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# The expression 1014 - 120 is divisible by all of the following integer

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Joined: 02 Sep 2009
Posts: 51185
The expression 1014 - 120 is divisible by all of the following integer  [#permalink]

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25 Jul 2018, 00:44
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5% (low)

Question Stats:

85% (00:51) correct 15% (00:46) wrong based on 132 sessions

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The expression 10^14 - 120 is divisible by all of the following integers EXCEPT

(A) 2

(B) 3

(C) 4

(D) 8

(E) 10

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Posts: 1452
Concentration: Nonprofit
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The expression 1014 - 120 is divisible by all of the following integer  [#permalink]

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Updated on: 25 Jul 2018, 01:04
3
If X is a multiple of Z and Y is a multiple of Z then X-Y is a multiple of Z

$$10^{14}$$ is a multiple 2,4,8 and 10

=> $$10^{14}$$ is a multiple of all option choices except option B

120 is a multiple of all option choices 2,3,4,8 and 10

=> 120 is a multiple of all option choices

So $$10^{14} - 120$$ is multiple of 2,4,8 and 10 except 3

Hence option B
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Originally posted by workout on 25 Jul 2018, 00:53.
Last edited by workout on 25 Jul 2018, 01:04, edited 1 time in total.
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The expression 1014 - 120 is divisible by all of the following integer  [#permalink]

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25 Jul 2018, 01:02
1
Bunuel wrote:
The expression 10^14 - 120 is divisible by all of the following integers EXCEPT

(A) 2

(B) 3

(C) 4

(D) 8

(E) 10

$$10^{14}$$ must end with 14 zeros. Now we can reduce the power and deduct 120 from the result.

$$10^3 =1000$$

1000 - 120 = 880

880 is divisible by all except 3.

$$10^4 = 10000$$

10000 -120 = 9880

9880 is divisible by all except 3.

This is true for $$10^{14}$$ also.

The best answer is B.
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Joined: 30 Mar 2017
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The expression 1014 - 120 is divisible by all of the following integer  [#permalink]

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25 Jul 2018, 04:36
first find last three digits of the big number =1000-120=880

(A) 2 [divisible by 2 because the number has 0 in unit digit
(B) 3[not divisible by 3]
(C) 4 [divisible by 4 because last two digit of the number 80 is divisible by 4]
(D) 8 [divisible by 8 because last three digit of the number 880 is divisible by 8]
(E) 10 [divisible because last digit has 0]

so B is the right answer
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Re: The expression 1014 - 120 is divisible by all of the following integer  [#permalink]

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26 Jul 2018, 15:28
Bunuel wrote:
The expression 10^14 - 120 is divisible by all of the following integers EXCEPT

(A) 2

(B) 3

(C) 4

(D) 8

(E) 10

Since 120 is divisible by 3 but 10^14 is not, their difference is not divisible by 3.

Answer: B
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Joined: 16 Jul 2018
Posts: 1
Re: The expression 1014 - 120 is divisible by all of the following integer  [#permalink]

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28 Aug 2018, 20:17
I found prime factors of 10 and 120 here

then prime factors were 10 = 2,5 and 120 = 2^3, 3, 5

Then I chose B because 3 was not commonly present in both numbers.

Is this a lucky coincident?
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Joined: 07 Oct 2017
Posts: 261
Re: The expression 1014 - 120 is divisible by all of the following integer  [#permalink]

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28 Aug 2018, 21:56
2
awchoi1213 wrote:
I found prime factors of 10 and 120 here

then prime factors were 10 = 2,5 and 120 = 2^3, 3, 5

Then I chose B because 3 was not commonly present in both numbers.

Is this a lucky coincident?
Yes, it was a lucky co-incidence.

3 properties--->

1) if both integers a and b are multiple of some integer k (k>1), their sum and difference will be divisible by k

2) if only one integer out of a and b is multiple of integer k (k>1), their sum and difference will not be a multiple of k

3) if none of integer a and b are multiple of integer k (k>1), their sum and difference may be or may not be divisible by k

Eg: a=5, b=4
K= 3

Hope this helps

Thank you = Kudos
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Re: The expression 1014 - 120 is divisible by all of the following integer  [#permalink]

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03 Sep 2018, 18:06
Bunuel wrote:
The expression 10^14 - 120 is divisible by all of the following integers EXCEPT

(A) 2

(B) 3

(C) 4

(D) 8

(E) 10

We see that 120 is divisible by 3, but 10^14 is not. Thus, the difference 10^14 - 120 is not divisible by 3, either.

Answer: B
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Jeffery Miller
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Re: The expression 1014 - 120 is divisible by all of the following integer &nbs [#permalink] 03 Sep 2018, 18:06
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# The expression 1014 - 120 is divisible by all of the following integer

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