GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 09 Dec 2018, 12:20

### 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

## Events & Promotions

###### Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### Free GMAT Algebra Webinar

December 09, 2018

December 09, 2018

07:00 AM PST

09:00 AM PST

Attend this Free Algebra Webinar and learn how to master Inequalities and Absolute Value problems on GMAT.
• ### Free lesson on number properties

December 10, 2018

December 10, 2018

10:00 PM PST

11:00 PM PST

Practice the one most important Quant section - Integer properties, and rapidly improve your skills.

# If d=1/(2^3*5^7) is expressed as a terminating decimal, how

Author Message
TAGS:

### Hide Tags

Manager
Joined: 02 Dec 2012
Posts: 177
If d=1/(2^3*5^7) is expressed as a terminating decimal, how  [#permalink]

### Show Tags

20 Dec 2012, 05:11
11
89
00:00

Difficulty:

65% (hard)

Question Stats:

57% (01:07) correct 43% (01:21) wrong based on 2360 sessions

### HideShow timer Statistics

If d=1/(2^3*5^7) is expressed as a terminating decimal, how many nonzero digits will d have?

(A) One
(B) Two
(C) Three
(D) Seven
(E) Ten
Math Expert
Joined: 02 Sep 2009
Posts: 51035
Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how  [#permalink]

### Show Tags

20 Dec 2012, 05:12
57
45
If d=1/(2^3*5^7) is expressed as a terminating decimal, how many nonzero digits will d have?

(A) One
(B) Two
(C) Three
(D) Seven
(E) Ten

Given: $$d=\frac{1}{2^3*5^7}$$.

Multiply by $$\frac{2^4}{2^4}$$ --> $$d=\frac{2^4}{(2^3*5^7)*2^4}=\frac{2^4}{2^7*5^7}=\frac{2^4}{10^7}=\frac{16}{10^7}=0.0000016$$. Hence $$d$$ will have two non-zero digits, 16, when expressed as a decimal.

_________________
Intern
Joined: 24 Aug 2013
Posts: 5
Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how  [#permalink]

### Show Tags

27 May 2014, 02:29
7
Another approach:

$$\frac{1}{(2^3*5^7)}$$ =$$\frac{1}{(2^3*5^3*5^4)}$$ by splitting denominator.

= $$\frac{1}{(10^3*5^4)}$$ = $$\frac{10^{-3}}{5^4}$$

Representing numerator as$$\frac{(10^4*10^{-7})}{5^4}$$ = $$2^4*10^{-7}$$ = $$16*10^{-7}$$

=.0000016 , Hence 2 digits.

##### General Discussion
Intern
Joined: 19 Oct 2013
Posts: 9
Location: United States
Concentration: Finance, Technology
GMAT Date: 11-06-2013
GPA: 3.5
WE: Engineering (Investment Banking)
Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how  [#permalink]

### Show Tags

24 Oct 2013, 02:15
1/2^3*5^7 = 2^-3*5^-7 =.002 * .0000007. So there are 2 non zero digits!!
Math Expert
Joined: 02 Sep 2009
Posts: 51035
Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how  [#permalink]

### Show Tags

24 Oct 2013, 02:28
5
1
Puneethrao wrote:
1/2^3*5^7 = 2^-3*5^-7 =.002 * .0000007. So there are 2 non zero digits!!

Unfortunately this is not correct:

$$2^{-3}=\frac{1}{8}=0.125$$ not 0.002, which is 2/10^3 and $$5^{-7}=\frac{1}{78,125}=0.0000128$$ not 0.0000007, which is 7/10^7.

Hope it helps.
_________________
Intern
Joined: 19 Oct 2013
Posts: 9
Location: United States
Concentration: Finance, Technology
GMAT Date: 11-06-2013
GPA: 3.5
WE: Engineering (Investment Banking)
Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how  [#permalink]

### Show Tags

24 Oct 2013, 02:53
Bunuel wrote:
Puneethrao wrote:
1/2^3*5^7 = 2^-3*5^-7 =.002 * .0000007. So there are 2 non zero digits!!

Unfortunately this is not correct:

$$2^{-3}=\frac{1}{8}=0.125$$ not 0.002, which is 2/10^3 and $$5^{-7}=\frac{1}{78,125}=0.0000128$$ not 0.0000007, which is 7/10^7.

Hope it helps.

Thanks a lot!! I don't know what i was thinking , such a stupid mistake!! Thanks once again!
Manager
Joined: 13 Jul 2013
Posts: 66
GMAT 1: 570 Q46 V24
Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how  [#permalink]

### Show Tags

29 Dec 2013, 11:57
Bunuel wrote:
If d=1/(2^3*5^7) is expressed as a terminating decimal, how many nonzero digits will d have?

(A) One
(B) Two
(C) Three
(D) Seven
(E) Ten

Given: $$d=\frac{1}{2^3*5^7}$$.

Multiply by $$\frac{2^4}{2^4}$$ --> $$d=\frac{2^4}{(2^3*5^7)*2^4}=\frac{2^4}{2^7*5^7}=\frac{2^4}{10^7}=\frac{16}{10^7}=0.0000016$$. Hence $$d$$ will have two non-zero digits, 16, when expressed as a decimal.

