GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 02 Jun 2020, 10:57

### 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

# How many integers n are there such that -145 < -|n^2| < -120 ?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 64174
How many integers n are there such that -145 < -|n^2| < -120 ?  [#permalink]

### Show Tags

20 Mar 2020, 03:41
00:00

Difficulty:

55% (hard)

Question Stats:

52% (01:13) correct 48% (01:10) wrong based on 85 sessions

### HideShow timer Statistics

How many integers n are there such that $$-145 < -|n^2| < -120$$ ?

A. 0
B. 2
C. 4
D. 11
E. 12

_________________
Director
Joined: 14 Dec 2019
Posts: 666
Location: Poland
GMAT 1: 570 Q41 V27
WE: Engineering (Consumer Electronics)
Re: How many integers n are there such that -145 < -|n^2| < -120 ?  [#permalink]

### Show Tags

20 Mar 2020, 03:57
Bunuel wrote:
How many integers n are there such that $$-145 < -|n^2| < -120$$ ?

A. 0
B. 2
C. 4
D. 11
E. 12

n can be +11, -11, +12, -12

Hence 4 - Answer - C
CEO
Joined: 03 Jun 2019
Posts: 2927
Location: India
GMAT 1: 690 Q50 V34
WE: Engineering (Transportation)
How many integers n are there such that -145 < -|n^2| < -120 ?  [#permalink]

### Show Tags

20 Mar 2020, 04:01
Bunuel wrote:
How many integers n are there such that $$-145 < -|n^2| < -120$$ ?

A. 0
B. 2
C. 4
D. 11
E. 12

Asked: How many integers n are there such that $$-145 < -|n^2| < -120$$ ?

145 > n^2 > 120
120 < n^2 < 145
n^2 = {121, 144}
n = { -12, -11, 11, 12}

IMO C
_________________
Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com
GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4886
GMAT 1: 770 Q49 V46
How many integers n are there such that -145 < -|n^2| < -120 ?  [#permalink]

### Show Tags

Updated on: 11 Apr 2020, 09:37
1
Top Contributor
Bunuel wrote:
How many integers n are there such that $$-145 < -|n^2| < -120$$ ?

A. 0
B. 2
C. 4
D. 11
E. 12

To make things a little easier on our brains, we can take the given inequality $$-145 < -|n^2| < -120$$...
...and multiply all sides by -1 to get: $$145 > |n^2| > 120$$ [aside: Since we multiplied the inequality by a negative value, we reversed the direction of the inequality symbols]
So we're looking for squares of integers BETWEEN 120 and 145.
121 and 144 are the only squares of integers between 120 and 145

However, before we choose answer choice B, we must keep in mind that there are two values of $$n$$ such that $$n^2 = 121$$ and there are two values of $$n$$ such that $$n^2 = 144$$

If $$n^2 = 121$$, then $$n = 11$$ or $$n = -11$$
If $$n^2 = 144$$, then $$n = 12$$ or $$n = -12$$

So, there are FOUR possible values of n that satisfies the given conditions

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com

Originally posted by BrentGMATPrepNow on 20 Mar 2020, 05:01.
Last edited by BrentGMATPrepNow on 11 Apr 2020, 09:37, edited 1 time in total.
Manager
Joined: 21 Jan 2020
Posts: 66
Re: How many integers n are there such that -145 < -|n^2| < -120 ?  [#permalink]

### Show Tags

21 Mar 2020, 10:15
Bunuel wrote:
How many integers n are there such that $$-145 < -|n^2| < -120$$ ?

A. 0
B. 2
C. 4
D. 11
E. 12

4 values are there .

145>|n^2|>120
=> 145>n^2>120 [n^2 will always be positive , so we can remove the mod]

Therefor there are 4 values : -11,-12,11,12 (E)
Re: How many integers n are there such that -145 < -|n^2| < -120 ?   [#permalink] 21 Mar 2020, 10:15