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 Post subject: GMAT Fractions
PostPosted: Tue Apr 09, 2013 11:26 am 
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Joined: Tue Apr 13, 2010 8:48 am
Posts: 481
Which of the following fractions is the largest?
A. 11/14
B. 4/5
C. 9/14
D. 7/10
E. 5/6

(E) One way to solve this type of problem is to find the lowest common denominator for all of the fractions.To do this, first factor all of the denominators:
11/14: 14 factors into 2 and 7
4/5: 5 is prime
17/21: 21 factors into 3 and 7
29/35: 35 factors into 5 and 7
5/6: 6 factors into 2 and 3.

Then, to get a common denominator, we make sure that each of the factors is represented exactly once (since no factor is raised to a power in any denominator):
2 × 3 × 5 × 7 = 210.

Therefore, 210 is the lowest common denominator. Now we can express all the fractions in terms of the common denominator of 210 to see which is the largest:
11/14 × 15/15 = 165/210
4/5 × 42/42 = 168/210
9/14 × 15/15 = 135/210
7/10 × 21/21 = 147/210
5/6 × 35/35 = 175/210.

Therefore, 5/6 is the largest (175/210). The correct answer is choice (E).
-------------

I don't understand how you arrived at 15/15 , 42/42, 15/15 , 21/21, 35/35.
Can you please explain further.


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 Post subject: Re: GMAT Fractions
PostPosted: Tue Apr 09, 2013 11:27 am 
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Joined: Fri Apr 09, 2010 2:11 pm
Posts: 457
Once we find that the common denominator is 210, we need to convert all the fractions.

Let us convert the fraction 11/14 first.
210 / 14 = 15. Therefore wee need to multiple the denominator by 15 to get 210. In order to keep the fraction the same we need to multiply the numerator by 15 as well.
11/14 = (11 × 15)/(14 × 15) = 165/210.

The rest of the fractions are converted the same way.


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