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

Question

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

(A) 2

(B) 3

(C) 4

(D) 8

(E) 10

Nikhil · Answer

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

KSBGC · Answer

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.

respite-less · Answer

first find last three digits of the big number =1000-120=880 (A) 2 (B) 3 (C) 4 (D) 8 (E) 10 so B is the right answer

JeffTargetTestPrep · Answer

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

Answer: B

awchoi1213 · Answer

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?

sumit411 · Answer

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

JeffTargetTestPrep · Answer

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

SpyrosGkikopoulos · Answer

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

edlc313 · Answer

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

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

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Perfect 805 Score Debrief by Julia

My Rewards