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(101!) − (100!)/(99!) − (98!) is closest to which of the following?

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(101!) − (100!)/(99!) − (98!) is closest to which of the following?  [#permalink]

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New post 05 Apr 2016, 08:34
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

80% (01:23) correct 20% (01:38) wrong based on 74 sessions

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Re: (101!) − (100!)/(99!) − (98!) is closest to which of the following?  [#permalink]

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New post 05 Apr 2016, 10:00
If we let x=100!
and y=98!

Then the expression would look like this:

\(\frac{101x - x}{99y - y}\)

\(= \frac{100x}{98y}\)

But x=100! = 100*99*98! = 100*99*y

So if we substitute that in for x we get

\(\frac{100*100*99*y}{98y}\)

The y's cancel, and 99/98 is close to 1, so the expression becomes ~100*100 = 10,000

Answer: D
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Re: (101!) − (100!)/(99!) − (98!) is closest to which of the following?  [#permalink]

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New post 05 Apr 2016, 10:16
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Bunuel wrote:
\(\frac{(101!) − (100!)}{(99!) − (98!)}\) is closest to which of the following?

A. 10
B. 100
C. 1,000
D. 10,000
E. 100,000



\(\frac{(101!) − (100!)}{(99!) − (98!)}\)..
\(\frac{100!(101-1)}{98!(99-1)}\)...
\(\frac{100!*100}{98!*98}\)...
\(\frac{100*99*98!*100}{98!*98}\)...
slightly > 100*99 = 9900 closer to 10,000 in the choices
D
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Re: (101!) − (100!)/(99!) − (98!) is closest to which of the following?  [#permalink]

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New post 05 Apr 2016, 17:31
Well, this question is best suited for estimation as the given answer choices are far apart.

chetan: You can completely ignore 100 in numerator and 98 in denominator as both of them are much lesser comparing to their counterparts in factorial. Hence, you could straight away calculate 100!/98! which is easy.

Thanks!

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Re: (101!) − (100!)/(99!) − (98!) is closest to which of the following?  [#permalink]

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New post 05 Apr 2016, 19:23
HarisinghKhedar wrote:
Well, this question is best suited for estimation as the given answer choices are far apart.

chetan: You can completely ignore 100 in numerator and 98 in denominator as both of them are much lesser comparing to their counterparts in factorial. Hence, you could straight away calculate 100!/98! which is easy.

Thanks!

Posted from my mobile device



Thanks!
But I thought that is exactly what I have done
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Re: (101!) − (100!)/(99!) − (98!) is closest to which of the following?  [#permalink]

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Re: (101!) − (100!)/(99!) − (98!) is closest to which of the following?   [#permalink] 18 Oct 2018, 17:22
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