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Re: If n is a positive integer and (n + 1)(n + 3) [#permalink]
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If n is a positive integer and (n + 1)(n + 3) is odd , that means n must be even= 2,4,6,8 .........etc.

When n=2 then (n + 1)(n + 3) = 15 and (n + 2)(n + 4) = 24 that value are divisible by : 3 , 6 & 8

When n=4 then (n + 1)(n + 3) = 35 and (n + 2)(n + 4) = 48 that value are divisible by : 3 , 6 & 8

When n=6 then (n + 1)(n + 3) = 63 and (n + 2)(n + 4) = 80 that value are divisible by : 8 & 16

When n=8 then (n + 1)(n + 3) = 99 and (n + 2)(n + 4) = 120 that value are divisible by only 6 & 8

Question mentioned " must be a multiple" not could be, so can see in above calculation 8 is a must be multiple of (n + 2)(n + 4)

So, Answer must be only " 8 "
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Re: If n is a positive integer and (n + 1)(n + 3) [#permalink]
Hi Carcass,
Can you please explain the question, also suggest which is the correct option.
Thanks!
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Re: If n is a positive integer and (n + 1)(n + 3) [#permalink]
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The explanations above are correct but the OA was wrong. It is D
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Re: If n is a positive integer and (n + 1)(n + 3) [#permalink]
Why are A and C also not correct?
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If n is a positive integer and (n + 1)(n + 3) [#permalink]
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The explanations above are perfect

specifically the one above https://gre.myprepclub.com/forum/if-n-i ... tml#p81202

As you can see sometimes the number is divisible by 3,6, and 8

Sometimes 6 and 8

Sometimes 8 and 16

It depends

The only thing we do know for SUR is that n is even and that is ALWAYS divisible by 8

I suggest you to look at out theory about divisibility and number theory https://gre.myprepclub.com/forum/gre-ma ... 29264.html
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