(91!-90!+89!)/89!= : GMAT Problem Solving (PS)

(91!-90!+89!)/89!=

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Magoosh GMAT Instructor

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(91!-90!+89!)/89!= [#permalink]

18 Oct 2012, 12:04

00:00

Question Stats:

83% (01:35) correct

16% (01:30) wrong

based on 1 sessions

\frac{91!-90!+89!}{89!}=

A. 2
B. 90
C. 89^2+89
D. 90^2+1
E. 91^1-1

For a full discussion of this and other problems like it, see
http://magoosh.com/gmat/2012/gmat-factorials/

Mike :-)

[Reveal] Spoiler: OA

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Mike McGarry
Magoosh Test Prep

Last edited by Bunuel on 18 Oct 2012, 12:08, edited 1 time in total.

Renamed the topic and edited the question.

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Re: (91!-90!+89!)/89!= [#permalink]

18 Oct 2012, 12:11

\frac{91!-90!+89!}{89!}=

A. 2
B. 90
C. 89^2+89
D. 90^2+1
E. 91^1-1

Factor out 89!: \frac{91!-90!+89!}{89!}=\frac{89!(90*91-90+1)}{89!}=90*91-90+1.

Now, factor out 90: 90*91-90+1=90(91-1)+1=90^2+1.

Answer: D.
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Magoosh GMAT Instructor

Joined: 28 Dec 2011

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fraction with factorials [#permalink]

17 Jan 2013, 11:20

\frac{91!-90!+89!}{89!} =
(A) 2
(B) 90
(C) 89^2 + 89
(D) 90^2 + 1
(E) 91^2 - 1

For calculation tips involving factorials, as well as a complete solution to this problem, see this post:
http://magoosh.com/gmat/2012/gmat-factorials/

Mike :-)

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Mike McGarry
Magoosh Test Prep

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Re: fraction with factorials [#permalink]

17 Jan 2013, 11:40

break up the fraction;

(91!)/(89!) - (90!)/(89!) - (89!)/(89!)
which reduces to (91)(90) - (90) +1 = 90^2 + 1 (D)

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Re: fraction with factorials [#permalink]

17 Jan 2013, 12:26

take out the common factor from numerator and denominator which in this case would be 89!

Your numerator should look like

91*90* 89! - 90*89! + 89!

89![ 91*90 - 90 +1]/89!

Which leaves you with

91*90 - 89

Re: fraction with factorials [#permalink] 17 Jan 2013, 12:26

(91!-90!+89!)/89!=

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(91!-90!+89!)/89!=

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