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OG: If the units digit of 5,610.37/(10^k) is 6, what is the value of k?

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Re: OG: If the units digit of 5,610.37/(10^k) is 6, what is the value of k?

by Brent@GMATPrepNow » Mon May 18, 2020 6:22 am
AbeNeedsAnswers wrote: ↑
Sun May 17, 2020 8:20 pm
 If the units digit of 5,610.37/(10^k) is 6, what is the value of k?

A. 3
B. 2
C. 1
D. -1
E. -2

B
Useful property: x^(-n) = 1/(x^n)
We can also write the property in reverse order: 1/(x^n) = x^(-n)

This means we can take: 5,610.37/10^k and rewrite it as: 5,610.37 x 10^(-k)

Since we want the unit's digit to be 6, we want our resulting decimal to be 56.1037

In other words: 5,610.37 x 10^(-k) = 56.1037

So our goal is to move the decimal place two spaces to the left.

We can accomplish this by multiplying 5,610.37 by 10^(-2)

In other words: 5,610.37 x 10^(-2) = 56.1037

From this we can conclude: -k = -2, which means k = 2

Answer: B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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