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Challenge - divisibility and exponents (m05q33)

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Challenge - divisibility and exponents (m05q33) [#permalink] New post 08 Nov 2007, 21:33
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Question Stats:

69% (01:55) correct 31% (01:19) wrong based on 245 sessions
If t is a prime number, is 32t^3 - 16t^2 + 8t - 4 divisible by t^2?

(1) t^2 <25
(2) t^2-8t+12=0

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[Reveal] Spoiler: OA

Last edited by Bunuel on 23 Oct 2013, 05:21, edited 1 time in total.
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Re: Challenge - divisibility and exponents (m05q33) [#permalink] New post 25 Oct 2012, 04:23
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bmwhype2 wrote:
Is 4t^3 - 2t^2 - 8t + 16 divisible by t^2 ?

1. t \gt 1
2. t is an even prime number

[Reveal] Spoiler: OA
B

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How can i solve this quickly and intuitively? I can certainly bang out the roots but i want to know the shortcut


BELOW IS REVISED VERSION OF THIS QUESTION:

If t is a prime number, is 32t^3 - 16t^2 + 8t - 4 divisible by t^2?

Since first two terms of 32t^3 - 16t^2 + 8t - 4 are divisible by t^2 then the question becomes whether 8t-4 is divisible by t^2.

(1) t^2 <25 --> since t is a prime number then t=2 or t=3. If t=2 then 8t-4 is divisible by t^2=4 but if t=3 then 8t-4 is NOT divisible by t^2=9. Not sufficient.

(2) t^2-8t+12=0 --> t=2 (t=6 is not a valid solution since 6 is not a prime number). Sufficient.

Answer: B.

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Re: Challenge - divisibility and exponents (m05q33) [#permalink] New post 24 Oct 2013, 01:03
With Stement one, you can either have t = 2 or 3

With stement two, after doing the easy maths, you have t = 2.

Answer B, statement two alone is sufficient!

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Re: Challenge - divisibility and exponents (m05q33)   [#permalink] 24 Oct 2013, 01:03
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Challenge - divisibility and exponents (m05q33)

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