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# The product 7 x 6 x 5 x 4 x 3 is divisible by all of the fol

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Joined: 06 Sep 2013
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Concentration: Finance
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The product 7 x 6 x 5 x 4 x 3 is divisible by all of the fol [#permalink]  20 Sep 2013, 16:15
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Difficulty:

35% (medium)

Question Stats:

64% (02:05) correct 36% (01:17) wrong based on 99 sessions
The product 7 x 6 x 5 x 4 x 3 is divisible by all of the following EXCEPT:

(A) 120
(B) 240
(C) 360
(D) 840
(E) 1,260
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 27123
Followers: 4189

Kudos [?]: 40508 [0], given: 5540

Re: The product 7 x 6 x 5 x 4 x 3 is divisible by all of the fol [#permalink]  20 Sep 2013, 16:22
Expert's post
jlgdr wrote:
The product 7 x 6 x 5 x 4 x 3 is divisible by all of the following EXCEPT:

(A) 120
(B) 240
(C) 360
(D) 840
(E) 1,260

$$3*4*5*6*7=2^3*3^2*5*7$$.

(B) $$240=2^4*3*5$$ --> 2 has higher power here than in $$2^3*3^2*5*7$$.

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Re: The product 7 x 6 x 5 x 4 x 3 is divisible by all of the fol [#permalink]  08 Jan 2014, 03:43
Hi there!

I didn't get the answer right, because neither 120, nor 240 include the factor 7. Why do we just focus on the exponential term of 2 and not on the 7?
Thank you very much for your response.
Intern
Joined: 17 Oct 2013
Posts: 40
Schools: HEC '14
GMAT Date: 02-04-2014
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Kudos [?]: 11 [0], given: 21

Re: The product 7 x 6 x 5 x 4 x 3 is divisible by all of the fol [#permalink]  08 Jan 2014, 04:42
jlgdr wrote:
The product 7 x 6 x 5 x 4 x 3 is divisible by all of the following EXCEPT:

(A) 120
(B) 240
(C) 360
(D) 840
(E) 1,260

5*4*3= 120
240=5*4*3*2
hence 7*6*5*4*3 is not divisible by 240
Math Expert
Joined: 02 Sep 2009
Posts: 27123
Followers: 4189

Kudos [?]: 40508 [0], given: 5540

Re: The product 7 x 6 x 5 x 4 x 3 is divisible by all of the fol [#permalink]  08 Jan 2014, 04:51
Expert's post
Emanuel2410 wrote:
Hi there!

I didn't get the answer right, because neither 120, nor 240 include the factor 7. Why do we just focus on the exponential term of 2 and not on the 7?
Thank you very much for your response.

The question is: $$3*4*5*6*7=2^3*3^2*5*7$$ is divisible by all of the following EXCEPT... So, $$2^3*3^2*5*7$$ is dividend and the options are divisors, not vise-versa.

$$2^3*3^2*5*7$$ is NOT divisible only by $$240=2^4*3*5$$, because the power of 2 in the divisor is higher than the power of 2 in dividend.

Hope it's clear.
_________________
Re: The product 7 x 6 x 5 x 4 x 3 is divisible by all of the fol   [#permalink] 08 Jan 2014, 04:51
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