Last visit was: 22 Apr 2026, 23:26 It is currently 22 Apr 2026, 23:26
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: 22 Apr 2026
Posts: 109,763
Own Kudos:
810,702
 [18]
Given Kudos: 105,850
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,763
Kudos: 810,702
 [18]
−1 < a − b < 10, with b an integer such that −3 ≤ b ≤ 1. What most acc 13 Jun 2018, 11:26
1
Kudos
Add Kudos
17
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
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:

58% (02:06) correct 42% (02:04) wrong based on 516 sessions

History

Date
Time
Result
Not Attempted Yet
−1 < a − b < 10, with b an integer such that −3 ≤ b ≤ 1. What most accurately describes the range of \(a^2\) ?


A. −16 < a^2 < 11

B. −4 < a^2 < 11

C. 0 < a^2 < 16

D. 0 < a^2 < 121

E. 16 < a^2 < 121
ShowHide Answer
Official Answer
D
avatar
Sri21
avatar
Joined: 27 Oct 2016
Last visit: 10 Sep 2018
Posts: 8
Own Kudos:
9
 [2]
Given Kudos: 54
Posts: 8
Kudos: 9
 [2]
−1 < a − b < 10, with b an integer such that −3 ≤ b ≤ 1. What most acc 13 Jun 2018, 12:03
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
IMO D
For b=-3 ; -1<a+3<10
-4<a<7 , so a^2 =0,1,4,9,16,25,36
For b=-2 ; -1<a+2<10
-3<a<8 , so a^2 =0,1,4,9,16,25,36,49
b=-1; -1<a+1<10
-1<a<9 , so a^2 =0,1,4,9,16 ,25,36,49,64
b=0 ; -1<a<10
so a^2 =0,1,4,9,16,25,36,49,64,81
b=1; -1<a-1<10
0<a<11 so a^2 =0,1,4,9,16,25,36,49,64,81,100
Option D has possible range values for a^2
User avatar
gmatzpractice
User avatar
Joined: 07 Feb 2017
Last visit: 25 Nov 2024
Posts: 122
Own Kudos:
82
Given Kudos: 11
GMAT 1: 710 Q48 V40
GMAT 1: 710 Q48 V40
Posts: 122
Kudos: 82
−1 < a − b < 10, with b an integer such that −3 ≤ b ≤ 1. What most acc 13 Jun 2018, 14:35
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Test the end cases
b = -3
a - b = -1 = a+3; a=-4
a - b = 10 = a+3; a=7
b = 1
a - b = -1 = a-1; a= 0
a - b = 10 = a-1; a=11

0 < a^2 < 121
User avatar
JeffTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 04 Mar 2011
Last visit: 05 Jan 2024
Posts: 2,974
Own Kudos:
8,710
 [3]
Given Kudos: 1,646
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Expert
Expert reply
Posts: 2,974
Kudos: 8,710
 [3]
−1 < a − b < 10, with b an integer such that −3 ≤ b ≤ 1. What most acc 17 Jun 2018, 19:48
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
−1 < a − b < 10, with b an integer such that −3 ≤ b ≤ 1. What most accurately describes the range of \(a^2\) ?


A. −16 < a^2 < 11

B. −4 < a^2 < 11

C. 0 < a^2 < 16

D. 0 < a^2 < 121

E. 16 < a^2 < 121
Show more

Since b is an integer between -3 and 1, inclusive, b could be -3, -2, -1, 0 or 1.We only need to test the two extreme values of b, that is, b = -3 and b = 1:

If b = -3, then we have

-1 < a - (-3) < 10

-1 < a + 3 < 10

-4 < a < 7

0 ≤ a^2 < 49 (note: since a could be 0, the minimum value of a^2 is 0, not 16.)

If b = 1, then we have

-1 < a - 1 < 10

0 < a < 11

0 < a^2 < 121

So we see that a^2 can be almost as large as 121 and almost as small as 0 (a^2 can’t be exactly 0 since when b = 1, a can’t be exactly 0).

Answer: D
User avatar
blueviper
User avatar
Joined: 16 Jan 2018
Last visit: 01 Nov 2022
Posts: 81
Own Kudos:
164
 [4]
Given Kudos: 100
Location: New Zealand
Posts: 81
Kudos: 164
 [4]
−1 < a − b < 10, with b an integer such that −3 ≤ b ≤ 1. What most acc 23 Jul 2018, 11:52
4
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
−1 < a − b < 10, with b an integer such that −3 ≤ b ≤ 1. What most accurately describes the range of \(a^2\) ?


A. −16 < a^2 < 11

B. −4 < a^2 < 11

C. 0 < a^2 < 16

D. 0 < a^2 < 121

E. 16 < a^2 < 121
Show more


To find range of an inequality, we need to take the extreme values of the equation −3 ≤ b ≤ 1; which are -3 & 1


Case 1; b = -3

-1 < a - (-3) < 10 which gives

-4 < a < 7 (Squaring the inequality)

16 < a^2 < 49



Case 2; b = 1

-1 < a - (1) < 10 which gives

0 < a < 11 (Squaring the inequality)

0 < a^2 < 121


So, we need to take the extreme values to find the range and can conclude that range = 0 < a^2 < 121 Option D is the right answer.
User avatar
Akarsh97
User avatar
Joined: 28 Mar 2025
Last visit: 25 Mar 2026
Posts: 80
Own Kudos:
6
Given Kudos: 353
Posts: 80
Kudos: 6
−1 < a − b < 10, with b an integer such that −3 ≤ b ≤ 1. What most acc 12 May 2025, 02:26
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Wanted to mention a point

Squaring of an inequality is not same as normal expression

if -4 < a
0 < a^2

why?
ohk lets consider, a to be -1 (> -4)

and on squaring it becomes, a^2 = 1

Likewise,
if -4 < a < 11

then a^2 be, 0 < a^2 < 121
Moderators:
Bunuel
Math Expert
109763 posts
Krunaal
Tuck School Moderator
853 posts