Last visit was: 12 Sep 2026, 00:12 It is currently 12 Sep 2026, 00:12
Home
Messages
Tests
Schools
Events
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
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 12 Sep 2026
Posts: 113,474
Own Kudos:
840,753
 [2]
Given Kudos: 111,477
Products:
GMAT Club Tests
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 113,474
Kudos: 840,753
 [2]
The sum of two numbers is 216 and their H.C.F. is 27. The numbers are Updated on: 04 Aug 2021, 09:02
Originally posted by Bunuel on 04 Aug 2021, 06:45.
Last edited by chetan2u on 04 Aug 2021, 09:02, edited 1 time in total.
Edited
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

25% (medium)

Question Stats:

75% (01:30) correct 25% (01:49) wrong based on 64 sessions

History

Date
Time
Result
Not Attempted Yet
The sum of two positive integers is 216 and their highest common factor is 27. What are these numbers ?

(A) 27, 189
(B) 54, 162
(C) 81, 216
(D) 108, 118
(E) 116, 110
ShowHide Answer
Official Answer
A
User avatar
DHRJ0032
User avatar
Joined: 27 Feb 2020
Last visit: 20 Dec 2023
Posts: 101
Own Kudos:
111
Given Kudos: 124
Location: India
Concentration: Finance, Operations
Schools: Owen '25 (II)
GPA: 4
WE:Operations (Aerospace and Defense)
Schools: Owen '25 (II)
Posts: 101
Kudos: 111
The sum of two numbers is 216 and their H.C.F. is 27. The numbers are Updated on: 04 Aug 2021, 09:29
Originally posted by DHRJ0032 on 04 Aug 2021, 08:55.
Last edited by DHRJ0032 on 04 Aug 2021, 09:29, edited 1 time in total.
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Both A and C are the possible answers.

Posted from my mobile device
Attachments

File comment: bunuel has changed the option C from (81,135) to (81,216)

now, A will be the answer.
IMG_20210804_212406.jpg
IMG_20210804_212406.jpg [ 3.13 MiB | Viewed 3998 times ]

User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 11 Sep 2026
Posts: 11,292
Own Kudos:
46,142
Given Kudos: 339
Status:Math and DI Expert
Location: India
Concentration: Human Resources, General Management
GMAT Focus 1: 735 Q90 V89 DI81
Products:
My Reviews
Expert
Expert reply
GMAT Focus 1: 735 Q90 V89 DI81
Posts: 11,292
Kudos: 46,142
The sum of two numbers is 216 and their H.C.F. is 27. The numbers are 04 Aug 2021, 09:01
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
The sum of two positive integers is 216 and their highest common factor is 27. What are these numbers ?

(A) 27, 189
(B) 54, 162
(C) 81, 135
(D) 108, 118
(E) 116, 110
Show more


Let the numbers be 27a and 27b, where a and b are co prime.
So 27a+27b=216………a+b=8
Now a and b are co-primes, so they can be 1 and 7 or 3 and 5

Thus, possible solutions
1) 27*1=27 and 27*7=189
2) 27*3=81 and 27*5=135

A is in the options.

Use options

As the HCF is 27, we cannot have both numbers even.
B, D and E are out.
The total in C does not come to 216. Eliminate


A
User avatar
DHRJ0032
User avatar
Joined: 27 Feb 2020
Last visit: 20 Dec 2023
Posts: 101
Own Kudos:
111
Given Kudos: 124
Location: India
Concentration: Finance, Operations
Schools: Owen '25 (II)
GPA: 4
WE:Operations (Aerospace and Defense)
Schools: Owen '25 (II)
Posts: 101
Kudos: 111
The sum of two numbers is 216 and their H.C.F. is 27. The numbers are 04 Aug 2021, 09:33
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel has changed the option C from (81,135) to (81,216) after i posted the solution just to see my effort went into vain. :(
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 11 Sep 2026
Posts: 11,292
Own Kudos:
46,142
Given Kudos: 339
Status:Math and DI Expert
Location: India
Concentration: Human Resources, General Management
GMAT Focus 1: 735 Q90 V89 DI81
Products:
My Reviews
Expert
Expert reply
GMAT Focus 1: 735 Q90 V89 DI81
Posts: 11,292
Kudos: 46,142
The sum of two numbers is 216 and their H.C.F. is 27. The numbers are 04 Aug 2021, 09:41
Kudos
Add Kudos
Bookmarks
Bookmark this Post
DHRJ0032
Bunuel has changed the option C from (81,135) to (81,216) after i posted the solution just to see my effort went into vain. :(
Show more


A question cannot have two answers. So the options have been changed accordingly as there was an error in the options.
User avatar
DHRJ0032
User avatar
Joined: 27 Feb 2020
Last visit: 20 Dec 2023
Posts: 101
Own Kudos:
111
Given Kudos: 124
Location: India
Concentration: Finance, Operations
Schools: Owen '25 (II)
GPA: 4
WE:Operations (Aerospace and Defense)
Schools: Owen '25 (II)
Posts: 101
Kudos: 111
The sum of two numbers is 216 and their H.C.F. is 27. The numbers are 04 Aug 2021, 09:48
Kudos
Add Kudos
Bookmarks
Bookmark this Post
yeah for sure !
I said that because i checked my solution many times to arrive at the conclusion that both A and C are correct.
avatar
TarunKumar1234
avatar
Joined: 14 Jul 2020
Last visit: 28 Feb 2024
Posts: 1,101
Own Kudos:
1,365
Given Kudos: 351
Location: India
Posts: 1,101
Kudos: 1,365
The sum of two numbers is 216 and their H.C.F. is 27. The numbers are 04 Aug 2021, 10:04
Kudos
Add Kudos
Bookmarks
Bookmark this Post
The sum of two positive integers is 216 and their highest common factor is 27. What are these numbers ?

a +b = 216 and 3^3 * (x+y) = 216
so, x +y = 8, now, x and y must have HCF as 1.

(A) 27, 189 -> x = 1 and y= 7. Possible.
(B) 54, 162 -> x =2 and y = 8, not possible as HCF = 2.
(C) 81, 216 -> Sum not equal to 216.
(D) 108, 118 -> x = 4, y not an integer.
(E) 116, 110 -> x and y both are not integers.

So, I think A. :)
User avatar
ShaikhMoice
User avatar
Joined: 25 Jan 2021
Last visit: 25 Aug 2022
Posts: 91
Own Kudos:
41
Given Kudos: 475
Posts: 91
Kudos: 41
The sum of two numbers is 216 and their H.C.F. is 27. The numbers are 07 Aug 2021, 09:55
Kudos
Add Kudos
Bookmarks
Bookmark this Post
DHRJ0032
Both A and C are the possible answers.

Posted from my mobile device
Show more

Sum in case of C is more than 216
User avatar
DHRJ0032
User avatar
Joined: 27 Feb 2020
Last visit: 20 Dec 2023
Posts: 101
Own Kudos:
111
Given Kudos: 124
Location: India
Concentration: Finance, Operations
Schools: Owen '25 (II)
GPA: 4
WE:Operations (Aerospace and Defense)
Schools: Owen '25 (II)
Posts: 101
Kudos: 111
The sum of two numbers is 216 and their H.C.F. is 27. The numbers are 07 Aug 2021, 19:36
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ShaikhMoice
DHRJ0032
Both A and C are the possible answers.

Posted from my mobile device

Sum in case of C is more than 216
Show more

Yeah you are right. But earlier option C was (81,135).refer to my solution. When I posted the solution then only Bunuel has changed the option C to (81,216).🙄
Moderator:
Bunuel
Math Expert
113474 posts