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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
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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
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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
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