CAT quantitative section often scares a CAT aspirant. It is deemed to be tough and difficult to crack. So there is a considerable amount of time that one spends on mastering the subject. The truth however is that it is often based on very fundamental concepts in the areas of Arithmetic, Algebra and Geometry. The challenge in quant section is mostly one of maximizing attempts. Though the key to that is ‘decisiveness’ in attempting or not attempting a question, smart methods can add their value too.
Here are a few approaches that one could employ to boost the scores in quantitative ability section. These are questions that have appeared in Old CATs.
1. Use of choices: In any MCQ type of a test, if you are not using the choices, you may be wasting an excellent resource. Mastering this approach could lead to saving time, thus enabling more attempts. Here are two examples.
Example 1 : The owner of an art shop every once in a while he raises his prices by X%, then a while later he reduces all the new prices by X%. After one such updown cycle, the price of a painting decreased by Rs. 441. After a second up-down cycle the painting was sold for Rs. 1,944.81. What was the original price of the painting?
a. Rs. 2,756.25
b. Rs. 2,256.25
c. Rs. 2,500
d. Rs. 2,000
The conventional method would be to find X and so the original price. We shall use only choices here.
B and D cannot be the answers. In the first updown cycle the price reduced by Rs 441. So the final price should have gone below Rs 1944.81. So it has to be either A or C. It is easier checking with C, since 2500 is an easier number to work with. If it was Rs 2500, a drop of Rs. 441 is a drop of almost 17.5 % . So another drop of 17.5 % below (2500 – 441) would take the value below Rs 1944.81. So it cannot be the answer. Hence A has to be the answer. Please don’t waste your time checking A as well. All this can happen in a span of 45 s, if one is good at mental calculations.
Example 2 : Three runners A, B and C run a race, with runner A finishing 12 m ahead of runner B and 18 m ahead of runner C, while runner B finishes 8 m ahead of runner C. Each runner travels the entire distance at a constant speed. What was the length of the race?
a. 36 m
b. 48 m
c. 60 m
d. 72 m
I will start by assuming the race is 60 m long. I have chosen 60 since it is one of the two “middle“ choices. I could have started with 48 as well.
So when A runs 60 m, B runs 48 m and C runs 42 m.
So when B runs 60 m, C would run 52.5 m. B should have defeated C by 7.5 m. But it is given as 8m. So the race could not have been of 60 m.
But which choice do I choose next ? 72 m or 48 m.
Here there is some logic that is useful. Since 12 m, which is the distance that A has to still run to complete the race, is a smaller fraction of 72 than it is of 60. So the lead if the race was 72 m that B gives C would be lesser than 7.5m. Hence we must choose a smaller value than 60.
Check it out for 48m. You would find that this is the appropriate choice. Someone who is used to fast mental calculations and picking choices to solve questions would do this in less than a minute.
2. Short Cuts : This may actually be a misnomer. Some of the most efficient methods need great fundamentals. So a search for a better method when you anslyse the tests will get you to understand concepts better.
Let us take the Example 2 , from the previous case. We will do it by a faster method. You could call this a shortcut !!
When A has a lead of 12 m on B, B has a lead of 6m on C. This 6m finally becomes 8m, which is 4/3 times 6. This would be valid with the distance covered by B too. So the 12m that B has yet to cover is 1/3 of the distance that he has already covered. This means B must have covered 36 m, when A finishes the race. So the length of the race is 48m.
You cannot use these methods arbitrarily. The “decision” making must take as little time as possible. You would develop this skill only after a certain threshold level of practice. So do not ignore the ‘perspiration” behind these methods. And believe me each one of you would able to apply them wisely.
There is a caution though. While you are testing, if you cannot hit of any of the approaches within the first 30 s, do not feel bad about using the conventional time tested methods.