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

 It is currently 18 Aug 2019, 04:58

### 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?

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

### Hide Tags

Manager
Joined: 19 Apr 2017
Posts: 169
Concentration: General Management, Sustainability
Schools: ESSEC '22
GPA: 3.9
WE: Operations (Hospitality and Tourism)
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

### Show Tags

19 Jul 2019, 10:25
1
Which of the following fractions will lead to a terminating decimal?

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

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

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

To find out if a fraction is terminating or not, we would have to look at the denominator it has to be in the $$(2^n)(5^m)$$ form ( where n and m are non negative)

i) $$80 = 2*2*2*2*5 =(2^4)(5^1)$$

II) 120 = 4*10*3*10 => since 3 is found in the denominator, this fraction will be non terminating.

III) reducing the fraction = $$\frac{33}{480}$$ = $$\frac{11}{160}$$

=>$$160 = 2*2*2*2*(2*5)= 2^5*5^1$$

Director
Joined: 19 Oct 2018
Posts: 769
Location: India
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

### Show Tags

19 Jul 2019, 10:33
1
If the denominator of the fraction, in its reduced form, contains no other prime number facors other than 2 and 5, then the fraction is terminating.

I) $$\frac{83}{80}$$= $$\frac{83}{2^4*5}$$
Denominator contains only 2 and 5 as prime factors, hence $$\frac{83}{80}$$ leads to terminating decimal.

II) $$\frac{23}{120}$$= $$\frac{23}{2^3*3*5}$$
Denominator contains 2, 3 and 5 as prime factors, hence $$\frac{23}{120}$$ does not lead to terminating decimal.

III)$$\frac{33}{480}$$= $$\frac{3*11}{2^5*3*5}$$=$$\frac{11}{2^5*5}$$
Denominator contains only 2 and 5 as prime factors, hence $$\frac{33}{480}$$ leads terminating decimal.

IMO D
Senior Manager
Status: eternal student
Joined: 06 Mar 2018
Posts: 279
Location: Kazakhstan
GPA: 3.87
Which of the following fractions will lead to a terminating decimal?  [#permalink]

### Show Tags

Updated on: 19 Jul 2019, 23:41
1
Which of the following fractions will lead to a terminating decimal?

We just simply need to perform division calculations, and see do we have a terminating decimal or not:

I. 83/80
Attachment:

83.PNG [ 5.51 KiB | Viewed 53 times ]

II. 23/120
Attachment:

230.PNG [ 8.25 KiB | Viewed 53 times ]

III. 33/480
Attachment:

33.PNG [ 6.63 KiB | Viewed 53 times ]

If we will test by concept then:

Number will have finite number of integers after decimal of denominator consists of only 2, 5 or both.
I. Has both 2 and 5, so it will terminate
II. Has 2 and 5, but also 3, will not terminate
III. Has only 2 and 5, thus will terminate

A. None
B. I only
C. I and II only

D. I and III only
E. I, II, and III

D is the answer.
_________________
My SC approach flowchart

(no one is ideal, please correct if you see any mistakes or gaps in my explanation, it will be helpful for both of us, thank you)

___________________
Practice makes perfect!

It is pointless to try to study if it is not fun, then it becomes a chore. At that point, you will either hate your studies or became afraid of them.

Originally posted by GKomoku on 19 Jul 2019, 12:16.
Last edited by GKomoku on 19 Jul 2019, 23:41, edited 1 time in total.
Manager
Joined: 31 Dec 2017
Posts: 73
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

### Show Tags

19 Jul 2019, 12:20
1
Terminating decimal is the prime factor of the denominator of a fraction, and it contains only 2 and 5 or both.
I. 83/80--->80=(2^4)*5---->83/((2^4)*5---->Correct

II. 23/120---->120 =(2^3)*3*5---->It has 3 in the denominator---->Incorrect

III. 33/480--->480 =(2^5)*3*5---->33/((2^5)*3*5)---->11/((2^5)*5)---->Correct
---->Only I & III
Manager
Joined: 21 Jan 2019
Posts: 100
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

### Show Tags

19 Jul 2019, 12:21
1
Quote:
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

1. for simplicity we can check 83/ 8
=10.3741
hence terminating
2. 23/ 12
= 1.8166666
hence non terminating
3. 33/48
= $$\frac{33}{(4*12)}$$
33/4= 8.25
8.25/12 . is also terminating.

Hence 1 and 3 Option D
Manager
Joined: 10 Aug 2016
Posts: 68
Location: India
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

### Show Tags

19 Jul 2019, 12:39
1
Which of the following fractions will lead to a terminating decimal?

A little time consuming process of diving the number and solving till the decimal terminates.
Since denominators are small and easy numbers, can be done under 2 min.

I. $$\frac{83}{80}$$
83/80 = 1.0375 --> Terminating decimal.

II. $$\frac{23}{120}$$
23/120 = 0.191666... --> Non terminating decimal.

III. $$\frac{33}{480}$$
33/480 = 11/160 = 0.06875 --> terminating decimal.

Hence, fractions I and III lead to terminating decimal.

