It is currently 24 Feb 2018, 23:44

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# List L contains the 98 repeating decimals

Author Message
TAGS:

### Hide Tags

Manager
Joined: 01 Sep 2016
Posts: 207
GMAT 1: 690 Q49 V35
List L contains the 98 repeating decimals [#permalink]

### Show Tags

20 Sep 2017, 00:02
9
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

26% (01:51) correct 74% (01:10) wrong based on 46 sessions

### HideShow timer Statistics

List L contains the 98 repeating decimals 0.010101..., 0.020202..., ..., 0.989898....  If each value in list L is expressed as a fraction in lowest terms, what is the sum of the denominators of all 98 fractions?

(A) 5,096
(B) 5,608
(C) 6,770
(D) 6,894
(E) 9,702
[Reveal] Spoiler: OA

_________________

we shall fight on the beaches,
we shall fight on the landing grounds,
we shall fight in the fields and in the streets,
we shall fight in the hills;
we shall never surrender!

PS Forum Moderator
Joined: 25 Feb 2013
Posts: 947
Location: India
GPA: 3.82
List L contains the 98 repeating decimals [#permalink]

### Show Tags

20 Sep 2017, 06:33
1
KUDOS
2
This post was
BOOKMARKED
bkpolymers1617 wrote:
List L contains the 98 repeating decimals 0.010101..., 0.020202..., ..., 0.989898....  If each value in list L is expressed as a fraction in lowest terms, what is the sum of the denominators of all 98 fractions?

(A) 5,096
(B) 5,608
(C) 6,770
(D) 6,894
(E) 9,702

This is one hell of a question, that requires lot of calculations
A repeating decimals can be converted into fractions as -
let x=0.01010101...., multiply it by 100 to get

100x=1.0101010...., now subtract both the equation to get

99x=1, or x=$$\frac{1}{99}$$

So our question is to find the sum of denominators of the fractions: $$\frac{1}{99}+\frac{2}{99}+\frac{3}{99}+......\frac{98}{99}$$

Notice that the question asks "lowest terms" so fractions that are factors of 99 will get reduced. For eg. $$\frac{3}{99}=\frac{1}{33}$$ and so on.

so from 1 to 98 numbers that are multiples of 11 are 8 (you can use AP formula to get it, 1st term 11 last term 88 and common difference 11)

From 1 to 98 numbers that are multipples of 9 are 10, and

From 1 to 98 numbers that are multiples of 3 are 32. But here, 33 & 66 are already included in muliples of 11 and all multiples of 9 are multiples of 3 so remove them. The final count is 32-(2+10) = 20

Now remaining number from 1 to 98 are = 98-(8+10+20)=60

Now SUM
multiples of 11 except 33 & 66 will have denominator 9 and 33 & 66 will have denominator 3. So sum of all denominators = 2*3+9*6 = 60

multiples of 9 will have denominator 11. So sum of denominators = 10*11 =110

multiples of 3 will have denominator 33. So sum of denominators = 33*20 = 660

Remaining fractions will have denominator 99. So sum of denominators = 99*60 = 5940

Sum of all = 5940+660+110+60 = 6770

Option C
Senior Manager
Joined: 03 Apr 2013
Posts: 290
Location: India
Concentration: Marketing, Finance
Schools: Simon '20
GMAT 1: 740 Q50 V41
GPA: 3
List L contains the 98 repeating decimals [#permalink]

### Show Tags

29 Nov 2017, 23:16
bkpolymers1617 wrote:
List L contains the 98 repeating decimals 0.010101..., 0.020202..., ..., 0.989898....  If each value in list L is expressed as a fraction in lowest terms, what is the sum of the denominators of all 98 fractions?

(A) 5,096
(B) 5,608
(C) 6,770
(D) 6,894
(E) 9,702

Although I could do the question, but it took way more than 2 minutes..
Bunuel can something like this be expected? How to do it fast if yes?
_________________

Spread some love..Like = +1 Kudos

List L contains the 98 repeating decimals   [#permalink] 29 Nov 2017, 23:16
Display posts from previous: Sort by