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by Atekihcan » Sun May 05, 2013 8:59 pm
Number of non-zero digits on the right of decimal point in the product (0.0025)(0.025)(0.00025)*10^k is (4 + 3 + 5) = 12

So, minimum possible value of k is 12.

Answer : E
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by GMATGuruNY » Mon May 06, 2013 2:35 am
greenwich wrote: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?

A. -12
B. -6
C. 0
D. 6
E. 12
4.792 * 10 = 47.92
4.792 * 10² = 479.2
4.792 * 10³ = 4792.
For every factor of 10, the decimal point moves ONE PLACE to the right.

(0.0025)(0.025)(0.00025)*10^k.
To clear the decimals here:
The decimal point in the red factor must move 4 PLACES to the right.
The decimal point in the blue factor must move 3 PLACES to the right.
The decimal point in the green factor must move 5 PLACES to the right.
Total places to the right = 4+3+5 = 12.
Thus, the product must be multiplied by a factor of 10 at least 12 TIMES, implying that the LEAST possible value of k = 12.

The correct answer is E.
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by greenwich » Mon May 06, 2013 6:02 pm
What's wrong with A?

(0.0025)(0.025)(0.00025)*10^k.
Total places to the right = -4-3-5 = -12?
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by Atekihcan » Mon May 06, 2013 10:29 pm
greenwich wrote:What's wrong with A?

(0.0025)(0.025)(0.00025)*10^k.
Total places to the right = -4-3-5 = -12?
Let's just take a small example.
If (0.1)*(10^k) is an integer, what is the minimum possible value of k?
We need to shift the decimal point to the right by one place to make it integer.
So, minimum possible value of k is 1.
So, (0.1)*(10) = 1 ---> Integer

Now, by your logic, if k = -1, let's see what happens...
So, (0.1)*(10^(-1)) = (0.1)/(10) = 0.01 ---> We have shifted the decimal point to the left by one place and made the number a smaller decimal.

Hope that helps.
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