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

 It is currently 13 Nov 2019, 00:19

### 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

# Which of the following fractions will lead to a terminating decimal?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58993
Which of the following fractions will lead to a terminating decimal?  [#permalink]

### Show Tags

19 Jul 2019, 08:00
00:00

Difficulty:

75% (hard)

Question Stats:

57% (01:16) correct 43% (01:13) wrong based on 265 sessions

### HideShow timer Statistics

Which of the following fractions will lead to a terminating decimal?

I. $$\frac{83}{80}$$

II. $$\frac{23}{120}$$

III. $$\frac{33}{480}$$

A. None
B. I only
C. I and II only
D. I and III only
E. I, II, and III

 This question was provided by Experts Global for the Game of Timers Competition

_________________
Senior Manager
Joined: 16 Jan 2019
Posts: 498
Location: India
Concentration: General Management
WE: Sales (Other)
Which of the following fractions will lead to a terminating decimal?  [#permalink]

### Show Tags

Updated on: 19 Jul 2019, 08:28
1
2
A terminating decimal will have denominator in the 2^a*5^b

$$80 = 2^4*5^1$$

$$120 = 2^3*3^1*5^1$$

$$480 = 2^5*3^1*5^2$$ but in this case the numerator is a multiple of 3 so the 3 cancels out and we are left $$2^5*5^2$$ in the denominator so its a terminating decimal

I & III only

Originally posted by firas92 on 19 Jul 2019, 08:12.
Last edited by firas92 on 19 Jul 2019, 08:28, edited 1 time in total.
Manager
Joined: 08 Jan 2018
Posts: 129
Which of the following fractions will lead to a terminating decimal?  [#permalink]

### Show Tags

Updated on: 20 Jul 2019, 02:07
1
For a fraction to be terminating, the fraction in its lowest form should have a denominator that should have prime factors consisting of only 2 OR only 5 OR a combination of 2 and 5.

I. $$\frac{83}{80}$$
There is no common factor in Numerator and denominator to reduce the fraction.
Denominator 80 = 2 * 2 * 2 * 2 * 5 -> Only Prime factors of 2 and 5.

Hence, it will lead to a terminating decimal.

II. $$\frac{23}{120}$$
There is no common factor in Numerator and denominator to reduce the fraction.
Denominator 120 = 2 * 2 * 3 * 5 -> There are other factor besides 2 and 5.

Hence, it will NOT lead to a terminating decimal.

III. $$\frac{33}{480}$$
The fraction can be reduced to $$\frac{11}{160}$$
Denominator 160 = 2 * 2 * 2 * 2 * 2 * 5 -> Only Prime factors of 2 and 5.

Hence, it will lead to a terminating decimal.

Originally posted by Sayon on 19 Jul 2019, 08:14.
Last edited by Sayon on 20 Jul 2019, 02:07, edited 1 time in total.
Manager
Joined: 29 Nov 2018
Posts: 148
Location: India
Concentration: Entrepreneurship, General Management
GPA: 3.99
WE: Engineering (Computer Hardware)
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

### Show Tags

19 Jul 2019, 08:17
1
Which of the following fractions will lead to a terminating decimal?

I. 83/80

II. 23/120

III. 33/480

To find out answer to this question, we need to find out if any fraction simplifies into multiple of (1/3).
If we see the first fraction denominator is 80. Powers of 2 and 5. Hence terminating decimal.
Second fraction 23/120. Simplifying it we will get a fraction which is a multiple of 1/3. hence non terminating.
Third fraction 33/480. In first look at the denominator we feel it is a multiple of 3 hence non-terminating. But numerator and denominator both are multiple of 3. And highest power of 3 in both is 3^1. So they will cancel each other out. So simplified denominator will only be a multiple of 2 and 5. Hence terminating.

