In this post, I will cover some strategies and concepts required to build speed in the Quantitative and Data Interpretation section of CET. Most of these concepts might come across as extreme basics for some of you, however, a quick revision won’t hurt even the seasoned Math/DI nerds. At the same time, this should offer some tricks and tips to those who are struggling in these areas to stay afloat.
Tables: 1 to 30, Squares: 1 to 30, Cubes: 1 to 16, Reciprocals: 1 to 16
I am surprised that quite a few students don’t practice tables, squares, cubes, reciprocals enough and struggle with basic calculations such as 8*17. If you haven’t done this already, spend some time and get it in place. It will make a huge difference to your DI speed if you’re able to calculate orally. Let’s say the question asks you to find 28.56% of 77, what should immediately come to your mind is 2/7 of 77 = 22. Anything more than 5 seconds for this means that you’ve not practiced it thoroughly and will end up writing it on the rough sheet. One of the questions that I typically ask students is whether they’re able to picture 210 as 14*15 or 6^3 – 6 or whether they can relate to 342 as 7^3 – 1 or 68 as 4^3 + 4. This also helps in case of questions based on number series where one has to select/eliminate multiple possibilities. For example, can I write 30 as 5^2 + 5 or 6^2 – 6 or is it 3^3 + 3 or could it be product of two consecutive natural number 5 and 6? To be able to think this, one first needs to have the basics in place which eventually makes pattern identification easy.
What’s greater? 34% of 450 or 48% of 250? One can solve this question by calculating the exact answer. One can also do it as: 34% of 450 is nearly 33.33% of 450 which is 1/3rd of 450 = 150. 48% of 250 is same as 25% of 480 = 120. So, the one on the left is greater. Or, I can also do it as 250 is slightly more than half of 450 but 34 is far greater than half of 48 and hence will create more impact on the answer. Though this sounds a little difficult to do in the beginning, estimation is one of the best things that one can use to solve calculation intensive sets. You will make a few mistakes initially, but they offer immense learning as well. Try these three questions through observation instead of using pen & paper.
|Year \ Products||A||B||C||D||E|
- Which product has the highest total sales over the time period?
- Which Year saw the highest total sales of all the products?
- For which of the products, the percentage increase in any two consecutive years the highest?
- If we observe the values and ignore the last three digits, A becomes 1+6+6+5+6 = 24. The only product that comes closer would be either C or D and their totals are 21 and 18, respectively. Right answer: A
- Using the same logic from the previous question and considering higher values present in year 2/4/5, we can eliminate Year 1 and Year 3. Right answer: Year 4
- For this one, we will be looking at consecutive values vertically, and figure out where the factor is the highest. We can observe a few values that are doubling. for example, Product B from Year 3 to Year 4. So, let us concentrate on values that are more than doubling. Product A, D, and E have such values. Clearly, in the case of A, from Y1 to Y2, we have a factor of nearly 5.5 which is the highest. Right answer: Product A from Y1 to Y2.
Take this question from a SimCET:
The number of girls appearing for an admission process is twice the number of boys. If 30% of the girls and 45% of the boys get admission, the percentage of candidates who do not get admission is:
(a) 35 (b) 50 (c) 65 (d) 70 (e) None of the above
This is a fairly straightforward question and solving it step by step won’t take more than a minute. But if you’re in a time-crunch situation, you can reduce your possibilities. As 30% and 45% of the components have secured admission, the percentage of students who have been admitted will be between 30% to 45%. So, the percentage of students not admitted will be between (100-45) = 55% to (100-30) = 70%. There is only option that fits this description. Answer: (c) 65
Let’s look at another question:
3 distinct dice are rolled. Find the probability that the sum of the numbers is equal to 15 given that the sum of the numbers that appear is not more than 15?
(a) 1/20 (b) 5/103 (c) 10/209 (d) 5/108 (e) None of these
The first thing that one needs to crack is the denominator part. As there are 3 dice, the total number of outcomes is 6^3 = 216. And starting with maximum possible sum, we get sum 18 = 1 case, 17 = 3 cases from 6-6-5 formation, 16 = 6 cases from 6-6-4 or 6-5-5 formation. So that makes it 10 cases that are not possible. Hence, denominator is 206. From the options, there is only one option that has a factor of 206 which is option (b).
Let’s do one more:
What is the sum of 1^2 + 3^2 + 5^2 + … + 41^2?
(a) 12341 (b) 19455 (c) 11480 (d) 9450 (e) 16455
Square of an odd number is odd and adding 41 odd numbers will give us an odd outcome. So, the answer is clearly an odd number. If I just add the first five instances of this series, I get units digit as: 1 + 9 + 5 + 9 + 1 = 5. There will be 4 such sequences and an extra 1 from the 41^2 that we have at the end. So the answer is an odd number ending value which is not 5. That leaves us with only one choice which is (a) 12341
Option elimination doesn’t work in all the cases and may not even yield the right answer in some cases. However, the perspective that you get when you look at questions in this manner adds a lot of value to your approach. One needs to get out of the ‘solving mindset‘ and reach ‘finding the right answer mindset‘. Wherever required, you will solve. Wherever possible, you will eliminate!
Nothing beats practice when it comes to quantitative ability and data interpretation. The more questions you solve, the better you get. If you just take a pause after every question you solve and appreciate the underlying principle and revise the steps in your head, it will improve your understanding and will make you faster eventually.
I hope this helps. Do let me know if you want me to cover a specific question type in depth and I’ll try to do it in my future posts. If there are any queries, please leave them in the comments below and allow me a few days to get back. Share this with your friends and co-aspirants. Happy prepping! 🙂