How many integers n are there such thatandminus;145 andlt; andminus;-n2- andlt; andminus;120?a)0b)2c)4d)11e)12Correct answer is option 'C'. Can you explain this answer?

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How many integers n are there such that −145 < −|n²| < −120?

a)
0
b)
2
c)
4
d)
11
e)
12

Correct answer is option 'C'. Can you explain this answer?

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How many integers n are there such that−145 < −|n2| <...

To make things a little easier on our brains, we can take the given inequality −145 < −|n²| < −120...
...and multiply all sides by -1 to get: 145 > |n²| > 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 n² = 121 and there are two values of n such that n² = 144
If n²= 121, then n = 11 or n = −11
If n² = 144, then n = 12 or n = −12
So, there are FOUR possible values of n that satisfies the given conditions.

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How many integers n are there such that−145 < −|n2| < −120?a)0b)2c)4d)11e)12Correct answer is option 'C'. Can you explain this answer?

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