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

Manager
Joined: 12 Jan 2018
Posts: 112
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

### Show Tags

19 Jul 2019, 12:51
1
If a fraction contains just the powers of 2 and 5 in the denominator, it will definitely be a terminating decimal.
With this lets check the given fractions,

I. $$\frac{83}{80}$$; Denominator is $$2^{4}*5$$ -> Terminating Decimal
II. $$\frac{23}{120}$$; Denominator is $$2^{3}*5*3$$ -> Since it contains 3, Its a Non-Terminating Decimal
III.$$\frac{33}{480}$$;Upon reduction $$\frac{1}{160}$$; Denominator is $$2^{5}*5$$ -> Terminating Decimal

Ans :D
_________________
"Remember that guy that gave up?
Neither does anybody else"
Manager
Joined: 06 Feb 2019
Posts: 107
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

### Show Tags

19 Jul 2019, 13:37
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

All we need to remember about termination decimals are two simple rules:
1) the decimal is terminating if there is an integer 2, integer 5 or both in the denominator.
2) if there are any other prime factors in denominator, then the decimal is non-terminating (recurring)

so let's look through the given fractions:

1. 83/80
80 = (2^4)* 5
the the decimal is terminating

2. 23/120

120 = (2^3)*3*5
the the decimal is non-terminating

3. 33/480

480 =(2^5)*3*5
the decimal is terminating, because there is an integer 3 in numerator. So 3 in denominator is eliminated.

The answer is D
Manager
Joined: 06 Jun 2019
Posts: 114
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

### Show Tags

19 Jul 2019, 14:26
1
Note: If the denominator of the fraction consists of only $$2^{x}*5^{y}$$, then we will have a terminating decimal.

1. $$\frac{83}{80}$$ Since the denominator is $$2^{4}*5$$, yes terminating.

2. $$\frac{23}{120}$$ Since the denominator is $$2^{3}*3*5$$, not terminating.

3. $$\frac{33}{480}$$ Since the denominator is $$2^{5}*5$$, yes terminating.

Both $$1$$ and $$3$$ are terminating decimals.

Hence D
_________________
Bruce Lee: “I fear not the man who has practiced 10,000 kicks once, but I fear the man who has practiced one kick 10,000 times.”
GMAC: “I fear not the aspirant who has practiced 10,000 questions, but I fear the aspirant who has learnt the most out of every single question.”
Intern
Joined: 15 Sep 2017
Posts: 44
GPA: 3.4
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

### Show Tags

19 Jul 2019, 15:05
1

Question is asking which of the following fractions will lead to a terminating decimal?

I. 83/80

II. 23/120

III. 33/480

In order to know whether any fraction is terminating or non-terminating we just need to consider the denominator only and we need to see that whether the denominator contains only 2, 5 or both. If the denominator contains any number other than 2 or 5 then the fraction will be non-terminating.

I. 83/80
We can express 80 as 2^4 * 5. Since 80 has only 2 and 5 therefore the fraction is Terminating Decimal.

II. 23/120
We can express 120 as 2^3 * 3 * 5. We know that a fraction will be non-terminating if it has any number other than 2 and 5 since 120 has 3 along with 2 and 5 the fraction will be Non-Terminating Decimal.

III. 33/480
= 11/160. In its simplest form the fraction has 160 as its denominator now we need to see whether the fraction is terminating or non-terminating.
We can express 160 as 2^5 * 5. Since 160 has only 2 and 5 therefore the fraction is Terminating Decimal.

_________________
Tashin
Manager
Joined: 20 Mar 2018
Posts: 243
Location: Ghana
Concentration: Finance, Real Estate
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

### Show Tags

19 Jul 2019, 15:15
Which of the following fractions will lead to a terminating decimal?

Will terminate when the prime factorization of the denominator of the fraction has only prime factors of 2 and/or 5

I.83/80 =83/(2^4•5) will terminate

II. 23/120 =23/(2^3•3•5) has 3 as one of factors so Nope!

III. 33/480= 33/(2^5•3•5) has 3 as one of factors so Nope!

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

Posted from my mobile device
Manager
Joined: 29 May 2019
Posts: 95
GMAT 1: 530 Q48 V15
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

### Show Tags

19 Jul 2019, 18:43
1
Which of the following fractions will lead to a terminating decimal?

I. 83/80
If we divide 3 by 8 then we get terminating decimal

II. 23/120
If we divide 23 by 12 then we get 6 digit repetitive. So this is not terminating.

III. 33/480
If we divide 11 by 16 then we get terminating decimal.

Answer: I and III
D

Posted from my mobile device
_________________
Pick yourself up, dust yourself off, and start again.

Success is the sum of all small efforts.

