Last visit was: 23 Apr 2026, 00:41 It is currently 23 Apr 2026, 00:41
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
705-805 (Hard)|   Algebra|      
User avatar
siddhantvarma
User avatar
Joined: 12 May 2024
Last visit: 12 Jan 2026
Posts: 534
Own Kudos:
812
 [9]
Given Kudos: 197
GMAT Focus 1: 655 Q87 V85 DI76
GMAT Focus 1: 655 Q87 V85 DI76
Posts: 534
Kudos: 812
 [9]
If a and b are integers, and if 3 ( a b ) 2 + 5 b 2 = 48 , which of 10 Jun 2025, 23:26
Kudos
Add Kudos
9
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:

75% (hard)

Question Stats:

62% (02:48) correct 38% (02:53) wrong based on 141 sessions

History

Date
Time
Result
Not Attempted Yet
If a and b are integers, and if \(3( a − b )^2 + 5b^2 = 48\) , which of the following could be the value of a ?

(A) - 1
(B) 0
(C) 1
(D) 3
(E) 2
ShowHide Answer
Official Answer
E
User avatar
HarshavardhanR
User avatar
Joined: 16 Mar 2023
Last visit: 22 Apr 2026
Posts: 488
Own Kudos:
576
 [2]
Given Kudos: 67
Status:Independent GMAT Tutor
Affiliations: Ex - Director, Subject Matter Expertise at e-GMAT
Products:
GMAT Club Tests
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 488
Kudos: 576
 [2]
If a and b are integers, and if 3 ( a b ) 2 + 5 b 2 = 48 , which of 11 Jun 2025, 02:27
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post


Above is one way to solve this question

One important inference for me was that b has to be a 3-multiple here, given the integer constraints. We can use this information to figure out the possible values of "a" and "b" as shown. We can keep iterating till we arrive at a value of "a" that is in the options. Here the second iteration with \(b^2\) = 9 gave us "2" as a possible "a" value. Which is choice E.

---
Harsha
Show Spoiler
Attachment:
GMAT-Club-Forum-vh0iehew.png
GMAT-Club-Forum-vh0iehew.png [ 192.38 KiB | Viewed 2041 times ]
User avatar
Rohit_842
User avatar
Joined: 01 Feb 2024
Last visit: 23 Apr 2026
Posts: 118
Own Kudos:
33
Given Kudos: 117
Posts: 118
Kudos: 33
If a and b are integers, and if 3 ( a b ) 2 + 5 b 2 = 48 , which of 13 Jun 2025, 06:14
Kudos
Add Kudos
Bookmarks
Bookmark this Post
HarshavardhanR

How did you get (a-b)^2 values as 16, 1 and so on

HarshavardhanR


Above is one way to solve this question

One important inference for me was that b has to be a 3-multiple here, given the integer constraints. We can use this information to figure out the possible values of "a" and "b" as shown. We can keep iterating till we arrive at a value of "a" that is in the options. Here the second iteration with \(b^2\) = 9 gave us "2" as a possible "a" value. Which is choice E.

---
Harsha
Show Spoiler
Attachment:
GMAT-Club-Forum-vh0iehew.png
Show more
User avatar
HarshavardhanR
User avatar
Joined: 16 Mar 2023
Last visit: 22 Apr 2026
Posts: 488
Own Kudos:
576
 [1]
Given Kudos: 67
Status:Independent GMAT Tutor
Affiliations: Ex - Director, Subject Matter Expertise at e-GMAT
Products:
GMAT Club Tests
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 488
Kudos: 576
 [1]
If a and b are integers, and if 3 ( a b ) 2 + 5 b 2 = 48 , which of 13 Jun 2025, 07:21
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hey Rohit,

I am using the original equation -> 3 \((a-b)^2\) + \(5b^2\) = 48

(1) When \(b^2\) = 0

3 \((a-b)^2\) + 0 = 48

=> \((a-b)^2\) = 16

(2) When \(b^2\) = 9

3 \((a-b)^2\) + 45 = 48

=> \((a-b)^2\) = 1

Hope this helps.

---
Harsha
Rohit_842
HarshavardhanR

How did you get (a-b)^2 values as 16, 1 and so on

HarshavardhanR


Above is one way to solve this question

One important inference for me was that b has to be a 3-multiple here, given the integer constraints. We can use this information to figure out the possible values of "a" and "b" as shown. We can keep iterating till we arrive at a value of "a" that is in the options. Here the second iteration with \(b^2\) = 9 gave us "2" as a possible "a" value. Which is choice E.

---
Harsha
Show Spoiler
Attachment:
GMAT-Club-Forum-vh0iehew.png
Show more
User avatar
N0BU
User avatar
Joined: 04 Aug 2024
Last visit: 28 Mar 2026
Posts: 28
Own Kudos:
16
 [2]
Given Kudos: 89
Posts: 28
Kudos: 16
 [2]
If a and b are integers, and if 3 ( a b ) 2 + 5 b 2 = 48 , which of 24 Oct 2025, 07:15
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
siddhantvarma
If a and b are integers, and if \(3( a − b )^2 + 5b^2 = 48\) , which of the following could be the value of a ?

(A) - 1
(B) 0
(C) 1
(D) 3
(E) 2
Show more
Sharing a quick solution, let me know if you guys see any caveats in this --

Both (3(a-b)^2) and (5b^2) are either even or odd. Since their sum 48 is even, they must have the same parity.

That forces (b) and (a-b) to be either both even or both odd - in either case (a) is even. So only (a=0) or (a=2) are possible from the list.

Test (a=0): 3b^2+5b^2=8b^2=48 => b^2=6 --- not an integer.

So Answer = 2
Moderators:
Bunuel
Math Expert
109763 posts
Krunaal
Tuck School Moderator
853 posts