GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 03 Jul 2020, 22:52

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 04 Sep 2017
Posts: 318
If the units digit of 5,610.37/10^k is 6, what is the value of k?  [#permalink]

### Show Tags

20 Apr 2020, 10:57
1
4
00:00

Difficulty:

15% (low)

Question Stats:

71% (00:42) correct 29% (00:56) wrong based on 258 sessions

### HideShow timer Statistics

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
GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4952
GMAT 1: 770 Q49 V46
Re: If the units digit of 5,610.37/10^k is 6, what is the value of k?  [#permalink]

### Show Tags

30 Apr 2020, 09:28
3
Top Contributor
1
gmatt1476 wrote:
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

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: $$5,610.37 \times 10^{-k}$$

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

In other words: $$5,610.37 \times 10^{-k} = 56.1037$$

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: $$5,610.37 \times 10^{-2} = 56.1037$$

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

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
##### General Discussion
PS Forum Moderator
Joined: 18 Jan 2020
Posts: 988
Location: India
GPA: 4
Re: If the units digit of 5,610.37/10^k is 6, what is the value of k?  [#permalink]

### Show Tags

20 Apr 2020, 11:05
Not sure but I guess the units tens hundred digit is countable before decimals only.
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
Intern
Joined: 05 Apr 2020
Posts: 10
Re: If the units digit of 5,610.37/10^k is 6, what is the value of k?  [#permalink]

### Show Tags

20 Apr 2020, 11:07
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.
Intern
Joined: 02 Mar 2020
Posts: 43
Re: If the units digit of 5,610.37/10^k is 6, what is the value of k?  [#permalink]

### Show Tags

20 Apr 2020, 11:42
gmatt1476 wrote:
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

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 .
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 6416
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
If the units digit of 5,610.37/10^k is 6, what is the value of k?  [#permalink]

### Show Tags

21 Apr 2020, 09:04
gmatt1476 wrote:
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

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
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 11009
Location: United States (CA)
Re: If the units digit of 5,610.37/10^k is 6, what is the value of k?  [#permalink]

### Show Tags

13 May 2020, 06:24
1
gmatt1476 wrote:
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

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.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
225 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

Intern
Joined: 30 May 2020
Posts: 19
Re: If the units digit of 5,610.37/10^k is 6, what is the value of k?  [#permalink]

### Show Tags

30 May 2020, 20:11
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
_________________
Founder
Perfect Review
http://www.perfectreview.co.in
Re: If the units digit of 5,610.37/10^k is 6, what is the value of k?   [#permalink] 30 May 2020, 20:11