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If (n+2)!/n!=90, then n=?

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If (n+2)!/n!=90, then n=?  [#permalink]

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New post 02 Aug 2018, 02:21
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[Math Revolution GMAT math practice question]

If \(\frac{(n+2)!}{n!}=90\), then \(n=?\)

\(A. 8\)
\(B. 9\)
\(C. 10\)
\(D. 11\)
\(E. 12\)

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If (n+2)!/n!=90, then n=?  [#permalink]

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New post 02 Aug 2018, 02:25
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If \(\frac{(n+2)!}{n!}=90\), then \(n=?\)

\(A. 8\)
\(B. 9\)
\(C. 10\)
\(D. 11\)
\(E. 12\)



Option A: 8

back solve it.

\(\frac{10!}{8!}\)

= \(\frac{8! * 9 * 10}{8!}\)

= 90.

The best answer is A.
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If (n+2)!/n!=90, then n=?  [#permalink]

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New post Updated on: 02 Aug 2018, 02:52
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If \(\frac{(n+2)!}{n!}=90\), then \(n=?\)

\(A. 8\)
\(B. 9\)
\(C. 10\)
\(D. 11\)
\(E. 12\)


\(\frac{(n+2)!}{n!}=90\)
Or, \(\frac{(n!*(n+1)*(n+2))}{n!}\)=\(90\)
Or, (n+1)(n+2)=9*10
Or, n+1=9 and n+2=10
So, n=8.

Ans. (A)
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Originally posted by PKN on 02 Aug 2018, 02:47.
Last edited by PKN on 02 Aug 2018, 02:52, edited 1 time in total.
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Re: If (n+2)!/n!=90, then n=?  [#permalink]

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New post 02 Aug 2018, 02:50
I approached it from what was given:

(n+1)(n+2) = 90

The multiplication of two consecutive integers equals 90.

=> 9 and 10
=> n = 8

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Re: If (n+2)!/n!=90, then n=?  [#permalink]

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New post 02 Aug 2018, 02:54
(n+2)! = 1 x 2 x 3 x ... x n x (n+1) x (n+2)

n! = 1 x 2 x 3 x ... x n

So (n+2)! / n! = (n+1)(n+2) = 90

Let's try the answers. I will start with B: n = 9. Replacing in (n+1)(n+2) the answer is 110. Too high. So the best answer is A.
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Re: If (n+2)!/n!=90, then n=?  [#permalink]

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New post 02 Aug 2018, 07:20
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MathRevolution wrote:
[Math Revolution GMAT math practice question]

If \(\frac{(n+2)!}{n!}=90\), then \(n=?\)

\(A. 8\)
\(B. 9\)
\(C. 10\)
\(D. 11\)
\(E. 12\)


(n+2)! = (n+2)(n+1)(n)(n-1)(n-2)....(3)(2)(1)
n! = (n)(n-1)(n-2)....(3)(2)(1)

Given: (n+2)!/n! = 90
Rewrite as: (n+2)(n+1)(n)(n-1)(n-2)....(3)(2)(1)/(n)(n-1)(n-2)....(3)(2)(1) = 90
Simplify: (n+2)(n+1) = 90
At this point, we can simply test the answer choices.

A) n = 8
Take (n+2)(n+1) = 90 and replace n with 8 to get: (8+2)(8+1) = 90
It works!!
Answer: A

Alternatively, we can start with (n+2)(n+1) = 90
Expand to get: n² + 3n + 2 = 90
Subtract 90 from both sides to get: n² + 3n - 88 = 0
Factor: (n + 11)(n - 8) = 0
So, EITHER n = -11 OR n = 8
Since we can't have negative factorials, it must be the case that n = 8
Answer: A

Cheers,
Brent
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Re: If (n+2)!/n!=90, then n=?  [#permalink]

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New post 05 Aug 2018, 19:05
=>

\(\frac{(n+2)!}{n!}= (n+2)(n+1) = 90 = 10*9.\)
Thus, \(n + 2 = 10\) or \(n = 8.\)

Therefore, the answer is A.
Answer : A

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Re: If (n+2)!/n!=90, then n=? &nbs [#permalink] 05 Aug 2018, 19:05
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