Senior Manager
Joined: 27 Aug 2014
Posts: 357
Location: Netherlands
Concentration: Finance, Strategy
Schools: LBS '22, ISB '21
GPA: 3.9
WE: Analyst (Energy and Utilities)
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

### Show Tags

19 Jul 2019, 08:19
1

First number will lead to 83/(8*10), as denominator has all even numbers, definitely terminate
second number: 23/120 = 23/3*40. 23/3 is a non terminating decimal. so non terminating
third number: 33/48*10 =11/16*10, all even numbers at the denominator, so terminate

D
Senior Manager
Joined: 05 Mar 2017
Posts: 261
Location: India
Concentration: General Management, Marketing
GPA: 3.6
WE: Marketing (Hospitality and Tourism)
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

### Show Tags

19 Jul 2019, 08:21
1
Which of the following fractions will lead to a terminating decimal?

I. 83/80

II. 23/120

III. 33/480

The key to answering this question is knowing the theory behind terminating decimals. Terminating decimals are 1.09 and non-terminating decimals are 1.33333.
In order to check for terminating decimals, you need to check if the denominator is 2^x or 5^y or both.

Now let's take each of the options check for the same.

80 = 8*10 = 2^4 & 5^1
Hence this is correct.

120 = 12*10 = 2^3 , 3^1 , 5^1, Since it has 3 it is incorrect.

480 again only has 2 and 5, so it is correct.

which means 1st and 3rd are correct.

A. None
B. I only
C. I and II only
D. I and III only
E. I, II, and III

Rice (Jones) School Moderator
Joined: 18 Jun 2018
Posts: 306
Location: United States (AZ)
Concentration: Finance, Healthcare
GMAT 1: 600 Q44 V28
GPA: 3.36
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

### Show Tags

19 Jul 2019, 08:29
1
We have terminating fractions if and only if the denominator contains only 2s and/or 5s

I: 83/80 = $$\frac{83}{2^{4} × 5}$$ (terminates)

II: 23/120 = $$\frac{23}{2^{3} × 3 × 5}$$ (does not terminate since denominator contains a 3)

III: 33/480 = $$\frac{33}{2^{5} × 3 × 5}$$ = $$\frac{11}{2^{5} × 5}$$ (terminates)

Therefore, only I and III are terminating decimals (answer is D)
Manager
Joined: 28 Feb 2014
Posts: 178
Location: India
GPA: 3.97
WE: Engineering (Education)
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

### Show Tags

19 Jul 2019, 08:30
To get a terminating decimal we need to have multiples of 2 or 5 or both (2 and 5).

Other than 2 or 5, the fraction will be non terminating decimal.
Lets consider prime factorisation of various denominators:
I 80 - 2^4 * 5 will have terminating decimal
II 120 - 2^3 * 3 * 5 will have non terminating decimal
III 480 - 2^5 * 3 * 5 will have non terminating decimal

B is correct
Manager
Joined: 26 Jan 2016
Posts: 180
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

### Show Tags

19 Jul 2019, 08:31
1. 83/80 gives a terminating decimal
While 2&3 doesn't terminate. So the answer is B

Posted from my mobile device
_________________
Your Kudos can boost my morale..!!

I am on a journey. Gradually I'll there..!!
Director
Joined: 28 Jul 2016
Posts: 642
Location: India
Concentration: Finance, Human Resources
GPA: 3.97
WE: Project Management (Investment Banking)
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

### Show Tags

19 Jul 2019, 08:31
1
Which of the following fractions will lead to a terminating decimal?

I. 83/80

II. 23/120

III. 33/480

A. None
B. I only
C. I and II only
D. I and III only
E. I, II, and III

important points
Numbers in 4 or 5 in fraction are always terminating whereas with fractions as 3 are non terminating

I. 83/80 it will of form $$83 * (\frac{1}{4}*\frac{1}{2} * \frac{1}{10})$$
= 83 * 0.125*0.5*0.1
It does not go indefinite hence acceptable

II. 23/120

this if form $$23 * (\frac{1}{4}*\frac{1}{3} * \frac{1}{10})$$
hence 0.3 is indefinite 0.333333333333 ....
hence non terminating
III. 33/480
it can further be simplified to
11/160
which is again of the form $$11 *(\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2} \frac{*1}{10})$$
all are terminating in fraction
Hence is III is acceptable
thus answer is D. I and III only
SVP
Joined: 03 Jun 2019
Posts: 1837
Location: India
Which of the following fractions will lead to a terminating decimal?  [#permalink]

### Show Tags

Updated on: 19 Jul 2019, 10:19
1
Which of the following fractions will lead to a terminating decimal?