MAKE IT HAPPEN
Director
Joined: 20 Jul 2017
Posts: 633
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

### Show Tags

19 Jul 2019, 20:21
1
I. 83/80
= 83/(2^4*5)
If the denominator has 2 or 5 or higher powers of 2 or 5. It will always be terminating decimal
--> Terminating

II. 23/120
= 23/(2^3*3*5)
Since the denominator has a multiple of 3 & numberator a non-multiple of 3, it will always be a recurring decimal
--> Non terminating

III. 33/480
= 33/2^5*3*5
= 11/2^5*5
If the denominator has 2 or 5 or higher powers of 2 or 5. It will always be terminating decimal
--> Terminating

IMO Option D

Pls Hit Kudos if you like the solution
Manager
Joined: 27 May 2010
Posts: 200
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

### Show Tags

19 Jul 2019, 20:55
1
Which of the following fractions will lead to a terminating decimal?

Fractions with numbers like 3, 7, 11 in the denominator will be non-terminating
I. 83/80 = 1.0375 Does not have 3,7,11 in the denominator

II. 23/120 = 0.1966666 Non-terminating

III. 33/480 = 11/160 = 0.06875 Terminating

Option D - I and III
_________________
Please give Kudos if you like the post
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 4464
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

### Show Tags

19 Jul 2019, 21:09
1
for no to be terminating decimal it should have 2*5 as no in denominator
out of given options
option i & iii are terminating decimals
83/80 ; 80 = 2^4*5^1 yes
23/120 ; 120 ; 2^3*3^1*5^1 ; no
33/480 ; 480 ; 2^5*3^1*5^1 ; yes
IMO D

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
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
Intern
Joined: 08 Jan 2018
Posts: 38
GMAT 1: 730 Q51 V38
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

### Show Tags

19 Jul 2019, 21:18
1
In order for a fraction to be a terminating decimal, denominator needs to be in the form of 2^x * 5^ when fraction is reduced.

I) 83/80 = 83/(16*5) = 83/(2^4*5) - Terminating
II) 23/120 = 23/(3*40) = 23/(3*2^3*5) - Not terminating
III) 33/480 = 11/160 = 11/(2^4*10) = 11/(2^5*5) - Terminating

Manager
Joined: 17 Apr 2018
Posts: 108
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

### Show Tags

19 Jul 2019, 21:25
1
Terminating Decimal - All the integer divided by any integer power of 2 or 5 gives terminating decimal.

1st statement - Denominator = 80
80 = 2^4.5

Hence statement 1 is terminating decimal.

2 - simplified form is 23/120
We have 3 in the denominator, number 3 will give recurring decimal

3 - 33/480 --> 11/160

The denominator is a factor or 2 and 5 only hence terminating.

So Statement 1 and 3 are terminating decimal

Hence, D is the Answer.
Manager
Joined: 17 Jul 2014
Posts: 111
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

### Show Tags

19 Jul 2019, 21:26
Which of the following fractions will lead to a terminating decimal?

As the given 3 fractions have common factors in denominator its easier to multiply each fraction by 40 and reduce the denominator

$$\frac{83}{80}*40 = \frac{83}{2}$$

$$\frac{23}{120}*40 = \frac{23}{3}$$

$$\frac{33}{480}*40 = \frac{33}{12}$$

this division is easier to tackle than larger denominators. Only $$\frac{83}{2}$$ leads to terminating decimal

B is the answer!
Manager
Joined: 30 May 2019
Posts: 107
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

### Show Tags

19 Jul 2019, 21:33
1
A number will terminate if its denominator consists of only 2's, 5's or both. Let's check denominators of the following fractions:

I. $$\frac{83}{80}$$=$$\frac{83}{2^4*5^1}$$ - will terminate because denominator has 2's and 5's only

II. $$\frac{23}{120}$$=$$\frac{23}{2^3*5^1*3^1}$$ - will not terminate because denominator has 3

III. $$\frac{33}{480}$$=$$\frac{11}{2^5*5^1}$$- will terminate because denominator has 2's and 5's only.

As we saw above, only I and III work, answer is D
Manager
Status: Not Applying
Joined: 27 Apr 2009
Posts: 179
Location: India
Schools: HBS '14 (A)
GMAT 1: 730 Q51 V36
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

### Show Tags

19 Jul 2019, 21:45
1
For a fraction to be a terminating decimal, the denominator must only have 2s and 5s as factor.

A) 83/80
80 = 2^4 * 5
Hence, this is terminating

B) 23/120
120 = 2^3 * 3 * 5
As the denominator has 3 as a factor, this is not terminating.

C) 33/480
33 = 3 * 11
480 = 2^5 * 3 * 5
Simplifying, it becomes 11/160, which is terminating

Hence, I and III are terminating.
_________________
http://www.wizius.in
Better Prep. Better Scores. Better Schools

Guaranteed Admission to Top-50 MBA Programs
You either get-in or get your money-back.
Re: Which of the following fractions will lead to a terminating decimal?   [#permalink] 19 Jul 2019, 21:45

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

Display posts from previous: Sort by

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

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

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