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If 10^x is multiple of 40, what is the least possible value of x?

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Intern
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Joined: 21 Apr 2015
Posts: 5
If 10^x is multiple of 40, what is the least possible value of x?  [#permalink]

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New post 19 Oct 2017, 08:55
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C
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If 10^x is multiple of 40, what is the least possible value of x?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Retired Moderator
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Joined: 28 May 2014
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GMAT 1: 730 Q49 V41
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Re: If 10^x is multiple of 40, what is the least possible value of x?  [#permalink]

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New post 19 Oct 2017, 09:06
Using trial and error method, we can get 10^3 = 1000 is divisible by 40.

Hence, answer is C
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Re: If 10^x is multiple of 40, what is the least possible value of x?  [#permalink]

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New post 19 Oct 2017, 09:08
Top Contributor
vinhthi wrote:
If 10^x is multiple of 40, what is the least possible value of x?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5


There's a "mathematical" solution to this question, but on the GMAT, our sole goal is to answer questions as quickly as possible.
Scanning the answer choices, I can see that the values are small. So, the fastest approach is most likely testing the answer choices...

(A) x = 1
Is 10^1 a multiple of 40?
10^1 = 10, and 10 is NOT a multiple of 40
ELIMINATE A

(B) x = 2
Is 10^2 a multiple of 40?
10^2 = 100, and 100 is NOT a multiple of 40
ELIMINATE B

(C) x = 3
10^3 = 1000, and 1000 IS a multiple of 40, since (40)(25) = 1000
DONE!

Answer:

Cheers,
Brent
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Concentration: Finance
GMAT 1: 610 Q36 V36
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WE: Consulting (Mutual Funds and Brokerage)
Re: If 10^x is multiple of 40, what is the least possible value of x?  [#permalink]

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New post 19 Oct 2017, 11:25
1
I feel like the easiest and quickest method would be prime factorization. If we break down 40, we 10*4 which breaks down to 5*2*2*2 or 5*2^3, so we need at least one "5" in common and three "2"s. 10 is 5*2 which covers the "5" and one of the "2"s. In order to get three "2"s, we need an exponent of at least 3. Answer Choice C.

Some people may find the plug method above quicker, but here is another way of doing it.
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Re: If 10^x is multiple of 40, what is the least possible value of x? &nbs [#permalink] 19 Oct 2017, 11:25
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