# Calculating Faster - Online Article

## Calculating Faster

Speed in solving questions is of crucial importance if one wants to crack the MBA entrance exams. In fact, the only two skills tested in the Data Interpretation section are those of understanding data or interpreting information from raw data and calculating fast.

In this article we will look at the basic groundwork you must do before you can even think of doing calculations involving complex divisions within 20 seconds.

One needs to thoroughly learn:

- Tables up to 30 × 30
- Squares up to 30
- Cubes up to 15
- Square roots up to 10
- Cube roots up to 5
- Reciprocal percentage equivalents up to 30

It seems like a very tedious and time consuming task. However, it is not as tough as it seems. Try this -- what is 7 × 8? I bet anyone would have answered 56. Now, what is 14 × 8? Even if I don't know the tables, I can understand it would be twice of 7 × 8, i.e. twice of 56, i.e. 112. Even though one did not know table of 14, one could have arrived at the answer within couple of seconds. Thus, except tables of prime numbers, i.e. 13, 17, 19, 23 and 29 all other tables till 30 can be done in this way if one knows the tables till 12.

### Reciprocal Percentage Equivalents

Reciprocal percentage equivalents are the reciprocals of numbers 1 to 30 in percentages, e.g. the reciprocal of 3 is 0.3333 or 33.33%. Reciprocal percentage equivalent of 5 is 20%, of 6 is 16.66% and so on. Reciprocal percentage equivalents are an absolute must for one to crack quantitative section. Not only do they immensely help in division but also in many quant questions. So be sure to learn them by heart. You can also make and use flashcards to help you in memorizing them.

### Memorising Reciprocal Percentage Equivalents

Let's see how reciprocals can be memorized. Almost everyone knows that reciprocal of 2 is 50%, of 3 is 33.33% and of 5 is 20%. If reciprocal of 2 is 50%, the reciprocal of 4 is half of 50%…25%? The reciprocal of 8 will be half of 25%...12.5%. Similarly, reciprocal of 16 will be 6.25%. Also if I know reciprocal of 3 as 33.33%, I can also conclude reciprocal of 6, 9 will be 16.66% and 11.11% respectively.

Thus, from 1 to 10, one has to only mug up reciprocal of 7 which is 14.28% (simple two times 7 is 14 and two times 14 is 28…thus 14.28).

If reciprocal of 9 is 11.11, reciprocal of 11 is 09.090909. Reciprocal of 9 is composed of 11s and reciprocal of 11 is composed of 09s.

Reciprocal of 12 will be half of reciprocal of 6, i.e. half of 16.66%, i.e. 8.33%.

Thus, we see that except for prime numbers, we can very easily remember the reciprocals of all others. Thus, effectively we need to mug up reciprocals of only 7, 13, 17, 19, 23 and 29.

Some other numbers that can be remembered easily and the methods are:

- Reciprocal of 20 is 5%. Reciprocal of 21 is 4.76% and of 19 is 5.26%. Thus, we can easily remember the reciprocals of 19, 20, 21 as 5.25%, 5, 4.75% respectively.
- Reciprocal of 29 is 3.45% (i.e. 345 in order) and reciprocal of 23 is 4.35% (same digits but order is different)
- Reciprocal of 22 is half of 09.0909%, i.e. 4.545454%, i.e. consists of 4s and 5s.
- Reciprocal of 18 is half of 11.1111%, i.e. 5.55555%, i.e. consists of only 5s.

Thus, the work may seem to be a huge task, but if we use a smart approach, it is hardly anything. And compare it with the time it can save and the confidence it leads to. . . if any calculation has 9 in the denominator, I know for sure the decimal part will be only 0909. . . or 1818… or 2727… or 3636…, e.g. 84/9 will be 9.272727, and can be found out in a jiffy

One can also calculate any fraction of the type (n-1)/n (n <= 30) within two seconds if one knows the reciprocal percentage equivalent. e.g. 11/12 is nothing but 1 – 1/12, i.e. the complement of 0.08333 which is 0.91666. Similarly, if I know 1/23 is 0.0435, 22/23 will be 0.9565.

Thus, the work may seem to be a huge task, but if we use a smart approach, it is hardly anything. And compare it with the time it can save and the confidence it leads to. . . if any calculation has 9 in the denominator, I know for sure the decimal part will be only 0909. . . or 1818… or 2727… or 3636…, e.g. 84/9 will be 9.272727, and can be found out in a jiffy

One can also calculate any fraction of the type (n-1)/n (n <= 30) within two seconds if one knows the reciprocal percentage equivalent. e.g. 11/12 is nothing but 1 – 1/12, i.e. the complement of 0.08333 which is 0.91666. Similarly, if I know 1/23 is 0.0435, 22/23 will be 0.9565.

### Factorisation

Factorisation is a process which goes a long way in reducing the calculations required. Factorisation in its basic sense has been used by many of us, e.g. if we want to find 17 × 21, we would do 17 × 20 + 17, i.e. 357. We have factorised 21 as

20 + 1.

Let's see how we can use this for even more tougher problems.

Let's say we want to find 14.25% of 3267.

What will 10% of 3267 be… 326.7

And 1%… obviously 32.67. Then what would 4% be… 128 for 32 and 2.68 for 0.67..., i.e. 130.6

Thus, 14% will be 326.7 + 130.6, i.e. 457.3

If I want an even more accurate answer, if 1% is 32.6, then 0.25% will be 1/4 of 32.6, i.e 8.15

14.25% of 3267 will be 465.4

The best part of this method is that I have the liberty of deciding how accurate an answer do I require. Thus, if alternatives are wide apart, I may stop the process in-between.

Knowing reciprocal percentage equivalent, I should have thought of an even better factorisation as 14.28% – 0.03% and since 14.28% is nothing but 1/7, the answer can directly be found by dividing 3267 by 7, i.e. 466.7

Factorisation can also be used in division. If I have to find 1465/320, I would write it as

(1280 + 185)/320 which is nothing but 4 + (160 + 25)/320, which is 4.5 + 25/320.

So my answer will be slightly more than 4.5 and less than 4.6

Let's see another example where I can save a lot of calculations.

If I have to find 4835/7280 is of what percentage and the alternatives to choose from, are:

- 59.6%
- 63.8%
- 66.4%
- 71.4%

Just focus on denominator. 10% of the denominator would be 728. Thus, the answer will be definitely less than 70% (since 7* 10% i.e. 70% of the denominator will be more than 4900 i.e. more than the numerator) and also answer will be more than 60% (since 6*10% will be around 4360). 2/3 of 7280 will be 4860. Since the numerator is less than 4860, the answer choice has to be less than 2/3 or 66.66% and hence (c) is the obvious choice.

For making use of approximations, one must make sure that he treats the alternatives as also a part of the questions. Thus, one must consciously use the process of elimination immediately after finishing reading the questions, this will force the person to have a look at the alternatives.

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Prashant Gaur on A good article for the person who is interested in solving aptitude questions...!!! |