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Which of the following is equivalent to (8! + 9!)/10!?

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Bunuel
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Which of the following is equivalent to (8! + 9!)/10!? [#permalink] New post   28 Aug 2018, 20:39
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A
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C
D
E

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Which of the following is equivalent to \(\frac{8!+9!}{10!}\)?

A. 1/72
B. 9/100
C. 1/9
D. 9/10
E. 17/10
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C
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Re: Which of the following is equivalent to (8! + 9!)/10!? [#permalink] New post   28 Aug 2018, 21:00
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Take 8 factorial common from numerator, this will render
\(\frac{8!(1+9)}{10*9*8!}\)

= \(\frac{1}{9}\)
Option C
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Which of the following is equivalent to (8! + 9!)/10!? [#permalink] New post   28 Aug 2018, 20:44
Bunuel wrote:
Which of the following is equivalent to \(\frac{8!+9!}{10!}\)?

A. 1/72
B. 9/100
C. 1/9
D. 9/10
E. 17/10


Express all the terms in terms of the lowest magnitude of factorial,

\(\frac{8!+9!}{10!}\)=\(\frac{8!+8!*9}{8!*9*10}\)=\(\frac{8!(1+9)}{8!*9*10}\)=\(\frac{8!*10}{8!*9*10}\)
=\(\frac{1}{9}\)

Ans. (C)
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Re: Which of the following is equivalent to (8! + 9!)/10!? [#permalink] New post   28 Aug 2018, 20:45
= (8!+9*8!)/10!

= 8!(1+9)/10!

= 10/10*9

= 1/9

C is the answer

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Re: Which of the following is equivalent to (8! + 9!)/10!? [#permalink] New post   28 Aug 2018, 20:58
Bunuel wrote:
Which of the following is equivalent to \(\frac{8!+9!}{10!}\)?

A. 1/72
B. 9/100
C. 1/9
D. 9/10
E. 17/10


\(\frac{8!+9!}{10!}\)

\(\frac{8!(1+9)}{10!}\)

Reducing 8! --> \(\frac{10}{10*9}\)

\(\frac{1}{9}\)

Hence C
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Re: Which of the following is equivalent to (8! + 9!)/10!? [#permalink] New post   29 Aug 2018, 08:20
Bunuel wrote:
Which of the following is equivalent to \(\frac{8!+9!}{10!}\)?

A. 1/72
B. 9/100
C. 1/9
D. 9/10
E. 17/10

\(\frac{8!+9!}{10!}\)

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

= \(\frac{8! ( 1 + 9)}{8!(9*10)}\)

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

= \(\frac{1}{9}\), Answer must be (C)
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Re: Which of the following is equivalent to (8! + 9!)/10!? [#permalink] New post   03 Sep 2018, 19:01
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Bunuel wrote:
Which of the following is equivalent to \(\frac{8!+9!}{10!}\)?

A. 1/72
B. 9/100
C. 1/9
D. 9/10
E. 17/10



Factoring out 8! from the numerator and denominator, we have:

8!(1 + 9)/[8!(9 x 10)]

Canceling the 8!, we have:

10/90

1/9

Answer: C
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Re: Which of the following is equivalent to (8! + 9!)/10!? [#permalink]
03 Sep 2018, 19:01
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