BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Easy Way to Solve...

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Newbie | Next Rank: 10 Posts
Posts: 4
Joined: Sun Jun 19, 2011 4:07 am

Easy Way to Solve...

by s.gandham » Mon Jan 30, 2012 10:36 am
Hi,

Can anyone help me to solve the question with some trick/shortcuts.

Q)Find the largest number of the following.

1. 11/13
2. 13/15
3. (11/13)^2
4. (11/13)^3
5. (11/13)^4

Thanks & Regards,
Sekhar
Top
Source: — Problem Solving |
User avatar
Legendary Member
Posts: 588
Joined: Sun Oct 16, 2011 9:42 am
Location: New Delhi, India
Thanked: 130 times
Followed by:9 members
GMAT Score:720

by rijul007 » Mon Jan 30, 2012 11:02 am
s.gandham wrote:Hi,

Can anyone help me to solve the question with some trick/shortcuts.

Q)Find the largest number of the following.

1. 11/13
2. 13/15
3. (11/13)^2
4. (11/13)^3
5. (11/13)^4

Thanks & Regards,
Sekhar
There is a property for comparing two fractions
lets say we need to compare two fractions
p/q and r/s

if q-p = s-r
and p>r
then p/q > r/s

similarly int his ques
11/13 < 13/15

when a fraction is raised to a power which is a positive integer, the value decreases
for eg.
1/2 > (1/2)^2 >(1/2)^3

Hence, 13/15 is the largest number
Top
Master | Next Rank: 500 Posts
Posts: 265
Joined: Mon Dec 28, 2009 9:45 pm
Thanked: 26 times
Followed by:2 members
GMAT Score:760

by mj78ind » Mon Jan 30, 2012 4:35 pm
s.gandham wrote:Hi,

Can anyone help me to solve the question with some trick/shortcuts.

Q)Find the largest number of the following.

1. 11/13
2. 13/15
3. (11/13)^2
4. (11/13)^3
5. (11/13)^4

Thanks & Regards,
Sekhar
For any fraction m, 0<m<1, m>m^2>m^3 ..... etc. Hence 11/13 is biggest in choices - 1,3,4 and 5. Now comparing 1 and 2, let's make the denominators same multiply and divide choice 1 by 15 = 165/13*15; multiply and divide by 13 for choice 2 - 169/13*15, hence 2 is bigger.

Hence answer is 2
Call me 1 - (412) 897 6727 (US) or leave a msg on BTG for GMAT advise / questions.
If you like the solution, check out my debrief at and leave a comment:
https://www.beatthegmat.com/760-done-dea ... 66740.html
Top
User avatar
GMAT Instructor
Posts: 509
Joined: Wed Apr 21, 2010 1:08 pm
Location: Irvine, CA
Thanked: 199 times
Followed by:85 members
GMAT Score:750

by tpr-becky » Tue Jan 31, 2012 10:41 am
I always compare fractions using the bow tie method - cross multiplying from bottom to top - the fraction with the larger product will be bigger - then do it one at a time (it really is fast)

11/13 - 13/15 is 165 vs 169 so B is larger.

121/169 vs 13/15 multiplying shows that that 121(15) is less than 169(13) so B is still larger

Now you can recognize a pattern that the 13^3 will be the same product you figured out for 169(13) and 11^3 is 1331

1331/2197 vs 13/15 - it is getting clearer that 2197(13) will be bigger than 1331(15) thus B is still greater following this pattern you know that B will be greater than E because the denominator will be much greater than the numerator.

Thus B is the answer.
Becky
Master GMAT Instructor
The Princeton Review
Irvine, CA
Top
Post new topic Post Reply
• Page 1 of 1