It is currently 19 Oct 2017, 04:44

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If S is the product of the integers from 1 to 100, inclusive

Author Message
TAGS:

### Hide Tags

Intern
Joined: 21 Feb 2013
Posts: 1

Kudos [?]: 4 [0], given: 0

If S is the product of the integers from 1 to 100, inclusive [#permalink]

### Show Tags

27 Feb 2013, 13:39
4
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

79% (01:12) correct 21% (01:58) wrong based on 87 sessions

### HideShow timer Statistics

If S is the product of the integers from 1 to 100, inclusive, and T is the product of the integers from 1 to 101, inclusive, what is 1/S+1/T in terms of T ?

A)T/101
B)T/100+100
C)100+T/T
D)102/T
E)T+1/100

Given: S=100! and T=101!.

1/S+1/T=1/100!+1/101!=101+1/101!
=102/T.

....

This part I fully understand: 1/100!+1/101!
But I am a little confused how this was determined: 101+1/101!
How are those "!" taken out on the numerator to get 101 and 1?

Can someone show me in detail please?
[Reveal] Spoiler: OA

Kudos [?]: 4 [0], given: 0

Math Expert
Joined: 02 Sep 2009
Posts: 41893

Kudos [?]: 128829 [0], given: 12183

Re: If S is the product of the integers from 1 to 100, inclusive [#permalink]

### Show Tags

27 Feb 2013, 14:54
Expert's post
3
This post was
BOOKMARKED
m24 q35

If S is the product of the integers from 1 to 100, inclusive, and T is the product of the integers from 1 to 101, inclusive, what is 1/S+1/T in terms of T ?

A. $$\frac{T}{101}$$
B. $$\frac{T}{100}+100$$
C. $$\frac{100+T}{T}$$
D. $$\frac{102}{T}$$
E. $$\frac{T+1}{100}$$

Given: S=100! and T=101!.

$$\frac{1}{S}+\frac{1}{T}=\frac{1}{100!}+\frac{1}{101!}=\frac{1}{100!}+\frac{1}{100!*101}=\frac{101+1}{100!*101}=\frac{101+1}{101!}=\frac{102}{T}$$.

_________________

Kudos [?]: 128829 [0], given: 12183

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7674

Kudos [?]: 17357 [1], given: 232

Location: Pune, India
Re: If S is the product of the integers from 1 to 100, inclusive [#permalink]

### Show Tags

27 Feb 2013, 20:56
1
KUDOS
Expert's post
aaroncorr wrote:
If S is the product of the integers from 1 to 100, inclusive, and T is the product of the integers from 1 to 101, inclusive, what is 1/S+1/T in terms of T ?

A)T/101
B)T/100+100
C)100+T/T
D)102/T
E)T+1/100

You can also substitute T for S right away to get the expression in terms of T.

Given: S=100! and T=101! Therefore, S = T/101

1/S+1/T = 101/T + 1/T = 102/T
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Kudos [?]: 17357 [1], given: 232

Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 627

Kudos [?]: 1355 [0], given: 136

Re: If S is the product of the integers from 1 to 100, inclusive [#permalink]

### Show Tags

28 Feb 2013, 03:10
aaroncorr wrote:
If S is the product of the integers from 1 to 100, inclusive, and T is the product of the integers from 1 to 101, inclusive, what is 1/S+1/T in terms of T ?

A)T/101
B)T/100+100
C)100+T/T
D)102/T
E)T+1/100

Can someone show me in detail please?

Nothing much to add. Just another method which might work for those who don't have enough time to understand/solve this question. ALL the options are more than 1, except D. The given expression 1/S+1/T will also be much much less than 1. Thus answer is D.
_________________

Kudos [?]: 1355 [0], given: 136

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16678

Kudos [?]: 273 [0], given: 0

Re: If S is the product of the integers from 1 to 100, inclusive [#permalink]

### Show Tags

09 Oct 2014, 09:10
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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 273 [0], given: 0

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16678

Kudos [?]: 273 [0], given: 0

Re: If S is the product of the integers from 1 to 100, inclusive [#permalink]

### Show Tags

23 Jun 2016, 18:29
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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 273 [0], given: 0

Senior Manager
Joined: 07 Sep 2014
Posts: 484

Kudos [?]: 30 [0], given: 342

Concentration: Finance, Marketing
Re: If S is the product of the integers from 1 to 100, inclusive [#permalink]

### Show Tags

23 Aug 2016, 04:45
If S is the product of the integers from 1 to 100, inclusive, and T is the product of the integers from 1 to 101, inclusive, what is 1/S+1/T in terms of T ?

A)T/101
B)T/100+100
C)100+T/T
D)102/T
E)T+1/100

S+T/ST???

100!+101!/ (100!)(101!)
=102/101! So D

Kudos [?]: 30 [0], given: 342

Re: If S is the product of the integers from 1 to 100, inclusive   [#permalink] 23 Aug 2016, 04:45
Display posts from previous: Sort by