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

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

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New post 20 Mar 2020, 03:41
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A
B
C
D
E

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  55% (hard)

Question Stats:

52% (01:14) correct 48% (01:09) wrong based on 94 sessions

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Re: How many integers n are there such that -145 < -|n^2| < -120 ?  [#permalink]

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New post 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
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How many integers n are there such that -145 < -|n^2| < -120 ?  [#permalink]

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New post 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
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How many integers n are there such that -145 < -|n^2| < -120 ?  [#permalink]

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New post 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

Answer: C

Cheers,
Brent
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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.
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Re: How many integers n are there such that -145 < -|n^2| < -120 ?  [#permalink]

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New post 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)
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Re: How many integers n are there such that -145 < -|n^2| < -120 ?   [#permalink] 21 Mar 2020, 10:15

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

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