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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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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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25% (medium)

Question Stats:

68% (02:05) correct 32% (01:19) wrong based on 125 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
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Joined: 02 Sep 2009
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Kudos [?]: 45493 [0], given: 6762

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.
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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, 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
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Posts: 28352
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Kudos [?]: 45493 [0], given: 6762

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.
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Re: The product 7 x 6 x 5 x 4 x 3 is divisible by all of the fol [#permalink]  04 Jul 2015, 00:04
Eliminate 0 in all options and 5*2 in multiple to get

7*3*2*2*3

12=3*2*2, Yes
24=2*2*2*3, No
36=2*3*3*2, Yes
84=2*7*3*2, Yes
126=2*7*3*3, Yes

B
Re: The product 7 x 6 x 5 x 4 x 3 is divisible by all of the fol   [#permalink] 04 Jul 2015, 00:04
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