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Which of the following is closest to (10!-9!)/(10!+9!)?

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Which of the following is closest to (10!-9!)/(10!+9!)?

by Max@Math Revolution » Tue Jul 05, 2016 8:16 pm
Which of the following is closest to (10!-9!)/(10!+9!)?
A. 0.01
B. 0.1
C. 0.2
D. 1
E. 10

*An answer will be posted in 2 days
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by regor60 » Wed Jul 06, 2016 5:30 am
=(10X-X)/(10X+X)

=9/11

=D
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by 800_or_bust » Wed Jul 06, 2016 5:36 am
Max@Math Revolution wrote:Which of the following is closest to (10!-9!)/(10!+9!)?
A. 0.01
B. 0.1
C. 0.2
D. 1
E. 10

*An answer will be posted in 2 days
(10!-9!)/(10!+9!)

((9!)(10-1))/((9!)(10+1))

(10-1)/(10+1)

9/11

Closest approximation among the answer choices is 1. Answer choice: D
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by Brent@GMATPrepNow » Wed Jul 06, 2016 5:36 am
Max@Math Revolution wrote:Which of the following is closest to (10!-9!)/(10!+9!)?
A. 0.01
B. 0.1
C. 0.2
D. 1
E. 10
Notice that 10! = (10)(9!)
So, we can factor out 9! from top and bottom.
(10! - 9!)/(10! + 9!) = [9!(10 - 1)]/[9!(10 + 1)]
= (10 - 1)/(10 + 1)
= (9)/(11)
≈ 1
Answer: D
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by Max@Math Revolution » Fri Jul 08, 2016 8:38 pm
(10!-9!)/(10!+9!)=(10-1)9!/(10+1)9!≒9/11=1. Hence, the correct answer is D
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