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Which of the following is greater than 2/3 and less than 5/6 ?

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Math Expert
Joined: 02 Sep 2009
Posts: 55709
Which of the following is greater than 2/3 and less than 5/6 ?  [#permalink]

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23 May 2019, 01:11
00:00

Difficulty:

25% (medium)

Question Stats:

79% (01:14) correct 21% (02:13) wrong based on 28 sessions

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Which of the following is greater than $$\frac{2}{3}$$ and less than $$\frac{5}{6}$$ ?

I. $$\frac{11}{18}$$

II. $$\frac{13}{18}$$

III. $$\frac{3}{4}$$

A. I only
B. II only
C. III only
D. II and III only
E. I, II and III

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Location: India
Concentration: Nonprofit, Sustainability
GMAT 1: 630 Q47 V30
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Re: Which of the following is greater than 2/3 and less than 5/6 ?  [#permalink]

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23 May 2019, 01:25
Bunuel wrote:
Which of the following is greater than $$\frac{2}{3}$$ and less than $$\frac{5}{6}$$ ?

I. $$\frac{11}{18}$$

II. $$\frac{13}{18}$$

III. $$\frac{3}{4}$$

A. I only
B. II only
C. III only
D. II and III only
E. I, II and III

Only 2.

How to solve these types of questions quickly?

here's my approach

2/3 __ 13/18
Cross multiply
36 < 39, so the fraction on right hand side is greater.

13/18 __ 5/6
Cross multiply
78 < 90, so the fraction on right hand side is greater.
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Re: Which of the following is greater than 2/3 and less than 5/6 ?  [#permalink]

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23 May 2019, 09:15
technique to solve such questions is to cross multiply the bases of the dr and see which is greater ; side which has greater value is bigger

between 2/3 & 11/8 ; 36>33 so 2/3>11/8 so this option is negated
13/18 & 2/3 ; 39>36 ; OKAY and 5/6 & 13/18 ; 90 >78 correct
3/4 & 2/3 ; 9>8 okay ; 3/4 & 5/6 ; 18<20
IMO D
LeoN88
how you negated option III?

Bunuel wrote:
Which of the following is greater than $$\frac{2}{3}$$ and less than $$\frac{5}{6}$$ ?

I. $$\frac{11}{18}$$

II. $$\frac{13}{18}$$

III. $$\frac{3}{4}$$

A. I only
B. II only
C. III only
D. II and III only
E. I, II and III

_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
ISB School Moderator
Joined: 08 Dec 2013
Posts: 433
Location: India
Concentration: Nonprofit, Sustainability
GMAT 1: 630 Q47 V30
WE: Operations (Non-Profit and Government)
Which of the following is greater than 2/3 and less than 5/6 ?  [#permalink]

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23 May 2019, 18:12
Archit3110 wrote:
technique to solve such questions is to cross multiply the bases of the dr and see which is greater ; side which has greater value is bigger

between 2/3 & 11/8 ; 36>33 so 2/3>11/8 so this option is negated
13/18 & 2/3 ; 39>36 ; OKAY and 5/6 & 13/18 ; 90 >78 correct
3/4 & 2/3 ; 9>8 okay ; 3/4 & 5/6 ; 18<20
IMO D
LeoN88
how you negated option III?

Bunuel wrote:
Which of the following is greater than $$\frac{2}{3}$$ and less than $$\frac{5}{6}$$ ?

I. $$\frac{11}{18}$$

II. $$\frac{13}{18}$$

III. $$\frac{3}{4}$$

A. I only
B. II only
C. III only
D. II and III only
E. I, II and III

Yes, you're right 2/3 <3/4< 5/6
Silly mistake Archit, thanks.
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CrackVerbal Quant Expert
Joined: 23 Apr 2019
Posts: 15
Re: Which of the following is greater than 2/3 and less than 5/6 ?  [#permalink]

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23 May 2019, 21:30
There are two ways you can compare fractions:

1. Cross multiply : This process will help you quickly figure out the greater between two fractions, but if we have 2 or more fractions, then we will have to compare the fractions taking two at a time.
2. LCM : This is the best process to compare two or more fractions. The process here involves keeping the denominators of the fractions the same and comparing the numerators.

The LCM is the more preferred of the two processes in questions such as this one. When working with fractions, the denominators of the fractions are key to solving the question. While dealing with word problems with fractions the LCM of the denominators of the fraction is the best value to plug in, instead of trying to solve the question with variables.

The fractions we are working with here are 2/3, 5/6, 11/18, 13/18 and 3/4. If we make the denominators the same, it will become easier to compare all of them together.

The LCM here is 36, so the fractions now become 24/36, 30/36, 22/36, 26/36 and 27/36.

Now the question asks for which of the following fractions are greater than 24/36 and less than 30/36, Clearly we have two possibilities here, 26/36 and 27/36 which are 13/18 and 3/4.

Re: Which of the following is greater than 2/3 and less than 5/6 ?   [#permalink] 23 May 2019, 21:30
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