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SAT problem solving explanation

Test 11

9. If x is an integer, which of the following could be x³?

I 1.25 x 1017
II 12.5 x 10-12
III 0.125 x 10-12

A. I only
B. II only
C. I and II only
D. I and III only
E. II and III only

Correct Answer: A

Explanation:

We can shift the decimal points so that we get 125 and a power of ten. 125 is a cube. If the power to which ten is raised is divisible by 3, then that is also a cube.
For statement I we get 125 x 1015 (We have multiplied the 1.25 by 100 and so we must divide 1017 by 100 which means we subtract 2 from the power). For statement II we get 125 x 10-13, and for III we get 125 x 10-15. But in the case of III the answer is a negative power making it a fraction NOT an integer.Only in the case of I is the power divisible by three.

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