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

 It is currently 22 Aug 2019, 13:51

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

Intern
Joined: 22 Jun 2019
Posts: 41
Concentration: Operations, Organizational Behavior
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

Show Tags

19 Jul 2019, 22:05
see the picture
Attachments

terminating - Copy.jpg [ 2.55 MiB | Viewed 282 times ]

Manager
Joined: 10 Nov 2014
Posts: 59
Location: United States
Concentration: Marketing, Strategy
Schools: Goizueta '22, IIM
Which of the following fractions will lead to a terminating decimal?  [#permalink]

Show Tags

19 Jul 2019, 22:40
1
Soln:

Concept to apply: A fraction will always be terminating if the denominator of fraction in the least form has NO PRIME FACTOR other than 2,5, or both 2 and 5

Now lets check each option :

I) 83/80
80 has prime factors - 2,2,2,2,5 (2^4 * 5^1)
only 2 and 5 in denominator.

So 83/80 is terminating decimal

II) 23/120
120 has prime factors - 2,2,2,5,3 (2^3*5^1*3^1)
- since prime factors includes 3 , other than 2 and 5 .

23/120 is non terminating decimal.

III) 33/480 - We can reduce 33/480 to 11/160 ( by dividing by 3). This is final reduced form, now check denominator.
- Prime Factors of 160 are 2,2,2,2,2,5 (2^5*5^1)
- Applying concept mentioned above since only 2 and 5 in denominator
33/480 is terminating decimal

Ans choice D is CORRECT[
Manager
Joined: 31 May 2018
Posts: 186
Location: United States
Concentration: Finance, Marketing
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

Show Tags

19 Jul 2019, 23:36
1
I. $$\frac{83}{80}$$
$$\frac{83}{8}$$*$$\frac{1}{10}$$
1.0375*$$\frac{1}{10}$$ = 0.10375 (yes this is a terminating decimal since this has finite number of digits after decimal point)

II. $$\frac{23}{120}$$
$$\frac{23}{40}$$*$$\frac{1}{3}$$
= 0.575 *$$\frac{1}{3}$$
=0.19166666666......(this will not end in a finite number of digits)
so this is not a terminating decimal

III. $$\frac{33}{480}$$
= $$\frac{33}{3}$$*$$\frac{1}{160}$$
= 11*$$\frac{1}{160}$$
= 11*$$\frac{1}{2}$$*$$\frac{1}{2}$$*$$\frac{1}{2}$$*$$\frac{1}{2}$$*$$\frac{1}{10}$$

=0.6875 (yes this is a terminating decimal)

Manager
Joined: 12 Mar 2018
Posts: 83
Location: United States
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

Show Tags

19 Jul 2019, 23:39
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

A simple condition that can be used to check for terminating decimals is to check for the presence of 2*5 as factors in the denominator.
In this case, I II and III all of them have multiples of 10 in the denominator, so all of them will lead to a terminating decimal.

Manager
Joined: 03 Aug 2009
Posts: 58
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

Show Tags

19 Jul 2019, 23:56
Which of the following fractions will lead to a terminating decimal?

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

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

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

Now, there is theorem (rarely published in GMAT materials) on which this questions is based: A fraction has terminating decimal if its denominator has prime factors of only 2 and 5 in any power.

Now, need to prime factorize denominators in the answers:
1. $$80 = 5*2*2*2*2$$ - only 2 and 5, therefore has terminating decimal
1. $$120 = 3*2*2*2*5$$ - there is 3 in it , therefore out
1. $$480 = 120*4$$ - as we seen, 120 has 3 in it, therefore out

Manager
Joined: 18 May 2019
Posts: 164
Which of the following fractions will lead to a terminating decimal?  [#permalink]

Show Tags

Updated on: 20 Jul 2019, 05:49
We are to determine which of the following will lead to a terminating decimal.

I. 83/80
83/80=8.3/8
but we know 1/8=0.125. Hence 8.3/8 = 8.3*0.125 = 83*125*10^-4
Since 83*125 leads to an integer, which is 10375, then 83*125*10^-4 = 10375/10000 = 1.0375.
therefore I leads to a terminating decimal.

