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Smallest & Largest Fractions: How To?

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Smallest & Largest Fractions: How To? [#permalink]

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New post 12 Jun 2010, 02:57
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If we are given a few fractions like:

Q1) 6/7 , 7/8 , 9/10 , 12/13 , 34/35

Q2) 3/8 , 5/7 , 7/8 , 9/12

And we are asked to find the smallest or the largest of the given fractions then what is the best, fool proof and above all the quickest strategy to solve such questions?
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Re: Smallest & Largest Fractions: How To? [#permalink]

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New post 12 Jun 2010, 05:13
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Question 1 - See the pattern -> difference between the numerator and denominator is 1 in all the options. So go with the option with largest integers (like 1/2 is always smaller than 2/3). Clearly the last option

Question 2 - Here the difference between numerator and denominator is not equal in all options

Use this method -> cross multiply the options. Lets take 3/8 on left side and 5/7 on right side (3/8 = 5/7). This will give 21 on left side 40 on right side (21 = 40). Option with greater number will always be greater, so in this case 5/7 is greater than 3/8. You can check all option this way.

I dont think GMAT ever gives large fractions without common difference between numerator and denominator.

Both the methods are full proof and can never go wrong.

Hope this helps
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Re: Smallest & Largest Fractions: How To? [#permalink]

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New post 12 Jun 2010, 11:33
Fully agree w/ Q1

My "strategy" for Q2 would be the following:

Q2) 3/8 , 5/7 , 7/8 , 9/12

1) Looking for "obvious" differences: e.g., > vs. < 0.5 in this case the only fraction <0.5 is 3/8 (3/8<4/8) - so we figured out our smallest fraction

2) Looking for options to "easy cancel out" 9/12 is similar to 6/8 - 6/8 is def. smaller than 7/8

3) Final check between 5/7 vs. 7/8 by cross multiplication (if needed)

Only step 3 requires "real" calculation
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Re: Smallest & Largest Fractions: How To? [#permalink]

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New post 18 Jun 2010, 08:30
farukhawais wrote:
If we are given a few fractions like:

Q1) 6/7 , 7/8 , 9/10 , 12/13 , 34/35

Q2) 3/8 , 5/7 , 7/8 , 9/12

And we are asked to find the smallest or the largest of the given fractions then what is the best, fool proof and above all the quickest strategy to solve such questions?


Honestly, you should probably know what 1/2, 1/3, 1/4, 1/5, 1/6, 1/7 and 1/8 are in decimal terms without having to do any calculations. This will be very handy on the exam.

If I were stuck, I'd use the above methods.
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Re: Smallest & Largest Fractions: How To? [#permalink]

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New post 18 Jun 2010, 11:44
Thanks for the response.

Do you have what you may call a "cheat sheet" or a "tips sheet" or a "cram sheet": that would have all the important things that I ought to remember. Especially containing fractions, multiplication tables, squares, cubes, square roots etc. Of course I can make my own any time but perhaps you would have something that has been aptly prepared while considering the type of arithmetic we would get to solve on GMAT.

Being an engineer, I normally have never learnt such things by heart. Calculator has always been my best friend. But now that I am planning to sit for GMAT, I would appreciate if you can share some relevant info; that is: things that I need to remember to shorten the time to answer quant questions.

Thanks again for the response.

Cheer,
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Re: Smallest & Largest Fractions: How To? [#permalink]

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New post 18 Jun 2010, 12:20
^I feel your pain.

After using the my fin. calculator for the last 2 years. Its been very hard to part from it. So tempted to use it, but I made sure to take out the batteries...
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Re: Smallest & Largest Fractions: How To? [#permalink]

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New post 15 Aug 2016, 01:38
Here are some rules that will help you compare the fractions=>
For question 1 => Adding same thing to both the numerator and the denominator brings the fraction closer to one.
Hence there are two cases => Case 1 - If the fraction is proper ->(0,1) :- then the value will increase
Case 2 => if the concerned fraction is Improper -> (1,∞) :- then the value of the concern fraction will decrease

For Question 2=> Just simply divide them here.
The fractions involved are too easy for the ease of calculations.


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Re: Smallest & Largest Fractions: How To? [#permalink]

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New post 16 Aug 2016, 12:16
I like to start these by finding pairs of numbers in which one is clearly greater/smaller than the other. Then, if you're looking for the greatest number, you can eliminate the smallest in any pair. For instance, in your second question, 7/8 is clearly greater than 3/8, so I eliminate 3/8. (Writing 'A B C D E' on your paper as you start can be helpful.) Then, notice that 9/12 = 3/4 = 6/8, which is also smaller than 7/8. The only two candidates remaining are 7/8 and 5/7, so cross-multiply those. Whichever one is greater is the answer.
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Re: Smallest & Largest Fractions: How To?   [#permalink] 16 Aug 2016, 12:16
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