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If p is any odd integer greater than 1, which of the following must be

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If p is any odd integer greater than 1, which of the following must be [#permalink]

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New post 15 Oct 2017, 09:58
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If p is any odd integer greater than 1, which of the following must be a multiple of 24?

a] p(p − 1)(p − 2)
b] p(p + 1)
c] p(p^2− 1)
d] p^3 − p^2
e] p(p + 3)(p + 2)
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If p is any odd integer greater than 1, which of the following must be [#permalink]

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New post 15 Oct 2017, 10:13
Harikrushna Kotadiya wrote:
If p is any odd integer greater than 1, which of the following must be a multiple of 24?

a] p(p − 1)(p − 2)
b] p(p + 1)
c] p(p^2− 1)
d] p^3 − p^2
e] p(p + 3)(p + 2)


We can assume a simple number for \(p\). let \(p=3\). Now substitute the value of \(p\) in the options and test whether it is multiple of \(24\).

Option A, B, D & E are not multiples of \(24\)

Option C is \(3(3^2-1)=24 =\) multiple of \(24\)

Option C
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Re: If p is any odd integer greater than 1, which of the following must be [#permalink]

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New post 15 Oct 2017, 19:23
Let p=3
Put this value in the below options and test
a) 3(3-1)(3-2)= 3*2*1= 6. Not multiple of 24.
b) 3(3+1)= 12. Not multiple of 24.
c) 3(\(3^2\)-1)= 3*8= 24. Multiple of 24.
d) \(3^3\)-\(3^2\)= 27-9= 18. Not multiple of 24
e) 3(3+3)(3+2)= 3*6*5= 90. Not a multiple of 24.

Answer: C.

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Re: If p is any odd integer greater than 1, which of the following must be [#permalink]

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New post 16 Oct 2017, 01:38
For any number to be divisible by 24 it must be divisible by 6 and 4 i.e. it should have 6*4 as factors.

You can put 3 in answer choices and check. Only C gives you 6*4.
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Re: If p is any odd integer greater than 1, which of the following must be   [#permalink] 16 Oct 2017, 01:38
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If p is any odd integer greater than 1, which of the following must be

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