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For how many positive integer values of p other than ‘1’, is

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For how many positive integer values of p other than ‘1’, is [#permalink] New post   28 Oct 2020, 01:16
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For how many positive integer values of p other than ‘1’, is (p + 4) (p + 6) divisible by p?

(A) Four

(B) Seven

(C) Eight

(D) Twelve

(E) Twenty four
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Re: For how many positive integer values of p other than ‘1’, is [#permalink] New post   13 Nov 2020, 23:53
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(p+4)*(p+6)=p^2+10*p+24

Now p^2 is divisible by p

10 p is divisible by p
so for the expression to be divisible by p 24 should be divisible by p
So the answer equals the factors of 24 minus 1 because one is excluded
The factors of 24 is 8 minus 1 equals 7
The answer is 7
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Re: For how many positive integer values of p other than ‘1’, is [#permalink]
13 Nov 2020, 23:53
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