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

 It is currently 23 Oct 2019, 16:46

### 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 when expressed as repeating decimals

Author Message
TAGS:

### Hide Tags

Intern
Joined: 06 Mar 2016
Posts: 13
Which of the following fractions when expressed as repeating decimals  [#permalink]

### Show Tags

09 Sep 2018, 08:53
3
5
00:00

Difficulty:

45% (medium)

Question Stats:

55% (01:24) correct 45% (01:20) wrong based on 82 sessions

### HideShow timer Statistics

Which of the following fractions when expressed as repeating decimals would have the longest sequence of different digits?

A) 17/44
B) 5/6
C) 41/66
D) 1/120
E) 2/41.
VP
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1011
WE: Supply Chain Management (Energy and Utilities)
Which of the following fractions when expressed as repeating decimals  [#permalink]

### Show Tags

10 Sep 2018, 09:19
7
4
divyajoshi12 wrote:
Which of the following fractions when expressed as repeating decimals would have the longest sequence of different digits?

A) 17/44
B) 5/6
C) 41/66
D) 1/120
E) 2/41.

Note:-
1) Prime numbers in the denominator except 2 and 5 yield repeating decimals, no matter what is the numerator.If the prime factorization of the denominator of a fraction has only factors of 2 and factors of 5, the decimal expression terminates. If there is any prime factor in the denominator other than 2 or 5, then the decimal expression repeats.
2) 1/3 = 0.3333…, 1/7=0.142857142857.., 1/11=0.090909...
3) Multiplying any integer value with 1/3 or 1/7 or 1/11 or 1/(prime number except 2,5) only shifts the decimal point.
4) As long as the fraction is in lowest terms, the numerator doesn’t matter at all.
Let's simplify options:-
A. 17/44=(17/$$2^2$$)*1/11 ; 17/4 has no role here. The number of recurring decimals(with different digits) solely depends on the number of recurring decimals of 1/11, that is 2.
B. 5/6=(5/2)*1/3; In line with the above reasoning, #recurring decimals would be 1.
C. 41/66=(41/2)*1/3*1/11; #recurring decimals would be 2. (since the #recurring decimals of 1/11 is 2)
D. 1/120=(1/($$2^3*5$$))*1/3; #recurring decimals would be 1. (since the #recurring decimals of 1/3 is 1)
E. I don't want to break my head here.It must contain the maximum number of repeating decimals(with different digits) by method of elimination.

Ans. (E)
_________________
Regards,

PKN

Rise above the storm, you will find the sunshine
##### General Discussion
Intern
Joined: 30 Jul 2019
Posts: 14
Location: India
Schools: YLP '20 (I)
GMAT 1: 770 Q50 V45
Re: Which of the following fractions when expressed as repeating decimals  [#permalink]

### Show Tags

03 Aug 2019, 06:45
PKN wrote:
divyajoshi12 wrote:
Which of the following fractions when expressed as repeating decimals would have the longest sequence of different digits?

A) 17/44
B) 5/6
C) 41/66
D) 1/120
E) 2/41.

Note:-
1) Prime numbers in the denominator except 2 and 5 yield repeating decimals, no matter what is the numerator.If the prime factorization of the denominator of a fraction has only factors of 2 and factors of 5, the decimal expression terminates. If there is any prime factor in the denominator other than 2 or 5, then the decimal expression repeats.
2) 1/3 = 0.3333…, 1/7=0.142857142857.., 1/11=0.090909...
3) Multiplying any integer value with 1/3 or 1/7 or 1/11 or 1/(prime number except 2,5) only shifts the decimal point.
4) As long as the fraction is in lowest terms, the numerator doesn’t matter at all.
Let's simplify options:-
A. 17/44=(17/$$2^2$$)*1/11 ; 17/4 has no role here. The number of recurring decimals(with different digits) solely depends on the number of recurring decimals of 1/11, that is 2.
B. 5/6=(5/2)*1/3; In line with the above reasoning, #recurring decimals would be 1.
C. 41/66=(41/2)*1/3*1/11; #recurring decimals would be 2. (since the #recurring decimals of 1/11 is 2)
D. 1/120=(1/($$2^3*5$$))*1/3; #recurring decimals would be 1. (since the #recurring decimals of 1/3 is 1)
E. I don't want to break my head here.It must contain the maximum number of repeating decimals(with different digits) by method of elimination.

