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

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pm; Thanked: 6 times; Followed by:5 members

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

by Vincen » Tue Oct 06, 2020 7:19 am

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

A. \(\dfrac1{72}\)

B. \(\dfrac9{100}\)

C. \(\dfrac19\)

D. \(\dfrac9{10}\)

E. \(\dfrac{17}{10}\)

Answer: C

Source: Veritas Prep

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Source: Beat The GMAT — Problem Solving | Tue Oct 06, 2020 7:19 am

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

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

by Scott@TargetTestPrep » Sat Oct 10, 2020 2:26 pm

Vincen wrote: ↑
Tue Oct 06, 2020 7:19 am
Which of the following is equivalent to \(\dfrac{8!+9!}{10!}?\)

A. \(\dfrac1{72}\)

B. \(\dfrac9{100}\)

C. \(\dfrac19\)

D. \(\dfrac9{10}\)

E. \(\dfrac{17}{10}\)

Answer: C

Solution:

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

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

After canceling 8! from the numerator and denominator, we have:

(1 + 9) / (9 x 10) = 10/90 = 1/9

Answer: C

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