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Which of the following is greatest?

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Which of the following is greatest?  [#permalink]

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New post 05 Dec 2010, 07:26
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Which of the following is greatest?

A. 7/12
B. (7/12)^2
C. 9/13
D. 17/20
E. (17/20)^2

i could solve the problem by brute force method. but that took time. is there any simpler method to arrive at the solution at a much faster rate?

thnx..

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Re: Which of the following is greatest?  [#permalink]

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New post 05 Dec 2010, 20:22
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krishnasty wrote:
which of the following is greatest?

a. 7/12
b. (7/12)^2
c. 9/13
d. 17/20
e. (17/20)^2

i could solve the problem by brute force method. but that took time. is there any simpler method to arrive at the solution at a much faster rate?

thnx..


First of all, let me reiterate whiplash2411's point:
You can immediately rule out the two square terms as they will be smaller than their respective square root terms.
When positive fractions less than 1 are squared, they become smaller.
Square of 1/2 is 1/4 which is smaller than 1/2.

So only 3 options to consider
a. 7/12
c. 9/13
d. 17/20
Many ways to quickly deal with it. Some have already been discussed above. Some I will take here:

Method 1:
Compare 7/12 and 17/20
I see that 17 is more than double of 7 but 20 is less than double of 12. So 17/20 is greater than 7/12
or look at it this way 7/12 = 14/24.
14/24 is less than 17/20 definitely because 17/20 has greater numerator and smaller denominator.

Compare 9/13 and 17/20
17 is almost double of 9 but 20 is quite less than the double of 13. So 17/20 is greater than 9/13.
So 17/20 is the greatest.

Method 2:
Compare 7/12 and 9/13. If I increase the numerator and denominator by the same number in a positive fraction less than 1, the fraction increases. e.g. 7/12 < \(\frac{7 +1}{12 + 1}\) i.e.
7/12 < 8/13. We know 8/13 is definitely less than 9/13. (Denominator same, numerator greater)

Now compare 9/13 and 17/20.
9/13 < \(\frac{9 +8}{13 + 8}\) i.e. 17/21.
We know 17/21 is definitely less than 17/20 (Numerator same, denominator smaller)
So 17/20 is the greatest.

Formal method:
Compare 7/12 and 9/13. Is 7*13 (=91) greater or 9*12 (=108) greater?
Since 9*12 is greater so 9/13 is the greater fraction. (Essentially you are making the denominator same 12*13 in this case but you don't need to calculate it. You just need to compare the numerators you will get)

Now compare 9/13 and 17/20. Is 9*20 (=180) greater or 17*13 (don't want to calculate but it is definitely much greater than 170, even greater than 200) so 17/20 is the greatest.
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Re: Which of the following is greatest?  [#permalink]

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New post 05 Dec 2010, 09:51
Try to convert them in decimal,
I did it in my head, as in this case :
17/20 = 0.8...
the other two fractions are 0.6....
So, don't try to waste more time there.

Again, when you multiply anything with less than 1 , the result will be lesser in value,

hence (17/20)^2 < 17/20.

Hope, it is clear.

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New post 05 Dec 2010, 10:26
krishnasty wrote:
which of the following is greatest?

a. 7/12
b. (7/12)^2
c. 9/13
d. 17/20
e. (17/20)^2

i could solve the problem by brute force method. but that took time. is there any simpler method to arrive at the solution at a much faster rate?

thnx..


You can immediately rule out the two square terms as they will be smaller than their respective square root terms.

Between 7/12, 9/13 and 17/20 you can just divide them out or convert them to a single denominator and see what the biggest number is, though I'd advise you to just convert them to decimal.

17/20 is 0.85, 7/12 is 0.583 and 9/13 is approximately 0.7. Hence D is your answer.
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New post 05 Dec 2010, 21:02
great method....thnks..
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Re: Which of the following is greatest?  [#permalink]

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New post 05 Dec 2010, 23:32
D. Then again, I'm quite familiar with basketball statistics.

Is this really a gmat question?
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Re: Which of the following is greatest?  [#permalink]

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New post 06 Dec 2010, 05:47
USCTrojan2006 wrote:
D. Then again, I'm quite familiar with basketball statistics.

