It is currently 15 Nov 2018, 02:05

### 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

# −1 < a − b < 10, with b an integer such that −3 ≤ b ≤ 1. Wha

Author Message
TAGS:
GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4710
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 90

Kudos [?]: 1606 [0], given: 375

−1 < a − b < 10, with b an integer such that −3 ≤ b ≤ 1. Wha [#permalink]  17 Mar 2018, 07:26
Expert's post
00:00

Question Stats:

0% (00:00) correct 100% (02:10) wrong based on 5 sessions
−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

Drill 2
Question: 5
Page: 497
[Reveal] Spoiler: OA

_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4710
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 90

Kudos [?]: 1606 [0], given: 375

Re: −1 < a − b < 10, with b an integer such that −3 ≤ b ≤ 1. Wha [#permalink]  18 Mar 2018, 07:00
Expert's post
Explanation

If a range of values for a can be found, then the range of values for $$a^2$$ can be found.

Start by testing the end values of b, –3 and 1.

Plug in –3 for b in the first given inequality then solve for a.

You find that –4 < a < 7. If b = 1, 0 < a <11; b could be any integer in the range –3 ≤ b ≤ 1, this means –4 < a < 11 overall.
Remember to take the last step, though!
The question is looking for the range of $$a^2$$, not a; $$a^2$$ is always positive (i.e., $$0 < a^2$$).
Because a < 11, $$a^2 < 121$$.

This means $$0 < a^2 < 121$$; the answer is choice (D).
_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

Manager
Joined: 15 Feb 2018
Posts: 53
Followers: 1

Kudos [?]: 17 [0], given: 33

Re: −1 < a − b < 10, with b an integer such that −3 ≤ b ≤ 1. Wha [#permalink]  22 Mar 2018, 00:52
I don't understand how the answer can be D.

If b = -3 then we have -4 < a < 7.

If b = 1 then we have 0 < a < 11.

So - 4 < a < 11.

Squaring the inequality yields, 16 < a^{2} < 121.

a^{2} > 16 > 0.

sandy wrote:
Explanation

If a range of values for a can be found, then the range of values for $$a^2$$ can be found.

Start by testing the end values of b, –3 and 1.

Plug in –3 for b in the first given inequality then solve for a.

You find that –4 < a < 7. If b = 1, 0 < a <11; b could be any integer in the range –3 ≤ b ≤ 1, this means –4 < a < 11 overall.
Remember to take the last step, though!
The question is looking for the range of $$a^2$$, not a; $$a^2$$ is always positive (i.e., $$0 < a^2$$).
Because a < 11, $$a^2 < 121$$.

This means $$0 < a^2 < 121$$; the answer is choice (D).
GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4710
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 90

Kudos [?]: 1606 [1] , given: 375

Re: −1 < a − b < 10, with b an integer such that −3 ≤ b ≤ 1. Wha [#permalink]  22 Mar 2018, 01:55
1
KUDOS
Expert's post
Put a=0 and b=0.

Now $$-1< a-b <10$$ is true as $$-1< 0 <10$$ holds true.

Also $$-3 \leq b \leq 1$$ holds true as $$-3 \leq 0 \leq 1$$ is true.

So clearly $$a^2$$ can have values less than 16.

Vizualize this: even though $$a>-4$$ and squaring both sides yields $$a^2>16$$ but a can take values such as 0 1, 2, .... so squaring would have values less than 16.
_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

Re: −1 < a − b < 10, with b an integer such that −3 ≤ b ≤ 1. Wha   [#permalink] 22 Mar 2018, 01:55
Display posts from previous: Sort by