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

 It is currently 21 Oct 2019, 23:56 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  Which of the following is a terminating decimal, when

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Intern  Joined: 24 Jul 2012
Posts: 12
Schools: Schulich '16
GMAT 1: 610 Q49 V26 WE: Consulting (Consulting)
Which of the following is a terminating decimal, when  [#permalink]

Show Tags

1
7 00:00

Difficulty:   15% (low)

Question Stats: 74% (00:57) correct 26% (01:22) wrong based on 348 sessions

HideShow timer Statistics

Which of the following is a terminating decimal, when expressed in decimals?

A. 17/223
B. 13/231
C. 41/3
D. 41/256
E. 35/324

Can we do this just by taking the unit digit in numerator and denominator?

Originally posted by Vamshi8411 on 17 Sep 2012, 06:26.
Last edited by Bunuel on 17 Sep 2012, 06:40, edited 1 time in total.
Edited the question.
Math Expert V
Joined: 02 Sep 2009
Posts: 58404
Re: Which of the following is a terminating decimal, when  [#permalink]

Show Tags

5
4
Vamshi8411 wrote:
Which of the following is a terminating decimal, when expressed in decimals?

A. 17/223
B. 13/231
C. 41/3
D. 41/256
E. 35/324

Can we do this just by taking the unit digit in numerator and denominator?

Reduced fraction $$\frac{a}{b}$$ (meaning that fraction is already reduced to its lowest term) can be expressed as terminating decimal if and only $$b$$ (denominator) is of the form $$2^n5^m$$, where $$m$$ and $$n$$ are non-negative integers. For example: $$\frac{7}{250}$$ is a terminating decimal $$0.028$$, as $$250$$ (denominator) equals to $$2*5^2$$. Fraction $$\frac{3}{30}$$ is also a terminating decimal, as $$\frac{3}{30}=\frac{1}{10}$$ and denominator $$10=2*5$$.

BACK TO THE QUESTION:

$$\frac{41}{256}=\frac{41}{2^8}$$, denominator has only prime factor 2 in its prime factorization, hence this fraction will be terminating decimal.

All other fractions (after reducing, if possible) have primes other than 2 and 5 in its prime factorization, hence they will be repeated decimals.

For more check Number Theory chapter of Math Book: math-number-theory-88376.html

Hope it helps..
_________________
Retired Moderator Joined: 16 Jun 2012
Posts: 988
Location: United States
Re: Which of the following is a terminating decimal, when  [#permalink]

Show Tags

5
1
prateekbhatt wrote:
Is it only limited to 2^m * 5^n or we can try try to break it in 2^m * 3^n as well??

Hi prateekbhatt

The fraction a/b is a terminating fraction only if the denominator b meets any of following conditions

(1) the denominator is a form of 2^n
(2) the denominator is a form of 5^m
(3) the denominator is a form of 2^n*5^m

If the denominator is a form of 2^n*3^m ==> The fraction is not terminating decimal.

Hope it helps.
_________________
Please +1 KUDO if my post helps. Thank you.

"Designing cars consumes you; it has a hold on your spirit which is incredibly powerful. It's not something you can do part time, you have do it with all your heart and soul or you're going to get it wrong."

Chris Bangle - Former BMW Chief of Design.
General Discussion
Director  Status: My Thread Master Bschool Threads-->Krannert(Purdue),WP Carey(Arizona),Foster(Uwashngton)
Joined: 28 Jun 2011
Posts: 809
Re: Which of the following is a terminating decimal, when  [#permalink]

Show Tags

1
Is it only limited to 2^m * 5^n or we can try try to break it in 2^m * 3^n as well??
Math Expert V
Joined: 02 Sep 2009
Posts: 58404
Re: Which of the following is a terminating decimal, when  [#permalink]

Show Tags

prateekbhatt wrote:
Is it only limited to 2^m * 5^n or we can try try to break it in 2^m * 3^n as well??

How can you break 2^m * 5^n into 2^m * 3^n?
_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 58404
Re: Which of the following is a terminating decimal, when  [#permalink]

Show Tags

2
1
pqhai wrote:
prateekbhatt wrote:
Is it only limited to 2^m * 5^n or we can try try to break it in 2^m * 3^n as well??

Hi prateekbhatt

The fraction a/b is a terminating fraction only if the denominator b meets any of following conditions

(1) the denominator is a form of 2^n
(2) the denominator is a form of 5^m
(3) the denominator is a form of 2^n*5^m

If the denominator is a form of 2^n*3^m ==> The fraction is not terminating.

Hope it helps.

That's correct if a/b is already reduced to its lowest term.

The denominator of 3/30 is not a form of 2^n*5^m but 3/30 IS a terminating decimal, because 3 can be reduced.

Questions to pracitice:
does-the-decimal-equivalent-of-p-q-where-p-and-q-are-89566.html
any-decimal-that-has-only-a-finite-number-of-nonzero-digits-101964.html
if-a-b-c-d-and-e-are-integers-and-p-2-a3-b-and-q-2-c3-d5-e-is-p-q-a-terminating-decimal-125789.html
700-question-94641.html
is-r-s2-is-a-terminating-decimal-91360.html
pl-explain-89566.html
which-of-the-following-fractions-88937.html
_________________
Current Student B
Joined: 22 Jul 2014
Posts: 120
Concentration: General Management, Finance
GMAT 1: 670 Q48 V34 WE: Engineering (Energy and Utilities)
Re: Which of the following is a terminating decimal, when  [#permalink]

Show Tags

bumpbot wrote:
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

----------

Is this a 600+ question? Or below 600? SVP  Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1747
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: Which of the following is a terminating decimal, when  [#permalink]

Show Tags

alphonsa wrote:
bumpbot wrote:
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

----------

Is this a 600+ question? Or below 600? This should be a 600+ question; however by perfect method used (as stated by Bunuel) it can be solved in hardly 5 seconds _________________
Kindly press "+1 Kudos" to appreciate Manager  Status: PLAY HARD OR GO HOME
Joined: 25 Feb 2014
Posts: 131
Location: India
Concentration: General Management, Finance
Schools: Mannheim
GMAT 1: 560 Q46 V22 GPA: 3.1
Re: Which of the following is a terminating decimal, when  [#permalink]

Show Tags

Yea,infact i actually solved in 5 seconds..! i just wish i c such type of problem in actual test _________________
ITS NOT OVER , UNTIL I WIN ! I CAN, AND I WILL .PERIOD.
Non-Human User Joined: 09 Sep 2013
Posts: 13384
Re: Which of the following is a terminating decimal, when  [#permalink]

Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: Which of the following is a terminating decimal, when   [#permalink] 13 Jun 2019, 04:38
Display posts from previous: Sort by

Which of the following is a terminating decimal, when

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  