Source: Official Guide for GMAT Review 2016 Problem Solving; #67

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# If k is an integer and (0.0025)( 0.025)( 0.00025) × 10^k is an integer

If k is an integer and (0.0025)( 0.025)( 0.00025) × 10^k is an integer, what is the least possible value of k?

### 1 Explanation

1

i got A.
pls. assist me to understand how it is E. Am surprised.

Nov 28, 2016 • Comment

Cydney Seigerman, Magoosh Tutor

Hi Amure :)

Happy to help!

First, let's rewrite the three given values as integers raised to powers of ten:

0.0025 = 25*10^-4
0.025 = 25*10^-3
0.00025 = 25*10^-5

(0.0025)(0.025)(0.00025)
= (25*10^-4)(25*10^-3)(25*10^-5)
= (25^3)*10^(-12)

Written this way, we can see that in order for the product to be an integer, k must be equal to at least the positive of the power to which 10 is raised (-12). That way, the product will be an integer. If k is less than 12, then the product will not be an integer.

(25^3)*10^(-12)*10^k = integer
(25^3)*10^(-12)*10^12 = 25^3*10^0 = 25^3

Therefore, k must be at least 12 (answer E).

Hope this clears up your doubts :)