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

Question

If the units digit of  \frac{5,610.37}{10^k}  is 6, what is the value of k?

(A) 3
(B) 2
(C) 1
(D) -1
(E) -2

PS81711.02

BrentGMATPrepNow · Accepted Answer

Useful property:  x^{-n}=\frac{1}{x^n}

We can also write the property in reverse order:    \frac{1}{x^n}= x^{-n}

This means we can take:  \frac{5,610.37}{10^k}  and rewrite it as:  5,610.37 	imes 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 	imes 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 	imes 10^{-2} = 56.1037

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

Answer: B

Cheers, 
Brent

ScottTargetTestPrep · Answer

If we move the decimal point of 5610.37 two places to the left, then the resulting number will be 56.1037, which has a units digit of 6.

We see that if k = 2, then 5610.37 / 10^2 = 56.1037 has a units digit of 6. So k must be 2.

Answer: B

yashikaaggarwal · Answer

Not sure but I guess the units tens hundred digit is countable before decimals only.
So answer is supposedly 2=k
5610.37 {here unit digit is 0}
In order to make 6 as unit digit we need 100 in denominator
So, 5610.37/100=56.1037
100=10^k
10^2=10^k
K=2
IOC is B

Posted from my mobile device

SameerGupta2001 · Answer

Since the Denominator is 10 raised to power k 
From identity of exponents number raised to power of 10 in denominator , the decimal points shifted towards left of the numerator
Similarly, if multiplied by 10 raised to some number, the decimal point shifted towards right.
 So answer is (B)=2

randomavoidplease · Answer

Without doing any math, since we are told of unit digit which we will get if the decimal point was moved 2 spaces to the left. Thus the answer should be B - 2 .

Archit3110 · Answer

we can re write the expression  \frac{5,610.37}{10^k} 
 \frac{5,61037}{10^ (k+2)} 
since unit digit we get is 6 ; so k has to be 2
OPTION B ; 2

perfectreview · Answer

This is a simple question.

If the decimal has to be right next to 6. Then the decimal has to shift left. If the decimal has to shift left then the value of k has to be negative.

In this option D and option E are eliminated.

If you observe the decimal has to shift left twice, in that case the value of k has to be negative 2.

OR

If we have to solve mathematically

5610.37 x  10^{-k}  = 56.1037

\frac{561037}{100}  x  10^{-k}  =  \frac{561037}{10000}

10^{-k}  =  \frac{1}{100}

10^{-k}  =  10^{-2}

therefore -k = -2 => k = 2

GMATinsight · Answer

Answer: Option B

Video solution by  GMATinsight

https://www.youtube.com/watch?v=pVInIdiDzI8

bumpbot · Answer

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

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

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