Is this really a gmat question?


GMAT also likes to give you questions which seem calculation intensive but really are just about logic and some manipulation. At first glance, a person might feel that he/she has to convert each of the options in decimals to compare. That is valuable time lost. You can see such questions in actual GMAT though they will be, lets say, 500- 600 level questions.
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Re: Which of the following is greatest?  [#permalink]

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New post 05 Mar 2016, 05:23
Compare 7/12 and 17/20
I see that 17 is more than double of 7 but 20 is less than double of 12. So 17/20 is greater than 7/12
or look at it this way 7/12 = 14/24.
14/24 is less than 17/20 definitely because 17/20 has greater numerator and smaller denominator.

We can solve this by making denominator same number as 60 by multiplying 12*5 and 20*3
So, 17/60 greater than 7/60

Can I solve this way karishama.
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Re: Which of the following is greatest?  [#permalink]

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New post 05 Mar 2016, 05:47
kanusha wrote:
Compare 7/12 and 17/20
I see that 17 is more than double of 7 but 20 is less than double of 12. So 17/20 is greater than 7/12
or look at it this way 7/12 = 14/24.
14/24 is less than 17/20 definitely because 17/20 has greater numerator and smaller denominator.

HI,
the logic in comparing 7/12 and 17/20 is CORRECT


Quote:
We can solve this by making denominator same number as 60 by multiplying 12*5 and 20*3
So, 17/60 greater than 7/60


Here you are wrong in your approach..
yes, to compare any two fractions, the real values will come when we convert the denominators to same value..
BUT you have to multiply the numerator too in the process..


example of 7/12 and 17/20..
common denominator yoy have taken is 60..
20*3= 60, so 17/20 = 17*3/20*3= 51/60
12*5=60, so 7/12=7*5/12*5=35/60..
now numerator 51> numerator 35, so 51/60 >35/60 or 17/20>7/12

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Re: Which of the following is greatest?  [#permalink]

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New post 28 Apr 2016, 01:09
first of all we can totally rule out the squares. they are obviously smaller than their under root.

Take two fractions:
17/20 and 9/13.
Multiply denominator of one with the numerator of another.
so it will be: 13*17=221 and 20*9=180
Since 221 is bigger, therefore the no. whose numerator was used is bigger i.e 17/20

u can try this for all pairs.
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Re: Which of the following is greatest?  [#permalink]

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New post 29 Jul 2019, 17:23
I used a combination of strategies to answer this question quickly.

1) Automatically cross out B and E since they are squares of fractions. Squares of fractions are always smaller than the fraction that is being squared.

2) Estimated values of A, C, D to see if can further identify smaller answers. A is \(\frac{7}{12}\) which is very close to \(\frac{6}{12}\) which is \(\frac{1}{2}\). C is \(\frac{9}{13}\) which is more than \(\frac{6}{12}\) which is \(\frac{1}{2}\). D is \(\frac{17}{20}\) which is more than \(\frac{10}{20}\) or else \(\frac{1}{2}\). Therefore A is out since it is clearly closer to \(\frac{1}{2}\).

3) Finally comparing C and D, used fraction comparison trick: cross multiply the fractions and the fraction with the higher product is the higher fraction. The products are matched to the fraction by the numerator.
Ex. \(\frac{A}{B} \frac{C}{D}\) --> B*C = Product for fraction \(\frac{C}{D}\) and A*D = Product for fraction \(\frac{A}{B}\).

Therefore \(\frac{9}{13}\) and \(\frac{17}{20}\) --> 13*17 = 221 (product for \(\frac{17}{20}\)) and 9*20 = 180 (product for \(\frac{9}{13}\)).
D \(\frac{17}{20}\) is the larger fraction.

krishnasty wrote:
Which of the following is greatest?

A. 7/12
B. (7/12)^2
C. 9/13
D. 17/20
E. (17/20)^2

i could solve the problem by brute force method. but that took time. is there any simpler method to arrive at the solution at a much faster rate?

thnx..
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Re: Which of the following is greatest?   [#permalink] 29 Jul 2019, 17:23
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