Number between 2/3 and 3/4

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independent: Junior | Next Rank: 30 Posts; Posts: 17; Joined: Sat Mar 17, 2012 2:27 pm; GMAT Score:600

by independent » Mon Aug 27, 2012 11:19 am

Ok guys, either am I doing something wrong or the OA is incorrect. Here is the problem:

Which of the following numbers does not fall between 2/3 and 3/4?

A: 5/7
B: 7/11
C: 8/11
D: 9/13
E: 11/14

OA: E

I got B

Thanks in advance.

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Source: Beat The GMAT — Problem Solving | Mon Aug 27, 2012 11:19 am

vk_vinayak: Legendary Member; Posts: 502; Joined: Tue Jun 03, 2008 11:36 pmFollowed by: 21 members; Thanked: 99 times

by vk_vinayak » Mon Aug 27, 2012 11:42 am

independent wrote:Ok guys, either am I doing something wrong or the OA is incorrect. Here is the problem:

Which of the following numbers does not fall between 2/3 and 3/4?

A: 5/7
B: 7/11
C: 8/11
D: 9/13
E: 11/14

OA: E

I got B

Thanks in advance.

2/3 =0.66 and 3/4=0.75 We need to find a number that is either less than 0.66 or more than 0.75

A: 5/7 = 0.71
B: 7/11 = 0.63
C: 8/11 = 0.72
D: 9/13 = 0.69
E: 11/14 = 0.78

Both B and E are correct.

- VK

I will (Learn. Recognize. Apply)

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independent: Junior | Next Rank: 30 Posts; Posts: 17; Joined: Sat Mar 17, 2012 2:27 pm; GMAT Score:600

by independent » Mon Aug 27, 2012 11:46 am

vk_vinayak wrote:
independent wrote:Ok guys, either am I doing something wrong or the OA is incorrect. Here is the problem:

Which of the following numbers does not fall between 2/3 and 3/4?

A: 5/7
B: 7/11
C: 8/11
D: 9/13
E: 11/14

OA: E

I got B

Thanks in advance.
2/3 =0.66 and 3/4=0.75 We need to find a number that is either less than 0.66 or more than 0.75

A: 5/7 = 0.71
B: 7/11 = 0.63
C: 8/11 = 0.72
D: 9/13 = 0.69
E: 11/14 = 0.78

Both B and E are correct.

Thanks. Then there is a mistake because only one was supposed to be correct.

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cypherskull: Senior | Next Rank: 100 Posts; Posts: 94; Joined: Sat Mar 31, 2012 3:39 am; Location: Calcutta; Thanked: 8 times

by cypherskull » Mon Aug 27, 2012 12:16 pm

Yep. I got the same thing. Both B & E are correct.

Although, I learned an interesting technique of comparing fractions which saves me a lot of time I used to take in calculating decimal equivalents. Sharing it just in case anyone finds it useful.

Considering the 2 fractions - 2/3 (LHS) and 3/4 (RHS). We want to determine which is greater.

1) Cross-multiply the 2 fractions - 2*4 (LHS) and 3*3 (RHS), i.e., 8 (LHS) and 9 (RHS).
2) As seen from step 1, RHS (right hand side) is higher.
3) So, 3/4 > 2/3.

Consider, 7/11 (LHS) & 11/12 (RHS).

Cross-multiplying yields, 84 and 121. So, 11/12 (RHS) is greater.

Apply it to any fraction...it works!!!

Regards,
Sunit

________________________________

Kill all my demons..And my angels might die too!

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Tue Aug 28, 2012 6:10 pm

cypherskull wrote: Sharing it just in case anyone finds it useful.

Considering the 2 fractions - 2/3 (LHS) and 3/4 (RHS). We want to determine which is greater.

1) Cross-multiply the 2 fractions - 2*4 (LHS) and 3*3 (RHS), i.e., 8 (LHS) and 9 (RHS).
2) As seen from step 1, RHS (right hand side) is higher.
3) So, 3/4 > 2/3.

Consider, 7/11 (LHS) & 11/12 (RHS).

Cross-multiplying yields, 84 and 121. So, 11/12 (RHS) is greater.

Apply it to any fraction...it works!!!

It might be useful to understand just why this works - it's something you've certainly done many times (but in a slightly different way) before learning it as a 'trick'. If you take the fractions 7/11 and 11/12, then one way to compare them is to get a common denominator. We can use 11*12. Then our fractions would be (7*11)/(11*12) and (11*11)/(11*12). Now whichever fraction has the larger numerator has the larger overall value. Notice the numerators here are exactly what you got using the 'cross-multiplying trick'.

So when you use that 'cross-multiplying' trick, you're just finding a common denominator, but you aren't writing that denominator down. One reason it can be useful to understand just what you're doing in these situations is that it may let you save a lot of time. If you need to compare the fractions 13/18 and 17/24, say, cross-multiplying certainly isn't very fast. It's much faster to notice we can use a common denominator of 72:

13/18 = 52/72
17/24 = 51/72

so 13/18 is larger.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

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mohan514: Senior | Next Rank: 100 Posts; Posts: 82; Joined: Wed Feb 08, 2012 8:33 pm; Location: india

by mohan514 » Fri Aug 31, 2012 8:50 am

contrvversial and easy to poinjt out question

both are satisfying the condition

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