I. 83/80 = 1 + 3/80

II. 23/120

III. 33/480 = 11/160

A. None
B. I only
C. I and II only
D. I and III only
E. I, II, and III

I. 83/80 = 1 + 3/80
3/80 = 3 * .0125 = .0375
83/80 = 1. 0375
Terminating decimal

II. 23/120
1/120 = .008333
23/120 = .1916666
Non terminating decimal

III. 33/480 = 11/160
11/160 = .06875
Terminating decimal

Alternatively,
If a simplified fraction, has only multiples of either 2 or 5 in denominator, then it is a terminating decimal.

I. 83/80
80=2^4.5 has only multiples of 2 and 5 in denominator => Terminating decimal

II. 23/120
120 = 2^3.3.5 has 3 in denominator => Non-terminating decimal

III. 33/480 = 11/160
160=2^5.5 has only multiples of 2 and 5 in denominator => Terminating decimal

IMO D
_________________
"Success is not final; failure is not fatal: It is the courage to continue that counts."

Please provide kudos if you like my post. Kudos encourage active discussions.

My GMAT Resources: -

Efficient Learning
All you need to know about GMAT quant

Tele: +91-11-40396815
Mobile : +91-9910661622
E-mail : kinshook.chaturvedi@gmail.com

Originally posted by Kinshook on 19 Jul 2019, 08:31.
Last edited by Kinshook on 19 Jul 2019, 10:19, edited 1 time in total.
Manager
Joined: 12 Apr 2017
Posts: 141
Location: United States
Concentration: Finance, Operations
GPA: 3.1
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

### Show Tags

19 Jul 2019, 08:33
only 1,

terminating decimals will occur only when a 2 and or 5 are the only prime factors in the denominator
Director
Joined: 04 Sep 2015
Posts: 663
Location: India
WE: Information Technology (Computer Software)
Which of the following fractions will lead to a terminating decimal?  [#permalink]

### Show Tags

Updated on: 19 Jul 2019, 09:01
1
IMO : D

Which of the following fractions will lead to a terminating decimal?

I. 83/80

II. 23/120

III. 33/480

A. None
B. I only
C. I and II only
D. I and III only
E. I, II, and III

Sol:

if the denominator has 2's and 5's as prime factors then it will be a terminating decimal,
and if the denominator has other primes like 3,7,11 then the decimal will be a non terminating decimal.

120 = 2 * 2 * 2 * 3 * 5
80 = 2 * 2 * 2 * 2 * 5
480=2* 2* 2* 2* 2* 3* 5

I)83/80 =83*1/2 * 2 * 2* 2 * 5 this means only 2's and 5's in the denominator and thus terminating decimal.
II)23/120=23/2 * 2 * 2 * 3 * 5 this means only 2's ,3's and 5's in the denominator and so this is a non terminating decimal because 3 exist in decimal.
III) 33/480= 3*11/2*2* 2* 2* 2* 3* 5 this gives 11/160 and 160 only have 2's and 5's so this will be a terminating decimal

SO D is correct.

Originally posted by abhishekdadarwal2009 on 19 Jul 2019, 08:33.
Last edited by abhishekdadarwal2009 on 19 Jul 2019, 09:01, edited 1 time in total.
Manager
Joined: 10 Mar 2019
Posts: 75
Location: Russian Federation
Schools: Haas '21
GPA: 3.95
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

### Show Tags

19 Jul 2019, 08:36
1
fractions will lead to a terminating decimal if the denominator multiplied 2 or 5 or both and nothing else.

