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# Which of the following integers is NOT a divisor of x

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

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13 Sep 2013, 08:45
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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

Press Kudos if you like the question.
[Reveal] Spoiler: OA

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

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13 Sep 2013, 08:52
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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.

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

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06 Oct 2014, 15:51
Thanks Bunuel! More elegant and less time-consuming than my answer!
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Re: Which of the following integers is NOT a divisor of x [#permalink]

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20 Feb 2016, 11:41
Does anyone have some similar practice problems? Thanks a lot!
Math Expert
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Posts: 5658
Re: Which of the following integers is NOT a divisor of x [#permalink]

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20 Feb 2016, 21:00
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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.

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

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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
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BANGALORE/-

Math Expert
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Re: Which of the following integers is NOT a divisor of x [#permalink]

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22 Feb 2016, 00:19
lpetroski wrote:
Does anyone have some similar practice problems? Thanks a lot!

Check our question bank: viewforumtags.php

Hope it helps.
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Re: Which of the following integers is NOT a divisor of x [#permalink]

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22 Feb 2016, 01:48
Bunuel wrote:
lpetroski wrote:
Does anyone have some similar practice problems? Thanks a lot!

Check our question bank: viewforumtags.php

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

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28 May 2017, 18:34
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.

First break the term down into its prime factors

x = 21*3^7 -112 = 3*7*3^7 -112 = 3^8*7 -112

x = 3^8*7-7*16

x = 7(3^8 - 16)

Now it's important to realize that 3^8 - 16 is a perfect square, albeit a hidden one. You can eliminate answer choice A.

x = 7(3^4-4)(3^4+4). Once again, notice that 3^4-4 is a perfect square.

x = 7(3^2+2)(3^2-2)(3^4+4).

At this stage, you can start to convert into the non-prime values

x = 7(11)(7)(85)

85 = 17*5, so only 15 is not a divisor of x.
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Joined: 25 Sep 2017
Posts: 16
Which of the following integers is NOT a divisor of x [#permalink]

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24 Nov 2017, 02:14
3
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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.

Hi Bunuel

Another way would be

if we consider it as A-B

3 divides A but not B

so any multiples of 3 cannot divide A-B

am I correct in my approach?
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GA800

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Posts: 43831
Re: Which of the following integers is NOT a divisor of x [#permalink]

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24 Nov 2017, 02:17
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Expert's post
GmatAvengers800 wrote:
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.

Hi Bunuel

Another way would be

if we consider it as A-B

3 divides A but not B

so any multiples of 3 cannot divide A-B

am I correct in my approach?

_______________
Yes, that's correct.
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Re: Which of the following integers is NOT a divisor of x   [#permalink] 24 Nov 2017, 02:17
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