II. 23/120.
23/120 = 23/(10*4*3) = 23*[(1/10*1/4*1/3)]. We know that 1/4 = 0.25 and 1/10 = 0.1.
hence 1/4*1/10=0.025.
However, 1/3 leads to a non-terminating decimal, and multiplying 0.025 by 1/3 leads to a non-terminating decimal.
Therefore II does not lead to a terminating decimal

III. 33/480
33/480 = 11/160 = 11*1/160 = 11/[(1/10*1/16)]. We know 1/10 = 0.1.
and 1/16 = 1/2*1/8 0.5*0.125 = 0.0625
hence 11/60 = 11*0.1*0.0625 = 0.06875, which is a terminating decimal.

The answer therefore is D. since only I and III leads to a terminating decimal.

Originally posted by eakabuah on 20 Jul 2019, 00:40.
Last edited by eakabuah on 20 Jul 2019, 05:49, edited 1 time in total.
Manager
Joined: 24 Jan 2019
Posts: 103
Location: India
Concentration: Strategy, Finance
GPA: 4
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

Show Tags

20 Jul 2019, 00:52
1
I. 83/80

83/80 = 1 + (3/80)
1/80 = 0.0125 , So (3/80) is also terminating.
No need to do the further calculation, from the above result we can directly say the (83/80) will lead to the terminating decimal.

II. 23/120

1/120 = 0.0083333..... (non terminating)
So, 23/120 is also non-terminating decimal.
Note: (a/120) will be terminating decimal if 'a' is multiple of '3'. Here, 23 is not a multiple of 3.

III. 33/480

33/480= 11/160
1/160 = 0.00625
1/160 is leading to terminating decimal. So, 11/160 will also lead to terminating decimal.

Manager
Joined: 07 Jul 2019
Posts: 54
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

Show Tags

20 Jul 2019, 00:53
1
Task is to find denominators with either 2 or 5 or both. Only I and III have 2 and 5. II has 2, 5, and 3 in its denominator (infinite number of digits).
Manager
Joined: 18 Jun 2013
Posts: 141
Location: India
Concentration: Technology, General Management
GMAT 1: 690 Q50 V35
GPA: 3.2
WE: Information Technology (Consulting)
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

Show Tags

20 Jul 2019, 01:01
1
Rule for Terminating or Non-Terminating Recurring decimals,

=> For fractions in their simplest form, if the denominator has only powers of 2 and 5 then the fraction will be terminating.

=> For fractions in their simplest form, if the denominator has powers other than for 2 and 5 then the fraction will be non terminating recurring.

Let us now check the 3 options given,

Option 1: 83/80

This fraction is in it's lowert form.

Also, 80 = 2^4 * 5

=> 83/80 will be terminating.

Option 2: 23/120

This fraction is in it's lowest form.

Also, 120 = 2^3 * 3 * 5

=> 23/120 will be non-terminating recurring.

Option 3: 33/480

33/480
=> 11/160

This fraction is in it's lowet form now.

Also, 160 = 2^5 * 5

=> 33/480 will be terminating.

Manager
Joined: 22 Oct 2018
Posts: 74
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

Show Tags

20 Jul 2019, 02:57
1
Which of the following fractions will lead to a terminating decimal?

I.
83
80

8380

II.
23
120

23120

III.
33
480

33480

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

Solution:

The concept in this question is that a fraction will lead to a terminating decimal if and only if the reduced fraction has a prime factorization that contains only 2's or5's or both.If the prime factorization of the reduced fraction contains denominatior anything other than 2s or 5s,the decimal equivalent will not terminate.
So considering the various options:

2 ) 23/120 = 23/($$2^3$$*3*5)

3)$$\frac{33}{480}$$ = $$\frac{11}{(2^5*5)}$$

1) $$\frac{83}{80}$$ = 83 /$$(2^4$$*5)

