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

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Math Expert
Joined: 02 Sep 2009
Posts: 55273
The expression 1014 - 120 is divisible by all of the following integer  [#permalink]

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25 Jul 2018, 01:44
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5% (low)

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85% (01:01) correct 15% (00:59) wrong based on 143 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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The expression 1014 - 120 is divisible by all of the following integer  [#permalink]

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Updated on: 25 Jul 2018, 02:04
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, 01:53.
Last edited by workout on 25 Jul 2018, 02:04, 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, 02:02
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.

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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, 05:36
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, 16:28
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.

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# Jeffrey Miller

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

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28 Aug 2018, 21:17
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: 258
Re: The expression 1014 - 120 is divisible by all of the following integer  [#permalink]

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28 Aug 2018, 22:56
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

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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, 19:06
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.

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# Jeffrey Miller

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

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11 Apr 2019, 14:45
if someone is not mathematically inclined or does not understand number theory then he can just simply do the following:
pick a random value for 10^x. For example, 1000. Then 1000-120=880. Therefore not divisible by 3. Same will happen for any value of 10^x>100
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The expression 1014 - 120 is divisible by all of the following integer  [#permalink]

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30 Apr 2019, 14:28
Bunuel wrote:
The expression 10^14 - 120 is divisible by all of the following integers EXCEPT

Hopefully I can help someone understand this question better. Testing values is the wrong way to approach this problem. Not learning the fundamentals for an easy question will hurt you.

For this questions, let's simply test divisibility rules - that's all it's asking. But instead, let's not actually solve anything here. Let's just try to take it at face value and test divisibility of the terms of the equation, not necessarily the difference of the equation.

Let's leave the terms separated as they are.

10^14 - 120

(A) 2
Is 10^14 divisible by 2? Yes, it's even
Is 120 divisible by 2? Yes, it's even

(B) 3
Is 10^14 divisible by 3? Hard to tell, let's not waste time here and move on
Is 120 divisible by 3? Yes (3 * 40)

(C) 4
Is 10^14 divisible by 4? Yes, 4 evenly goes into 100. (25 * 4)
Is 120 divisible by 4? Yes (4 * 30)

(D) 8
Is 10^14 divisible by 8? Yes, because it's divisible by both 2 and 4.
Is 120 divisible by 8? Yes (8 * 15)

(E) 10
Is 10^14 divisible by 10? Of course
Is 120 divisible by 10? Yes

We see that easily, 3 must be the answer
The expression 1014 - 120 is divisible by all of the following integer   [#permalink] 30 Apr 2019, 14:28
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