Last visit was: 18 Jul 2025, 06:46 It is currently 18 Jul 2025, 06:46
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
NoHalfMeasures
User avatar
Retired Moderator
Joined: 29 Oct 2013
Last visit: 11 Jul 2023
Posts: 220
Own Kudos:
2,385
 [60]
Given Kudos: 204
Concentration: Finance
GPA: 3.7
WE:Corporate Finance (Retail Banking)
Posts: 220
Kudos: 2,385
 [60]
Which of the following fractions can be written as the difference of 08 Jun 2014, 00:45
4
Kudos
Add Kudos
56
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

15% (low)

Question Stats:

79% (01:27) correct 21% (01:37) wrong based on 925 sessions

History

Date
Time
Result
Not Attempted Yet
Which of the following fractions can be written as the difference of reciprocals of two consecutive integers?

A. 1/24
B. 7/30
C. 1/45
D. 13/56
E. 1/72

PS04867
ShowHide Answer
Official Answer
E
Most Helpful Reply
User avatar
WoundedTiger
User avatar
Joined: 25 Apr 2012
Last visit: 25 Sep 2024
Posts: 523
Own Kudos:
2,482
 [19]
Given Kudos: 740
Location: India
GPA: 3.21
WE:Business Development (Other)
Products:
My Reviews
Posts: 523
Kudos: 2,482
 [19]
Which of the following fractions can be written as the difference of 08 Jun 2014, 01:25
12
Kudos
Add Kudos
7
Bookmarks
Bookmark this Post
MensaNumber
which of the following fractions can be written as the difference of reciprocals of two consecutive integers?

a) 1/24
b) 7/30
c) 1/45
d) 13/56
e) 1/72

Let the 2 consecutive integers be "a" and "a+1"

So we have \(\frac{1}{a}\) - \(\frac{1}{(a+1)}\)

Simplify and we get \(\frac{1}{a(a+1)}\)....So the answer needs to have 1 in numerator and denominator should be product of consecutive integers...

Option B and D can be ruled out

24=6*4 (Not consecutive)
45= 9*5 (not consecutive)
72=8*9 (Consecutive) and hence your answer.
avatar
PareshGmat
avatar
Joined: 27 Dec 2012
Last visit: 10 Jul 2016
Posts: 1,538
Own Kudos:
7,899
 [6]
Given Kudos: 193
Status:The Best Or Nothing
Location: India
Concentration: General Management, Technology
WE:Information Technology (Computer Software)
Posts: 1,538
Kudos: 7,899
 [6]
Which of the following fractions can be written as the difference of 13 Sep 2014, 08:48
5
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Difference of reciprocals means 1 has to be in the numerator;

So option B & D can be ignored

For option A, B & E, we require to search two consecutive numbers whose product is the denominator

24 = 4 * 6 ......... Ignore

45 = 5 * 9 ........ Ignore

72 = 8 * 9 ................ Answer

Answer = E
General Discussion
User avatar
PiyushK
User avatar
Joined: 22 Mar 2013
Last visit: 19 May 2023
Posts: 599
Own Kudos:
4,879
 [4]
Given Kudos: 235
Status:Everyone is a leader. Just stop listening to others.
Location: India
GPA: 3.51
WE:Information Technology (Computer Software)
Products:
My Reviews
Posts: 599
Kudos: 4,879
 [4]
Which of the following fractions can be written as the difference of 13 Sep 2014, 08:35
4
Kudos
Add Kudos
Bookmarks
Bookmark this Post
We can represent two consecutive numbers as n and n+1
Where n < n+1

Reciprocate them = \(\frac{1}{n}> \frac{1}{n+1}\)

Subtract small from big..

\(\frac{1}{n} - \frac{1}{n+1}\)
\(\frac{1}{n^2+n}\)

So we must have 1 in numerator and denominator term can can be expressed in the from of n^2+1.

5 + 25 = 30
6+ 36 = 42
7+ 49 = 56
8 + 64 = 72 <<< matched << we have one answer choice (E) with 72 in denominator.
User avatar
desaichinmay22
User avatar
Joined: 21 Sep 2012
Last visit: 22 May 2016
Posts: 191
Own Kudos:
437
Given Kudos: 31
Location: United States
Concentration: Finance, Economics
Schools: CBS '17
GPA: 4
WE:General Management (Consumer Packaged Goods)
Schools: CBS '17
Posts: 191
Kudos: 437
Which of the following fractions can be written as the difference of 13 Sep 2014, 10:56
Kudos
Add Kudos
Bookmarks
Bookmark this Post
let a and b be the consecutive integers.
1/b-1/a=(a-b)/ab

inverse of (a-b)/ab can be compared with inverse of each option

option 1 : ab/(a-b) = 24/1 .... no consecutive numbers have product as 24
option 2 : ab/(a-b) = 30/7.... denominator has to be 1 as a and b are consecutive numbers
option 3 : ab/(a-b) = 54/1 ..... no consecutive numbers have product as 54
option 4 : ab/(a-b) = 56/13 .... denominator has to be 1 as a and b are consecutive numbers
option 5 : ab/(a-b) = 72/1 ..... 8 & 9 satisfy the equation.