I have seen couple of more problem like this. One thing is still not clear to me. When you multiply whole denominator by 2^4 why is 5^7 getting ignored? Shouldn't 2^4 multiply both 2^3 as well as 5^7?

Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 51035
Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how  [#permalink]

### Show Tags

29 Dec 2013, 12:00
2
theGame001 wrote:
Bunuel wrote:
If d=1/(2^3*5^7) is expressed as a terminating decimal, how many nonzero digits will d have?

(A) One
(B) Two
(C) Three
(D) Seven
(E) Ten

Given: $$d=\frac{1}{2^3*5^7}$$.

Multiply by $$\frac{2^4}{2^4}$$ --> $$d=\frac{2^4}{(2^3*5^7)*2^4}=\frac{2^4}{2^7*5^7}=\frac{2^4}{10^7}=\frac{16}{10^7}=0.0000016$$. Hence $$d$$ will have two non-zero digits, 16, when expressed as a decimal.

I have seen couple of more problem like this. One thing is still not clear to me. When you multiply whole denominator by 2^4 why is 5^7 getting ignored? Shouldn't 2^4 multiply both 2^3 as well as 5^7?

Thanks

Frankly, the red part does not make any sense...

The denominator is $$2^7*5^7$$. Multiply it by $$2^4$$. What do you get?
_________________
Intern
Joined: 29 Jan 2014
Posts: 1
Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how  [#permalink]

### Show Tags

11 Mar 2014, 15:54
Bunuel wrote:
If d=1/(2^3*5^7) is expressed as a terminating decimal, how many nonzero digits will d have?

(A) One
(B) Two
(C) Three
(D) Seven
(E) Ten

Given: $$d=\frac{1}{2^3*5^7}$$.

Multiply by $$\frac{2^4}{2^4}$$ --> $$d=\frac{2^4}{(2^3*5^7)*2^4}=\frac{2^4}{2^7*5^7}=\frac{2^4}{10^7}=\frac{16}{10^7}=0.0000016$$. Hence $$d$$ will have two non-zero digits, 16, when expressed as a decimal.

What is it that you saw that indicated you should multiply by 2^4. Just looking at the problem that never occurred to me and I'd like to understand why it did to you.
Math Expert
Joined: 02 Sep 2009
Posts: 51035
Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how  [#permalink]

### Show Tags

11 Mar 2014, 22:36
1
1
WinterIsComing wrote:
Bunuel wrote:
If d=1/(2^3*5^7) is expressed as a terminating decimal, how many nonzero digits will d have?

(A) One
(B) Two
(C) Three
(D) Seven
(E) Ten

Given: $$d=\frac{1}{2^3*5^7}$$.

Multiply by $$\frac{2^4}{2^4}$$ --> $$d=\frac{2^4}{(2^3*5^7)*2^4}=\frac{2^4}{2^7*5^7}=\frac{2^4}{10^7}=\frac{16}{10^7}=0.0000016$$. Hence $$d$$ will have two non-zero digits, 16, when expressed as a decimal.

What is it that you saw that indicated you should multiply by 2^4. Just looking at the problem that never occurred to me and I'd like to understand why it did to you.

We need to multiply by 2^6/2^6 in order to convert the denominator to the base of 10 and then to convert the fraction into the decimal form: 0.xxxx.

Similar questions to practice:
if-t-1-2-9-5-3-is-expressed-as-a-terminating-decimal-ho-129447.html
if-d-1-2-3-5-7-is-expressed-as-a-terminating-decimal-128457.html

Hope this helps.
_________________
Intern
Joined: 31 Oct 2015
Posts: 33
Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how  [#permalink]

### Show Tags

05 Jan 2016, 06:03
2^7 * 1/(10^7) * 2^-3 = 2^4 * 1/(10^7) = 16/10000000 = .000000016

Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how  [#permalink]

### Show Tags

23 Jun 2016, 08:38
5
4
If d=1/(2^3*5^7) is expressed as a terminating decimal, how many nonzero digits will d have?

(A) One
(B) Two
(C) Three
(D) Seven
(E) Ten

Since actually dividing 1/(2^3*5^7) would be time consuming, we want to manipulate d so that we are working with a cleaner denominator. The easiest way to do that is to multiply d by a value that will produce a perfect power of 10 in the denominator. This means that the number of 2s in the denominator will equal the number of 5s in the denominator.

Thus, we can multiply 1/(2^3*5^7) by 2^4/2^4. This gives us:

2^4/(2^7*5^7)

2^4/10^7

16/10^7

16/10,000,000

We can stop here because we know that the 10,000,000 in the denominator means to move the decimal place after the 16 seven places to the left. The final value of d will be 0.0000016. Note that the division of 16 by 10,000,000 did not produce any additional non-zero digits. Thus d has 2 non-zero digits.

