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# What is the value of the expression (15! - 14!)/13!

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Math Expert
Joined: 02 Sep 2009
Posts: 58464
What is the value of the expression (15! - 14!)/13!  [#permalink]

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03 Mar 2019, 23:54
00:00

Difficulty:

15% (low)

Question Stats:

90% (00:50) correct 10% (01:02) wrong based on 31 sessions

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What is the value of the expression $$\frac{15! - 14!}{13!}$$ ?

A. 1
B. 14
C. 169
D. 196
E. 210

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e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3092
What is the value of the expression (15! - 14!)/13!  [#permalink]

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04 Mar 2019, 00:02

Solution

Given:
• An expression $$\frac{15!−14!}{13!}$$

To find:
• The value of the given expression

Approach and Working:
We can write
• 15! as 15 x 14 x 13!
• And similarly, 14! as 14 x 13!
• Therefore, the given expression = $$\frac{15!−14!}{13!} = \frac{13!(15 * 14 – 14)}{13!} = 14 (15 – 1) = 14 * 14 = 196$$

Hence, the correct answer is option D.

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Re: What is the value of the expression (15! - 14!)/13!  [#permalink]

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04 Mar 2019, 00:55
Bunuel wrote:
What is the value of the expression $$\frac{15! - 14!}{13!}$$ ?

A. 1
B. 14
C. 169
D. 196
E. 210

$$\frac{15! - 14!}{13!}$$
13! ( 15*14-14)/13!
or say
14*(15-1)
= 196
IMO D
Target Test Prep Representative
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Re: What is the value of the expression (15! - 14!)/13!  [#permalink]

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06 Mar 2019, 20:05
Bunuel wrote:
What is the value of the expression $$\frac{15! - 14!}{13!}$$ ?

A. 1
B. 14
C. 169
D. 196
E. 210

We can separate this into two fractions and simplify:

15!/13! - 14!/13! = 15 x 14 - 14 = 14(15 - 1) = 14 x 14 = 196

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Re: What is the value of the expression (15! - 14!)/13!   [#permalink] 06 Mar 2019, 20:05
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