If N is a prime number and 9N is less than 180 and greater than 81 then 13N -…

Explanation:

Given:

N is a prime number.
9N is greater than 81 and less than 180.

This can be written as:

81 < 9N < 180

Divide the entire inequality by 9:

9 < N < 20

The prime numbers lying between 9 and 20 are:

11, 13, 17, and 19.

Now evaluate 13N − 7 for each possible value of N:

If N = 11, then 13N − 7 = 13 × 11 − 7 = 143 − 7 = 136.
If N = 13, then 13N − 7 = 13 × 13 − 7 = 169 − 7 = 162.
If N = 17, then 13N − 7 = 13 × 17 − 7 = 221 − 7 = 214.
If N = 19, then 13N − 7 = 13 × 19 − 7 = 247 − 7 = 240.

Among the given options, 162 is the only possible value.

Hence, the correct answer is 162.