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

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Math Expert
Joined: 02 Sep 2009
Posts: 53020
(101!) − (100!)/(99!) − (98!) is closest to which of the following?  [#permalink]

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05 Apr 2016, 07:34
00:00

Difficulty:

25% (medium)

Question Stats:

79% (01:23) correct 21% (01:38) wrong based on 71 sessions

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$$\frac{(101!) − (100!)}{(99!) − (98!)}$$ is closest to which of the following?

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

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Manager
Joined: 09 Jul 2013
Posts: 110
Re: (101!) − (100!)/(99!) − (98!) is closest to which of the following?  [#permalink]

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05 Apr 2016, 09:00
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

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Dave de Koos

Math Expert
Joined: 02 Aug 2009
Posts: 7334
Re: (101!) − (100!)/(99!) − (98!) is closest to which of the following?  [#permalink]

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05 Apr 2016, 09:16
1
1
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
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

GMAT Expert

Intern
Joined: 21 Oct 2015
Posts: 46
GMAT 1: 620 Q47 V28
Re: (101!) − (100!)/(99!) − (98!) is closest to which of the following?  [#permalink]

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05 Apr 2016, 16:31
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!

Posted from my mobile device
Math Expert
Joined: 02 Aug 2009
Posts: 7334
Re: (101!) − (100!)/(99!) − (98!) is closest to which of the following?  [#permalink]

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05 Apr 2016, 18:23
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
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

GMAT Expert

Non-Human User
Joined: 09 Sep 2013
Posts: 9863
Re: (101!) − (100!)/(99!) − (98!) is closest to which of the following?  [#permalink]

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18 Oct 2018, 16:22
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: (101!) − (100!)/(99!) − (98!) is closest to which of the following?   [#permalink] 18 Oct 2018, 16:22
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