As we see that only 1 and 3 option have 5 and 2 in their denominators and hence they will lead to a terminating decimal. Optionn 2 have 3 also in its denominator hence it will not be a terminating decimal.Hence D is the answer IMO.
Intern
Joined: 24 Sep 2014
Posts: 39
Concentration: General Management, Technology
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

Show Tags

20 Jul 2019, 03:35
1
(i) 83/80 --> 83/(8*10) --> 83/(2^4*5), 1/(2^4*5) gives terminating decimal
(ii) 23/120 --> 23/(12*10) --> 23/(2^2*3*2*5) --> 23/(2^3*3*5) doesn't give a terminating decimal because of 3
(iii) 33/480 --> 3*11/(2^5*3*5) --> 11/(2^5*5), 1/(2^5*5) gives terminating decimal

Intern
Joined: 24 Mar 2018
Posts: 48
Location: India
Concentration: Operations, Strategy
Schools: ISB '21
WE: Project Management (Energy and Utilities)
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

Show Tags

20 Jul 2019, 03:48
A fraction leads to a terminating decimal only if its denominator has 2 or 5 as its prime factors. Any other prime factor in the denominator will make the decimal non-terminating.

I. $$\frac{83}{80} = \frac{83}{2^4*5^1}$$
As the denominator has only 2 and 5 as its factors, this is a terminating decimal.

II. $$\frac{23}{120} = \frac{23}{2^3*3^1*5^1}$$
As the denominator has 3 as one of its prime factors, this is a non-terminating decimal.

III. $$\frac{33}{480} = \frac{33}{2^5*3^1*5^1}$$
As the denominator has 3 as one of its prime factors, this is a non-terminating decimal.

Hence, Option (B)
Intern
Joined: 14 Mar 2017
Posts: 39
Location: United States (MD)
GPA: 2.9
WE: Science (Other)
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

Show Tags

20 Jul 2019, 04:14
Question: Which of the following fractions will lead to a terminating decimal?

If the prime factorization of the denominator of a fraction has only factors of 2 and factors of 5, the decimal expression terminates.

I. $$\frac{83}{80}$$
$\text{Prime Factorization Calculation }\\ \text{Example: 80} \\ \begin{pmatrix*} &&80&& \\ &\swarrow&|&\searrow&\\ 2&&\downarrow&&2^3\\ &&5&&\\ &&&&\\ &&&& \end{pmatrix*} \rightarrow \text{Prime Factors of 80 are } 2,2,2,2,5\\ \text{Terminating!}$
II. $$\frac{23}{120}$$
$\text{Prime Factorization Calculation }\\ \text{Example: N = 120} \\ \begin{pmatrix*} &&120&& \\ &\swarrow&|&\searrow&\\ 2^3&&\downarrow&&5\\ &&3&&\\ &&&&\\ &&&& \end{pmatrix*} \rightarrow \text{Prime Factors of 120 are } 2,2,2,3,5\\ \text{NOT Terminating!}$
III. $$\frac{33}{480}$$
$\text{Prime Factorization Calculation }\\ \text{Example: N = 480} \\ \begin{pmatrix*} &&480&& \\ &\swarrow&|&\searrow&\\ 2^5&&\downarrow&&5\\ &&3&&\\ &&&&\\ &&&& \end{pmatrix*} \rightarrow \text{Prime Factors of 480 are } 2,2,2,2,2,3,5\\ \text{NOT Terminating!}$
Correct Answer: B. $$\implies\text{I only}$$
_________________
"What is my purpose?"
"You pass butter."
"Oh my god..."
"Yeah, welcome to the club, pal."
Senior Manager
Joined: 25 Sep 2018
Posts: 396
Location: United States (CA)
Concentration: Finance, Strategy
GMAT 1: 640 Q47 V30
GPA: 3.97
WE: Investment Banking (Investment Banking)
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

Show Tags

20 Jul 2019, 04:15
1
Solution:

General property:
A fraction in its lowest term can be expressed as a terminating decimal if and only if the denominator has powers of only 2 and/or 5.

