# Faster Calculation methods applied on ‘Real Exam Questions’ – Part IV

Hi friends, today we will take up a Data Interpretation problem to discuss one of the most important and frequently used technique to arrive at answers faster where calculations are involved – “Reciprocal to Percentage conversion”. Here’s the question:

I will show you how this concept works for 2 (out of total 5) direct questions that were asked in this problem set. First question:

Although it is a direct question, the calculation that stares at us is:

An increase of 1.03 (9.45 minus 8.42) over the base value 8.42. The answer is a second away if we know that 1/8 = 12.5%. The option has to be less than 12.5 as the actual base is 8.42- answer option (E).

Now, the second problem:

Again a direct calculation-based question; the question is to find the value of : (9.28* 100/5.53). If we know that 1/18 is equal to 5.55% and 1/5.55 is 18% then the question can be converted into: 18 * 9.28, the result of which would be bit more than 162- Answer (c) 168.

Let us take one more real exam questionย to apply the same concept:

We should approach it in this way, rather than multiplying 22 with 450 and dividing by 100:

11% is 1/9, so 22% is 2/9. Since 1/9th of 450 is 50, answer would be 100- Option (2). If multiplying takes 20 seconds, the second approach should take 10 seconds or even lesser. ๐ Now that we have used this concept in quite a few problems and know for sure that it would come handy during calculations across various topics, let us come to the crucial part of our discussion and that is:-

How to remember reciprocal to percentage conversion?

The best way to ‘engrave’ this in your mind is to remember them in groups.

1/1 is 100%.

1/2 is 50%, thus 1/4, 1/8, 1/16 would be 25%, 12.5%, 6.25% respectively. You can extend this to 1/32, 1/64 also (3.125 %, 1.56 % respectively.

If 1/3 is 33.33%, 1/9 must be 11.11%. 1/9 and 1/11 can be remembered in this way- 1/9 consists of ‘ELEVENS’ (11.11%) and 1/11 consists of ‘NINES’ (09.09)

1/5 is 20% and 1/4 is 25% (Straight-forward).

1/6 is half of 1/3 or 16.6666

1/7 consists of 14 and 28 (multiples of 7); value is 14.28. Half of 1/7 is 1/14 so the value is 7.14.

1/12 is 8.33%

1/13 is 7.69 [ The square of 13 is 169, the last two digits are same as the decimal part].

Reciprocal of 15 and 18 can be remembered in this fashion. 1/15 consists of ‘SIXES’ i.e. 6.666 and 1/18 consists of ‘FIVES’ i.e. 5.55.

1/17 is 5.88 or approximate it to 5.89 [Square of 17 is 289, the last two digits is the decimal part].

The triplet of reciprocals of 19, 20, 21 vary from each other by 0.25 approximately.

Since it is easy to remember 1/20 as 5%, the reciprocal of 19 can be remembered as 5.25% and the reciprocal of 21 as 4.75%

We covered reciprocals till 21 which is a good range; you can also remember till 30 by formulating your own methods! ๐

NOW, you can extend this concept to another dimension by saying that if 1/6 is 16.66 %, then 1/16.66 is 6% (reversing the position). If 1/18 is 5.55, then 1/5.55 is 18% – we used this in the second problem. ๐ If 1/12 is 8.33% then 1/8.33 is 12% (verify that we could have used this concept also in the 1st problem ๐ . We used 11% as the starting point for the last problem.

Go through the entire post once every day for just one week and apply it to consolidate the learning.Request you to share your ‘calculation’ experiences here with everyone to help others also in learning the ‘efficacy’ of this technique!