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# For which of the following values of a does (a + 4)(a + 3)(a + 2)(a +

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Math Expert
Joined: 02 Sep 2009
Posts: 46284
For which of the following values of a does (a + 4)(a + 3)(a + 2)(a + [#permalink]

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19 Dec 2016, 05:29
1
5
00:00

Difficulty:

45% (medium)

Question Stats:

68% (02:00) correct 32% (02:01) wrong based on 131 sessions

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For which of the following values of a does (a + 4)(a + 3)(a + 2)(a + 1) = (a + 1)! ?

A. 9
B. 8
C. 7
D. 6
E. 5

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Joined: 13 Oct 2016
Posts: 367
GPA: 3.98
Re: For which of the following values of a does (a + 4)(a + 3)(a + 2)(a + [#permalink]

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19 Dec 2016, 06:32
3
Bunuel wrote:
For which of the following values of a does (a + 4)(a + 3)(a + 2)(a + 1) = (a + 1)! ?

A. 9
B. 8
C. 7
D. 6
E. 5

Or (a + 4)(a + 3)(a + 2) = a!

A) 9 + 4 will give us 13 but 9! does not have 13 as a factor. Impossible
B) 8 + 3 will give us 11 but 8! does not have 11 as a factor. Impossible.
C) Same logic 7 + 4 = 11 and 7! does not have 11 as it’s prime factor.
D) 10*9*8 = 720 = 6!
E) 5+2 will give us 7 and 5! Does not have 7 as its prime factor

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Re: For which of the following values of a does (a + 4)(a + 3)(a + 2)(a + [#permalink]

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19 Dec 2016, 09:29
1
vitaliyGMAT wrote:
(a + 4)(a + 3)(a + 2) = a!

Perfect solution...

At this point one can start testing the option...

When $$a = 6$$

$$(a + 4)(a + 3)(a + 2) = a!$$

Or, $$10*9*8 = 6!$$

Hence, correct answer must be (D) 6
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Senior Manager
Joined: 05 Dec 2016
Posts: 260
Concentration: Strategy, Finance
GMAT 1: 620 Q46 V29
Re: For which of the following values of a does (a + 4)(a + 3)(a + 2)(a + [#permalink]

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20 Dec 2016, 01:29
First, using the factorials rule we should express (a+1)!=(a+1)a!
Second, (a+4)(a+3)(a+2)(a+1)=(a+1)a! divide both sides by (a+1)
(a+4)(a+3)(a+2)=a!
(a+4)(a+3)(a+2)/a!=1
After substitution of all offered options it is clear that only 6 is possible, thus correct answer is D.
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Joined: 22 May 2015
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Re: For which of the following values of a does (a + 4)(a + 3)(a + 2)(a + [#permalink]

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18 Aug 2017, 09:15
Used substitution! Started from Option E. Found a = 6.
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Re: For which of the following values of a does (a + 4)(a + 3)(a + 2)(a +   [#permalink] 18 Aug 2017, 09:15
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