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Question:If 2x < 100 and x is an integer, how many of the 2x + 2 integers will be divisible by 3 and by 2? (a) 1 (b) 2 (c) 3 (d) 4 (d) 5 Answer:2^6 = 64 and 2^7 = 128. If 2^x < 100, then the highest x is x = 6
Possible values for x: 0 , 1 , 2 , 3 , 4, , 5 , 6. 2x + 2 can take the values 3 , 4 , 6 , 10 , 18 , 34 , 66 Out of these values, only 6 , 18 and 66 are divisible by 3 and by 2. The correct answer is (c).
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