Faster approach for such questions ??

Question

Which of the following, when squared, will yield a value greater than 3/4

a) 2/7
b) (.75)^2
c) 2/3
d) 6/7
e) 7/8

sudhir18n · Answer

the fastest way is, to know 3/4 = 0.75
and square of ~0.9 will be greater than 0.75( 9^2 = 81 >75)

7/8 = ~0.9 hence answer

Shoumik · Answer

When dealing with fractions, try to make the denominator 100.

\frac{3}{4}  is equal to  \frac{75}{100}

We can also note that if a fraction is less than one, and squared, the result will be a lower number. For example:
 (\frac{1}{2})^2 =  \frac{1}{4}  which is less than  \frac{1}{2} .

Since we are looking for a number when squared it will result a number higher than 0.75 or  \frac{75}{100} , we can cancel out options A, B and C because option A is less than 0.5 (numerator is less than half of what the denominator value is). We can cancel out B because  0.75 ^2  will result in a number that is smaller than 0.75 and we can cancel out C because 1/3 = 33% or 0.33, 2/3 = 66.667% or 0.6667..which is less than 0.75

This leaves us with option D & E. One way to look at it is: 4/5 is always greater than 3/4 which is always greater than 2/3 and so on. So we can easily state option E is greater than option D because 7/8 is greater than 6/7.

This can be compared to the analogy: 49/50 (98%) on an exam is less than 99/100 (99%).

Another way to look at it is:

For D:

\frac{6}{7} = \frac{(6*14)}{(7*14)} = \frac{84}{98}

For E:

\frac{7}{8} = \frac{(7*12.5)}{(8*12.5)} = \frac{87.5}{100}

In this case, answer choice E is greater than answer choice D.

KarishmaB · Answer

You can do it without any calculations.
When a positive number less than 1 is squared, it becomes even smaller. e.g. (1/2)^2 = 1/4. 1/4 is less than 1/2.

All the given options are less than 1. When you square them, they will become even smaller. So the answer must be greater than 3/4 to begin with and must be much greater than 3/4 so that even after squaring it remains greater than 3/4.
2/7 < 3/4 Ignore
(.75)^2 < .75 (which is 3/4) Ignore
2/3 < 3/4 Ignore
6/7 and 7/8 are both greater than 3/4.
If 6/7 were the answer and the square of 6/7 were greater than 3/4, since 7/8 is even greater than 6/7, its square would be greater than the square of 6/7 and hence it would be greater than 3/4 too. But we cannot have multiple answers. Hence, the square of only 7/8 must be greater than 3/4. Answer must be 7/8.

pike · Answer

I just dived right in and it was pretty quick

This was my thought process:

A and B clearly not going to happen

Let's square the rest
C) clearly not going to happen

D) 36/49
E) 49/64

Went to E first because it would be easier to work with. 64*3/4 = 48. 49 > 48.

Done. E. <1 min.

Now clearly in hindsight I could have done some things quicker. I should have disregarded C more quickly. Karishma gave some good insight in deciding between D and E. But once I got to that point, its just as easy to dive in and do the math.

As I study more and more for the GMAT I realise that if you think an approach that you know will work, then just jump in and do it.

krishp84 · Answer

Karishma - To be honest, really liked your approach. 
But is it really necessary to think in lateral manner for this question - as calculation was easy and we do not want to think too much for an easy question.
In other words, your approach will help us in really nasty fractions (some bigger numbers in nominator, denominator).

Can you please post a question on nasty fractions where we can apply your approach?
- This will really educate me to decide when to go for the above approach.
Thanks in advance - Here are my kudos !!!

HaasEWMBA2015 · Answer

On this problem you know one of the solutions has to be correct as it's a PS question. As all of the answers are fractions between 0 and 1 and anytime you square a fraction it gets smaller, all you need to do is find the fraction closest to one from the answer choices. E is the answer closest to 1 and it is also the only correct answer. No calculations required.

KarishmaB · Answer

This isn't an approach. It is a way of thinking, a way of solving questions. There are some basic things that get ingrained in our minds because they appear repetitively e.g. When you square a positive number less than 1, it becomes even smaller. When you square a number greater than 1, it becomes larger.
When I provide solutions, I write what comes to my mind first. The way I approached the problem when I solved it on seeing it. As I said, it is a way of doing things.. I am a very lazy person. I hate it if I have to pick up my pen and paper for a non-diagram question. So this is how I approached each option - 2/7 - that's already less than 3/4. Move on. (.75)^2 - same story as above. Move on...
Last two options - Only one answer so the greater one has to be it.
Took me a few seconds and hence I shared it... 
Coming to your question - Should you think for an easy question? I think thinking is far easier than moving my fingers (told you I am lazy).. plus I save a lot of time... Once this way of solving questions is the natural way for you, you will see how convenient it is.. Don't learn it up as an approach because it isn't one. Every question needs a different approach but once you know the basics, your mind will find the right approach in moments. Plus, build up on what you learn. I liked what GZR4DR said above - Don't bother... Just pick the largest value since there is only one answer. Logical next thought once you pick E out of D and E.

Faster approach for such questions ??

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