It is currently 28 Nov 2020, 15:47

### 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

# S is the set of all fractions

Author Message
TAGS:
Founder
Joined: 18 Apr 2015
Posts: 13916
GRE 1: Q160 V160
Followers: 315

Kudos [?]: 3683 [0], given: 12939

S is the set of all fractions [#permalink]  14 May 2018, 14:05
Expert's post
00:00

Question Stats:

38% (00:37) correct 61% (00:56) wrong based on 85 sessions
S is the set of all fractions of the form $$\frac{n}{n+1}$$, where n is a positive integer less than 20.

 Quantity A Quantity B The product of all the fractions that are in S $$\frac{1}{20}$$

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

_________________

New to the GRE, and GRE CLUB Forum?
GRE: All you do need to know about the GRE Test | GRE Prep Club for the GRE Exam - The Complete FAQ
Posting Rules: QUANTITATIVE | VERBAL
FREE Resources: GRE Prep Club Official LinkTree Page | Free GRE Materials - Where to get it!! (2020)
Free GRE Prep Club Tests: Got 20 Kudos? You can get Free GRE Prep Club Tests
GRE Prep Club on : Facebook | Instagram

Questions' Banks and Collection:
ETS: ETS Free PowerPrep 1 & 2 All 320 Questions Explanation. | ETS All Official Guides
3rd Party Resource's: All Quant Questions Collection | All Verbal Questions Collection
Books: All GRE Best Books
Scores: The GRE average score at Top 25 Business Schools 2020 Ed. | How to study for GRE retake and score HIGHER - (2020)
How is the GRE Score Calculated -The Definitive Guide (2021)
Tests: GRE Prep Club Tests | FREE GRE Practice Tests [Collection] - New Edition (2021)
Vocab: GRE Prep Club Official Vocabulary Lists for the GRE (2021)

Moderator
Joined: 07 Jan 2018
Posts: 697
Followers: 11

Kudos [?]: 785 [2] , given: 88

Re: S is the set of all fractions [#permalink]  15 May 2018, 06:28
2
KUDOS
From the given expression,
1st fraction = $$1/2$$
2nd fraction = $$2/3$$
3rd fraction = $$3/4$$

Here we can observe a $$pattern$$
the numerator begins with 1 and ultimately will end in 19
the denominator begins with 2 and ultimately will end in 20

when we multiply all the fractions our end product will be $$\frac{1*2*3*4*5.........19}{2*3*4*5.......20}$$At this point we can cancel off all the numerators except 1 with all the denominators except 20 finally reducing the term to $$1/20$$
option c
_________________

Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos

GRE Instructor
Joined: 10 Apr 2015
Posts: 3908
Followers: 164

Kudos [?]: 4775 [1] , given: 70

Re: S is the set of all fractions [#permalink]  01 Oct 2019, 09:25
1
KUDOS
Expert's post
Carcass wrote:
S is the set of all fractions of the form $$\frac{n}{n+1}$$, where n is a positive integer less than 20.

 Quantity A Quantity B The product of all the fractions that are in S $$\frac{1}{20}$$

Let's get a better idea of what Set S looks like.
We're told that n can have any integer value from 1 to 19 inclusive.

When n = 1, the corresponding fraction is $$\frac{1}{1+1}=\frac{1}{2}$$

When n = 2, the corresponding fraction is $$\frac{2}{2+1}=\frac{2}{3}$$

When n = 3, the corresponding fraction is $$\frac{3}{3+1}=\frac{3}{4}$$
.
.
.
.
.
When n = 18, the corresponding fraction is $$\frac{18}{18+1}=\frac{18}{19}$$

When n = 19, the corresponding fraction is $$\frac{19}{19+1}=\frac{19}{20}$$

So, Quantity B $$= (\frac{1}{2})(\frac{2}{3})(\frac{3}{4})(\frac{4}{5})......(\frac{17}{18})(\frac{18}{19})(\frac{19}{20})$$

$$=\frac{(1)(2)(3)(4)(5)....(17)(18)(19)}{(2)(3)(4)(5)....(17)(18)(19)(20)}$$

$$=\frac{1}{20}$$

We get:
QUANTITY A: $$\frac{1}{20}$$

QUANTITY B: $$\frac{1}{20}$$

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com

Retired Moderator
Joined: 21 Sep 2019
Posts: 160
Followers: 0

Kudos [?]: 126 [1] , given: 2

Re: S is the set of all fractions [#permalink]  24 Dec 2019, 06:14
1
KUDOS
A -> (1/2) (2/3) (3/4) .....(19/20)
Cancelling the denominator of the term with the numerator of next term
= 1/20

A = B

Retired Moderator
Joined: 16 Sep 2019
Posts: 187
Followers: 1

Kudos [?]: 189 [2] , given: 5

Re: S is the set of all fractions [#permalink]  26 Dec 2019, 20:41
2
KUDOS
When n = 1 the fraction is $$\frac{1}{2}$$.
Now, A says product of all the fractions that are in S.
It means $$\frac{1}{2}*\frac{2}{3}*.....\frac{19}{20}$$ Since N is less than 20.
The denominator and numerator will cancel out and we will be left with $$\frac{1}{20}$$

Hence, C
Carcass wrote:
S is the set of all fractions of the form $$\frac{n}{n+1}$$, where n is a positive integer less than 20.

 Quantity A Quantity B The product of all the fractions that are in S $$\frac{1}{20}$$

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

_________________

If you like my solution, do give kudos!

Re: S is the set of all fractions   [#permalink] 26 Dec 2019, 20:41
Display posts from previous: Sort by