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# (60! − 59!)/58! =

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Math Expert
Joined: 02 Sep 2009
Posts: 64068

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15 Dec 2019, 23:50
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Difficulty:

35% (medium)

Question Stats:

71% (00:40) correct 29% (01:02) wrong based on 34 sessions

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$$\frac{60! − 59!}{58!} =$$

A. 59*58
B. 60*59
C. 58^2
D. 59^2
E. 60^2

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Math Expert
Joined: 02 Aug 2009
Posts: 8584
Re: (60! − 59!)/58! =  [#permalink]

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15 Dec 2019, 23:55
Bunuel wrote:
$$\frac{60! − 59!}{58!} =$$

A. 59*58
B. 60*59
C. 58^2
D. 59^2
E. 60^2

$$\frac{60! − 59!}{58!} =\frac{60*59*58!-59*58!}{58!}=\frac{58!(60*59-59)}{58!}=59(60-1)=59^2$$

D
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Re: (60! − 59!)/58! =  [#permalink]

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16 Dec 2019, 00:02
$$\frac{60! − 59!}{58!} =$$

Taking Common 58! - $$\frac{58![60*59 - 59]}{58!}$$

Cancelling 58! and taking 59 common - $$59[60 - 1]$$
Solving - 59*59 - $$59^2$$
Option 'D'
Bunuel wrote:
$$\frac{60! − 59!}{58!} =$$

A. 59*58
B. 60*59
C. 58^2
D. 59^2
E. 60^2

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Joined: 16 Sep 2014
Posts: 477
Location: United States
GMAT 1: 780 Q51 V45
GRE 1: Q170 V167
Re: (60! − 59!)/58! =  [#permalink]

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16 Dec 2019, 13:24
= $$\frac{60!}{58!} - \frac{59!}{58!} = 60*59 - 59 = (60 - 1) * 59 = 59^2$$

Ans: D

Bunuel wrote:
$$\frac{60! − 59!}{58!} =$$

A. 59*58
B. 60*59
C. 58^2
D. 59^2
E. 60^2

_________________
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Re: (60! − 59!)/58! =   [#permalink] 16 Dec 2019, 13:24