The number of integers x such that 0.25 2^x 200, and 2^x + 2

• Numbers

The number of integers x such that 0.25 < 2^x < 200, and 2^x + 2 is perfectly divisible by either 3 or 4, is

Answer

0.25 ≤ 2^x < 200

Possible values of x satisfying the above inequality are –2, –1, 0, 1, 2, 3, 4, 5, 6, 7.

When x = 0, 1, 2, 4 and 6, 2^x + 2 is divisible by 3 or 4.

So, the number of values of x is 5.

The correct answer is 5.