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Number property Integer question

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by transfer9858 » Sun Mar 04, 2012 2:23 pm
If k is an integer, and (35^2-1)/k is an integer, then k could be each of the following, EXCEPT

A) 8
B) 9
C) 12
D) 16
E) 17

If you work out the question its 1224 and the prime factors can be broken down to 2^6 and 3^3. This is from "advanced math gmat questions". It says the answer is D and after the using the calculator it is D, but 16 can be broken down into 2^4 which is clearly divisibly into 2^6 so im really confused. Any help would be awesome thanks.
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by krusta80 » Sun Mar 04, 2012 2:28 pm
transfer9858 wrote:If k is an integer, and (35^2-1)/k is an integer, then k could be each of the following, EXCEPT

A) 8
B) 9
C) 12
D) 16
E) 17

If you work out the question its 1224 and the prime factors can be broken down to 2^6 and 3^3. This is from "advanced math gmat questions". It says the answer is D and after the using the calculator it is D, but 16 can be broken down into 2^4 which is clearly divisibly into 2^6 so im really confused. Any help would be awesome thanks.
1224 = 8*153 = 8*9*17 = 2^3 * 3^2 * 17^1

Not sure where you got 2^6 from as part of the breakdown?
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by transfer9858 » Sun Mar 04, 2012 2:33 pm
O man sorry about that, dumb mistake, thanks though.
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by krusta80 » Sun Mar 04, 2012 2:39 pm
transfer9858 wrote:O man sorry about that, dumb mistake, thanks though.
No problem. :)

Remember, as Spock said best, "If you eliminate the impossible, whatever remains, however improbable, must be the truth." In other words, if something doesn't make sense, then you likely missed something dumb or simple.

And yes, I just quoted Spock. lol
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by Brent@GMATPrepNow » Sun Mar 04, 2012 2:40 pm
transfer9858 wrote:If k is an integer, and (35^2-1)/k is an integer, then k could be each of the following, EXCEPT

A) 8
B) 9
C) 12
D) 16
E) 17

If you work out the question its 1224 and the prime factors can be broken down to 2^6 and 3^3. This is from "advanced math gmat questions". It says the answer is D and after the using the calculator it is D, but 16 can be broken down into 2^4 which is clearly divisibly into 2^6 so im really confused. Any help would be awesome thanks.
I'd like to point out a short cut that will help prevent the slight calculation error you made here.

Our goal is to find the prime factorization of 35^2 - 1.
One way to do this is to first evaluate 35^2 - 1 to get 1224 and then rewrite this big number as the product of primes. Takes a bit of time.

The faster way to do this is to recognize that 35^2 - 1 is a difference of squares (like x^2 - y^2).
As such, we can factor it to get: 35^2 - 1 = (35+1)(35-1) = (36)(34)
From here, we can factor 36 and 34 to get: (2)(2)(3)(3)(2)(17)
= (2^3)(3^2)(17)

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by transfer9858 » Sun Mar 04, 2012 3:26 pm
Awesome tips guys, thanks! A month ago (when I started prep) if I saw my own question, talking about primes and what not I would have thought it was chinese. Awesome to see my own improvement. Thanks again!
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by krusta80 » Sun Mar 04, 2012 3:29 pm
transfer9858 wrote:Awesome tips guys, thanks! A month ago (when I started prep) if I saw my own question, talking about primes and what not I would have thought it was chinese. Awesome to see my own improvement. Thanks again!
Keep it up! :)
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