Question:
The number of integers x such that 0.25 < 2x < 200, and 2x +2 is perfectly divisible by either 3 or 4, is
Correct Answer: 5
$0.25 \leq 2^{x} \leq 200$
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.
The number of values of x is 5
$0.25 \leq 2^{x} \leq 200$
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.
The number of values of x is 5
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