I. 80=8*10=2^4*5. Ok.
II.120=12*10=3*2^3*5. It has 3 thus not terminating
III. 480=2^5*3*5. But here we can reduce 3 in the numerator and denominator and thus this fraction is terminating.

IMO D
Director
Joined: 22 Nov 2018
Posts: 562
Location: India
GMAT 1: 640 Q45 V35
GMAT 2: 660 Q48 V33
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

### Show Tags

19 Jul 2019, 08:39
1
A fraction will be a terminating fraction when at its simplest form the denominator must be only of the form 2^n*5^m (were n,m can also be 0) without any other prime factors.

I)83/(2^4*5^1) - Terminating fraction (as denominator when prime factorized contains only 2 and 5 raised to different powers)
II) 23/(3^1*2^3*5^1) - Non terminating fraction (as denominator contains a 3^1 apart from 2^3*5^1)
III) Can be simplified to 11/(2^5*5^1) - Terminating fraction (as denominator when prime factorized contains only 2 and 5 raised to different powers)

IMO D - I and III Only
_________________
Give +1 kudos if this answer helps..!!
Manager
Joined: 08 Jan 2018
Posts: 98
Location: India
GPA: 4
WE: Information Technology (Computer Software)
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

### Show Tags

19 Jul 2019, 08:39
1
A terminating decimal is a number which has finite digits after the decimal point.

1. 83/80 = 1.0375
2. 23/120 = 0.19166666666666666....
3. 33/480 = 0.06875

Thus only 1 and 3 have finite numbers after the decimal point.

Please hit kudos if you like the solution.
Senior Manager
Joined: 10 Jan 2017
Posts: 329
Location: India
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

### Show Tags

19 Jul 2019, 08:41
IMO the correct answer is option B- I only
Explanation given as attachment -
Attachments

IMG_20190719_210648.JPG [ 874.98 KiB | Viewed 1485 times ]

_________________
Good, better, best. Never let it rest. 'Till your good is better and your better is best.
Please hit +1 Kudos if you like my Post.
Manager
Joined: 18 Feb 2017
Posts: 93
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

### Show Tags

19 Jul 2019, 08:42
1
IMO D.

By just finding out the values, we can know if the fraction is terminating-

I. \frac{83}{80} = 1.0375

II. \frac{23}{120} = 0.19166666...

III. \frac{33}{480} = 0.06875

Hence, I and III give us terminating decimal points making option D the answer.
Manager
Joined: 30 May 2018
Posts: 157
GMAT 1: 710 Q49 V36
GPA: 3.8
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

### Show Tags

19 Jul 2019, 08:44
1
D

I think this kind of problem should not be posted for competition because everyone has access to calculator, and can quickly check the answers without knowing the logic properly.

Anyways, here is my reasoning. In order to have a fraction that is fully terminable, the denominator of the fraction needs to be in the form of 2^n*5^m, after the fraction has been reduced to its simplest form.

I. 83/80, 80 can be factored as 2^4*5, so fraction is terminable

II. 23/120, 120 can be factored as 2^3*3*5, so fraction cant be terminable because of 3 in the denominator

III. 33/480 = 11/160, 160 can be factored as 2^5*5, so fraction is terminable

Only I and III
Manager
Joined: 21 May 2017
Posts: 99
Location: India
GMAT 1: 660 Q49 V31
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

### Show Tags

19 Jul 2019, 08:47
Which of the following fractions will lead to a terminating decimal?

I. 83808380

II. 2312023120

III. 3348033480

A. None
B. I only
C. I and II only
D. I and III only
E. I, II, and III

B is the ans
Re: Which of the following fractions will lead to a terminating decimal?   [#permalink] 19 Jul 2019, 08:47

Go to page    1   2   3   4   5    Next  [ 81 posts ]

Display posts from previous: Sort by