Ans. (E)

If we have 2 primes in the denominator ( other than 2 and 5) then the number of repeating decimals depends on which number? Is the larger prime or the prime with more repeating decimals?

Posted from my mobile device
Senior Manager
Joined: 15 Feb 2018
Posts: 372
Re: Which of the following fractions when expressed as repeating decimals  [#permalink]

### Show Tags

22 Aug 2019, 03:34
divyajoshi12
Do you have the official explanation?

Are there another methods other than that explained by PKN?

We should memorise division by which numbers? 3, 7, 11, any others?

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9705
Location: Pune, India
Re: Which of the following fractions when expressed as repeating decimals  [#permalink]

### Show Tags

23 Aug 2019, 04:39
1
divyajoshi12 wrote:
Which of the following fractions when expressed as repeating decimals would have the longest sequence of different digits?

A) 17/44
B) 5/6
C) 41/66
D) 1/120
E) 2/41.

Check out these posts on terminating/nonterminating decimals:
https://www.veritasprep.com/blog/2013/1 ... -the-gmat/
https://www.veritasprep.com/blog/2014/0 ... fractions/

You should know 1/3, 1/6, 1/7, 1/9, 1/11
_________________
Karishma
Veritas Prep GMAT Instructor

GMAT Tutor
Joined: 24 Jun 2008
Posts: 1806
Re: Which of the following fractions when expressed as repeating decimals  [#permalink]

### Show Tags

23 Aug 2019, 09:11
1
philipssonicare wrote:
We should memorise division by which numbers? 3, 7, 11, any others?

The question in the OP isn't a realistic GMAT problem (partly because to confirm the right answer, E, you need long division). So I wouldn't worry about it much, but PKN's method is about as fast as you can get here.

I cannot imagine a GMAT situation where there would be any advantage to knowing the exact decimal equivalent of 1/7 (which is a six-digit repeating pattern). It should be enough to know that it's roughly 0.14. It is occasionally useful to know the exact decimals of 1/9 and 1/11 though (and how to find related decimal expansions, like 3/11 or 1/99).

yashbhati wrote:
If we have 2 primes in the denominator ( other than 2 and 5) then the number of repeating decimals depends on which number? Is the larger prime or the prime with more repeating decimals?

The theory behind this is miles beyond the GMAT, and you'll never need to know about it for the test. But if you do have a fraction 1/(pq), where p and q are different primes not equal to 2 or 5, then if the decimal equivalent of 1/p repeats in a pattern that is D digits long, and the decimal equivalent of 1/q repeats in a pattern that is E digits long, the decimal of 1/(pq) will repeat in a pattern that is LCM(D, E) (the least common multiple of D and E) digits long.

So for example, since 1/11 repeats in a pattern 2 digits long, and 1/111 repeats in a pattern 3 digits long, 1/(11)(111) = 1/1221 would repeat in a pattern 6 digits long, because 6 is the LCM of 2 and 3. Or, as another example, 1/(7)(11) = 1/77 will repeat in a pattern 6 digits long, because 1/7 has a 6-digit pattern, and 1/11 has a 2-digit pattern, and 6 is the LCM of 6 and 2. You can confirm those results with any calculator.

You'll never need that on the GMAT though.
_________________
GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com
Re: Which of the following fractions when expressed as repeating decimals   [#permalink] 23 Aug 2019, 09:11
Display posts from previous: Sort by