Would appreciate an approach to handle this problem:
Thanks in advance
Lucas
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Brent@GMATPrepNow
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Here's a nice discussion about this question: https://www.beatthegmat.com/veritas-quan ... 79772.html
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Brent
Cheers,
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MartyMurray
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If a and b are integers, then (ab)� = (all of the prime factors of a and b)�.lucas211 wrote:If a and b are integers and (ab)� = 96y, y could be
(a) 5
(b) 9
(c) 27
(d) 81
(e) 125
So the prime factors in 96y have to all be raised to the fifth power.
96 = 3 x 32 = 3 x 2�.
2 is raised to the fifth power, but 3 is not. So y must include in its prime factors at least 3�.
3� = 81. Seeing that, you can immediately choose answer choice D.
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Hi lucas211,
This question is essentially about prime-factorization - the idea that any positive integer greater than 1 is either prime or the product of a bunch of primes.
Here, we're told that (AB)^5 = 96Y, and that A and B are integers, which means...
(AB)(AB)(AB)(AB)(AB) = 96Y
We can rewrite this as....
(A^5)(B^5) = (2^5)(3)(Y)
We're asked for what Y COULD equal. This means that Y could be MORE than one value...so we should start by looking for the smallest value that Y could equal.
Notice how 2^5 could "account for" either A or B, so we need to make sure that the "Y", when combined with the "3" that's already there, could account for the other variable....
If Y = 3^4, then 96Y would = (2^5)(3^5), which gives us two integers raised to the 5th power.
Y COULD = 3^4 = 81
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
This question is essentially about prime-factorization - the idea that any positive integer greater than 1 is either prime or the product of a bunch of primes.
Here, we're told that (AB)^5 = 96Y, and that A and B are integers, which means...
(AB)(AB)(AB)(AB)(AB) = 96Y
We can rewrite this as....
(A^5)(B^5) = (2^5)(3)(Y)
We're asked for what Y COULD equal. This means that Y could be MORE than one value...so we should start by looking for the smallest value that Y could equal.
Notice how 2^5 could "account for" either A or B, so we need to make sure that the "Y", when combined with the "3" that's already there, could account for the other variable....
If Y = 3^4, then 96Y would = (2^5)(3^5), which gives us two integers raised to the 5th power.
Y COULD = 3^4 = 81
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
