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

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

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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