Ans- E
User avatar
generis
User avatar
Senior SC Moderator
Joined: 22 May 2016
Last visit: 18 Jun 2022
Posts: 5,293
Own Kudos:
36,956
Given Kudos: 9,464
Products:
GMAT Club Tests
Expert
Expert reply
Posts: 5,293
Kudos: 36,956
Which of the following fractions can be written as the difference of 21 Oct 2017, 13:01
Kudos
Add Kudos
Bookmarks
Bookmark this Post
NoHalfMeasures
Which of the following fractions can be written as the difference of reciprocals of two consecutive integers?

A. 1/24
B. 7/30
C. 1/45
D. 13/56
E. 1/72
Look only at the denominators to start.

Which denominators are a product of two consecutive integers?

B) 7/30 (5*6 = 30)

D) 13/56 (7*8 = 56)

E 1/72 (8*9 = 72)

Now numerators. There is only one choice: a numerator of 1. The difference between two consecutive integers is 1.
(9-8) = 1.

That is Answer E.
User avatar
RashedVai
User avatar
Joined: 24 Feb 2017
Last visit: 03 Apr 2025
Posts: 173
Own Kudos:
436
Given Kudos: 114
Status:wake up with a purpose
Location: Bangladesh
Concentration: Accounting, Entrepreneurship
Schools: Kelley '22 Marshall '22 Iowa State '22 Carey Arizona "22 Simon '22 Neeley '22
Schools: Kelley '22 Marshall '22 Iowa State '22 Carey Arizona "22 Simon '22 Neeley '22
Posts: 173
Kudos: 436
Which of the following fractions can be written as the difference of 06 Apr 2019, 23:25
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Two consecutive integers have no common factor except 1.
If we subtract the reciprocals of two consecutive integer, Then we actually multiply them in the denominator. So, we want their product in the denominator.

again, if we subtract the reciprocals of two consecutive integer, their difference will be in the numerator, which will be always 1.

Only (E), satisfies both of the restrictions.
9*8=72 and 9-8=1

Posted from my mobile device
avatar
aborja87
avatar
Joined: 03 Aug 2017
Last visit: 25 Mar 2020
Posts: 9
Own Kudos:
4
Given Kudos: 77
Posts: 9
Kudos: 4
Which of the following fractions can be written as the difference of 12 Mar 2020, 13:13
Kudos
Add Kudos
Bookmarks
Bookmark this Post
WoundedTiger
MensaNumber
which of the following fractions can be written as the difference of reciprocals of two consecutive integers?

a) 1/24
b) 7/30
c) 1/45
d) 13/56
e) 1/72

Let the 2 consecutive integers be "a" and "a+1"

So we have \(\frac{1}{a}\) - \(\frac{1}{(a+1)}\)

Simplify and we get \(\frac{1}{a(a+1)}\)....So the answer needs to have 1 in numerator and denominator should be product of consecutive integers...

Option B and D can be ruled out

24=6*4 (Not consecutive)
45= 9*5 (not consecutive)
72=8*9 (Consecutive) and hence your answer.

In addition to this, it has to be even so you can eliminate 45 (option c) with ease as well...
User avatar
Basshead
User avatar
Joined: 09 Jan 2020
Last visit: 07 Feb 2024
Posts: 927
Own Kudos:
287
 [1]
Given Kudos: 432
Location: United States
Posts: 927
Kudos: 287
 [1]
Which of the following fractions can be written as the difference of 17 Nov 2020, 13:21
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Two consecutive integers = \(x, x+1\)

\(\frac{1}{x} - \frac{1}{x-1} = \frac{1}{x(x-1)}\)

At this point we can look at the answer choices

\(\frac{1}{72} = \frac{1}{8(9)}\)

Perfect match!
User avatar
Fish181
User avatar
Joined: 13 Dec 2023
Last visit: 22 Jan 2025
Posts: 137
Own Kudos:
788
Given Kudos: 53
Status:Applying in R1 of 2024 to t15
Affiliations: University of Tennessee
Location: United States (CO)
Concentration: Strategy, Finance
Schools: Darden '27 (A$$) Fuqua '27 Tuck '27 Cornell '26 (S) Yale '27 (S) Owen '27 (S)
GMAT Focus 1: 605 Q76 V84 DI80
GMAT Focus 2: 615 Q78 V86 DI78
GPA: 3.62
WE:Analyst (Consumer Packaged Goods)
Schools: Darden '27 (A$$) Fuqua '27 Tuck '27 Cornell '26 (S) Yale '27 (S) Owen '27 (S)
GMAT Focus 2: 615 Q78 V86 DI78
Posts: 137
Kudos: 788
Which of the following fractions can be written as the difference of 01 Mar 2024, 09:01
Kudos
Add Kudos
Bookmarks
Bookmark this Post
strategy: write what it's asking algebraically and then plug and play the answer choices. You know that the number has to be 1/x(x+1) therefore 1 / (multiplication of two consecutive integers)
User avatar
DanTheGMATMan
User avatar
Joined: 02 Oct 2015
Last visit: 17 Jul 2025
Posts: 354
Own Kudos:
172
Given Kudos: 9
Expert
Expert reply
Posts: 354
Kudos: 172
Which of the following fractions can be written as the difference of 15 May 2024, 06:55
Kudos
Add Kudos
Bookmarks
Bookmark this Post
­Look for a pattern wrt the difference between reciprocals of consecutives:

­
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 37,442
Own Kudos:
1,013
Posts: 37,442
Kudos: 1,013
Which of the following fractions can be written as the difference of 25 May 2025, 20:45
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
Moderators:
Bunuel
Math Expert
102614 posts
Krunaal
PS Forum Moderator
698 posts