Which of the following is greatest?

Question

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..

KarishmaB · Accepted Answer

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.

anshumishra · Answer

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.

Posted from my mobile device

whiplash2411 · Answer

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.

krishnasty · Answer

great method....thnks..

USCTrojan2006 · Answer

D. Then again, I'm quite familiar with basketball statistics.

Is this really a gmat question?

KarishmaB · Answer

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.

kanusha · Answer

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.

chetan2u · Answer

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

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

tallyho_88 · Answer

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.

jmwon · Answer

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.

Vishal120 · Answer

Quick trick

Ignore all square because denominator are big they will get smaller by squaring

So here in this image
Take difference of numerator and denominator and take lcm of all then

Multiple each numerator by respective multiplier as shown highest fraction will answer

Posted from my mobile device

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Which of the following is greatest?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Which of the following is greatest?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards