permutations are possible of a set of A alphabets, of which x alphabets are each repeated B times, y alphabets each repeated C times and z alphabets each repeated D times within the set ?"
The answer to this question is exactly the expression above, and we know that since it is the answer to a counting question, it must be an integer.
This is one of those questions me and a friend of mine made up to test each other (both of us have GMATs coming up). So I have a solution with me, but it is rather unconventional :
It is easy to prove that (1) alone cant be the answer since there is no constraint on x,y,z and one can make these big enough to exceed the numerator. Eg 7! / (2!^40 * 3!^20 * 1!^1)
To show that (2) alone is sufficient :
Consider the question "How many permutations are possible of a set of A alphabets, of which x alphabets are each repeated B times, y alphabets each repeated C times and z alphabets each repeated D times within the set ?"
The answer to this question is exactly the expression above, and we know that since it is the answer to a counting question, it must be an integer.
23 Oct 2010, 03:55
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It's a tricky one, but if you look at the solution above, it's almost like saying c(n,r) will always be an integer.
Just that in this case we are talking about a different kind of arrangement with a different formula.
Posted from my mobile device
Just that in this case we are talking about a different kind of arrangement with a different formula.
Posted from my mobile device