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4271
Location: India
GPA: 3.5
Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how  [#permalink]

### Show Tags

23 Jun 2016, 10:35
1
If d=1/(2^3*5^7) is expressed as a terminating decimal, how many nonzero digits will d have?

(A) One
(B) Two
(C) Three
(D) Seven
(E) Ten

$$d$$ = $$\frac{1}{(2^3*5^7)}$$

=>$$d$$ = $$\frac{1}{(2^3*5^3*5^4)}$$

=>$$d$$ = $$\frac{1}{(10^3*5^4)}$$

$$\frac{1}{5}$$ = $$0.20$$

$$\frac{1}{25}$$ = $$\frac{0.20}{5}$$ => $$0.04$$

$$\frac{1}{125}$$ = $$\frac{0.04}{5}$$ => $$0.008$$

$$\frac{1}{625}$$ = $$\frac{0.008}{5}$$ => $$0.0016$$

Hence there will be 2 non zero digits...

Feel free to revert in case of any doubt ( I have used some shortcuts , would love to explain if needed )

_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Manager
Joined: 24 May 2014
Posts: 87
Location: India
GMAT 1: 590 Q39 V32
GRE 1: Q159 V151

GRE 2: Q159 V153
GPA: 2.9
Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how  [#permalink]

### Show Tags

12 Sep 2016, 07:11
I solved the question in the following method, not sure whether it is correct:

1/2^3 x 5^7 = 1/2^3 x 5^3 [Equating the power of 2 & 5 to get the number of zeros], left with 1/5^4 = 1/625 = 0.00105. Only 1 & 5 are the non-zero digits.
Manager
Joined: 24 Aug 2016
Posts: 68
Location: India
WE: Information Technology (Computer Software)
If d=1/(2^3*5^7) is expressed as a terminating decimal, how  [#permalink]

### Show Tags

12 Sep 2016, 07:23
I did it this way.

d = $$\frac{1}{8*25*25*25*5}$$ = $$\frac{4*4*4*2}{8*100*100*100*10}$$ = 16 * 10 ^ -6 ==> 2 non zero digits.
_________________

"If we hit that bullseye, the rest of the dominos will fall like a house of cards. Checkmate."

Intern
Status: Studying for GMAT (April '19)
Joined: 15 Jan 2017
Posts: 11
Location: United Kingdom
Concentration: Finance, General Management
GPA: 3.5
If d=1/(2^3*5^7) is expressed as a terminating decimal, how  [#permalink]

### Show Tags

25 Jan 2017, 12:45
(First ever post!)

I realise I'm a little late submitting my answer here, but my answer was 2 non-zero digits: 2 & 5.

My answer is based on the following:

1 / (2^3*5^7) = 1 / (2*(2^2))*(5^7) =
1 / (4x10^7) =
25 x 10^8 .

I'm guessing my mistake was in factoring the denominator, specifically factoring of 2^3 as 2x2^2?

Any input greatly appreciated,

Ben

EDIT:

Not to worry, I've gone over some other exponent materials and came up with the correct solution.
Director
Joined: 02 Sep 2016
Posts: 683
If d=1/(2^3*5^7) is expressed as a terminating decimal, how  [#permalink]

### Show Tags

01 Apr 2017, 05:35
d=1/(2^3*5^7)

2*5=10 (Happy to know in such questions!!)
Write 2^3*5^3 together. (This will be equal to 2*2*2*5*5*5= 10^3)

d= 1/(10^3)(5^4)
d= [1/(10^3)] *(0.2)^4
d=[1/(10^3)] *(1.6)

Thus the non-zero digits in the final answer would be 2 i.e. 1 and 6.
_________________

Help me make my explanation better by providing a logical feedback.

If you liked the post, HIT KUDOS !!

Don't quit.............Do it.

Manager
Joined: 13 Dec 2013
Posts: 156
Location: United States (NY)
GMAT 1: 710 Q46 V41
GMAT 2: 720 Q48 V40
GPA: 4
WE: Consulting (Consulting)
Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how  [#permalink]

### Show Tags

29 Apr 2017, 10:47
1/[(2^3)(5^7)] = 1/(10^3)(5^4)
1/(10^3)=0.001
0.001/(5^4)=0.0000016
Intern
Joined: 25 Mar 2017
Posts: 1

### Show Tags

27 May 2017, 06:17
Split the two fraction 1/2^7 * 1/5^7
1/5^7 = (1/5)^7 = 0.2^7 = (2*10^-1)^7 = 2^7 * 10^-7
Multiply by 1/2^3 now you get:
2^7/2^3 * 10^-7 = 2^4 * 10^-7 = 16*10^-7

The two non zero digits are then 1 and 6.
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4271
Location: India
GPA: 3.5
Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how  [#permalink]

### Show Tags

27 May 2017, 07:15
narendran1990 wrote:
I solved the question in the following method, not sure whether it is correct:

1/2^3 x 5^7 = 1/2^3 x 5^3 [Equating the power of 2 & 5 to get the number of zeros], left with 1/5^4 = 1/625 = 0.00105. Only 1 & 5 are the non-zero digits.

Check the highlighted part

$$\frac{1}{625} = 0.0016$$

There will be 2 non zero digits...

_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how &nbs [#permalink] 27 May 2017, 07:15

Go to page    1   2    Next  [ 25 posts ]

Display posts from previous: Sort by