Lets prime factorize the division.

I. $$\frac{83}{2^4 X 5}$$ , Hence we see that the division only contains 2 & 5. So this fraction will be terminating.

II.$$\frac{23}{2^3 X 3 X 5}$$We observe that there is 3 in the prime factorization , Hence this fraction is non terminating

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

=$$\frac{{11 X 3}}{2^5 X 3 X 5}$$, we observe that 3 gets cancelled with the 3 in the numerator leaving only 2 & 5 as factors in the denominator. Hence this fraction will be terminating.

So the answer here must be D
_________________
Why do we fall?...So we can learn to pick ourselves up again
Manager
Joined: 01 Oct 2018
Posts: 111
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

Show Tags

20 Jul 2019, 05:05
1
Which of the following fractions will lead to a terminating decimal?

I. 83/80 = 1.0375

II. 23/120 = 0.19166(6)

III. 33/480 = 0.06875

A. None
B. I only
C. I and II only
D. I and III only
E. I, II, and III
Manager
Joined: 17 Jan 2017
Posts: 83
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

Show Tags

20 Jul 2019, 05:13
1
Which of the following fractions will lead to a terminating decimal?

I. 83/80

II. 23/120

III. 33/480

For a decimal to be terminating, the denominator must be in power of 2's or 5's or both.

i) 80= 5*2^4
ii) 120= 5*3*2^3
iii) 160 = 5*2^5

so, the correct answer choice is (D)
Manager
Joined: 25 Jul 2018
Posts: 199
Which of the following fractions will lead to a terminating decimal?  [#permalink]

Show Tags

20 Jul 2019, 05:33
1
As we know, we call the Terminating decimal if and only if the denominator has powers of only 2 and/or 5.

I. 83/80=83/(16*5)=83/(2^4*5) (yes, denominator consists of only powers of 2 and 5)

II. 23/120=23/(2^3*3*5) (No, it is not terminating decimal, denominator has power of 3.)

III. 33/480 (we can divide both parts of fraction by 3) --> 11/160
--> 11/160=11/(16*10)=11/(2^5*5) (yes, denominator consists of only powers of 2 and 5)

We got only I and III right
Manager
Joined: 27 Mar 2018
Posts: 73
Location: India
Which of the following fractions will lead to a terminating decimal?  [#permalink]

Show Tags

20 Jul 2019, 06:31
1
For a fraction to be a terminating decimal, the denominator must be in the form 2^m*5^n in reduced form.

1) 80 = 2^4*5. Hence it will be lead to a terminating decimal.
2) 120= 2^3 * 3 * 5. Non terminating
3) Reducing fraction further it can be written as $$\frac{11}{160}$$.
160=2^5*5. Terminating

Hence option D
_________________
Thank you for the kudos. You are awesome!
Intern
Joined: 09 Jul 2019
Posts: 38
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

Show Tags

20 Jul 2019, 06:38
1
Only options 1 and 3 have denominators in forms of 2^a*5^b. Option 2 has 2^a*3^b*5^c.
Senior Manager
Joined: 18 Jan 2018
Posts: 308
Location: India
Concentration: General Management, Healthcare
Schools: Booth '22, ISB '21, IIMB
GPA: 3.87
WE: Design (Manufacturing)
Re: Which of the following fractions will lead to a terminating decimal?  [#permalink]

Show Tags

20 Jul 2019, 06:38
1
I. 83/80 =83/8 *10 = 10.3875/10 = 1.03875 --> Terminating decimal

II. 23/120 = 23/12*10 = 1.916666666.. /10 = 0.19166666666... ---> is not a terminating decimal

III. 33/480 = 11*3/4*3*4*10 = 11/16*10 =0.9=6875/10 = 0.06875--> terminating decimal

D. I and III only--- Is the correct answer
Re: Which of the following fractions will lead to a terminating decimal?   [#permalink] 20 Jul 2019, 06:38

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

Display posts from previous: Sort by