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Which of the following integers is NOT a divisor of x if x = (21)(3^7) – (112)?

A 7 B 11 C 15 D 17 E 35

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\(21*3^7-112=3^8*7-2^4*7=7(3^8-2^4)=7(3^4-2^2)(3^4+2^2)=7*77*85=7^2*11*5*17\) --> the product is NOT divisible by 3, thus it's not divisible by 15=3*5 either.

Which of the following integers is NOT a divisor of x if x = (21)(3^7) – (112)?

A 7 B 11 C 15 D 17 E 35

Press Kudos if you like the question.

Hi, here, we donot require to do any calculations at all... the choices itself give away the answer...

merely playing with choices given, this 700 level Q can turn into a SUB-600 level Q.. In (21)(3^7) – (112).. (21)(3^7) is a multiple of both 3 and 7, but 112 is a multiple of 7 and not 3.. so addition or subtraction of these terms will be multiple of 7, but not of 3..

However C is 15, which is a multiple of 3,.. hence not possible

Also, check similar questions block at the end of this page.

Hope it helps.

Hi Brunel - actually I tried both those options before even posting this request with no success! I was hoping for some problems that are exactly like this one, but if you don't have any easily accessible, no problem. Since I can't find them I assume this is not a usual problem that would come up. Thanks anyway.

Which of the following integers is NOT a divisor of x [#permalink]

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24 Nov 2017, 02:14

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Bunuel wrote:

Transcendentalist wrote:

Which of the following integers is NOT a divisor of x if x = (21)(3^7) – (112)?

A 7 B 11 C 15 D 17 E 35

Press Kudos if you like the question.

\(21*3^7-112=3^8*7-2^4*7=7(3^8-2^4)=7(3^4-2^2)(3^4+2^2)=7*77*85=7^2*11*5*17\) --> the product is NOT divisible by 3, thus it's not divisible by 15=3*5 either.

Which of the following integers is NOT a divisor of x if x = (21)(3^7) – (112)?

A 7 B 11 C 15 D 17 E 35

Press Kudos if you like the question.

\(21*3^7-112=3^8*7-2^4*7=7(3^8-2^4)=7(3^4-2^2)(3^4+2^2)=7*77*85=7^2*11*5*17\) --> the product is NOT divisible by 3, thus it's not divisible by 15=3*5 either.