# You Got It Right – Playing with numbers

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By R. Sreenivasan (Co-FOunder, CL), article appeared in THE HINDUSTAN TIMES (Enhance). www.sreeni.org

The two principles of data interpretation are –

1.Â Understand the graph thoroughly

2.Â Build your speed and answer as fast as you can

But more important is to be comfortable with numbers and play with them. Towards this end you need to –

• Master tables up to 30 X 30, reciprocals upto 30
• Faster conversions from %ges to fractions and fractions to %ges with the help of knowledge of reciprocals
• Knowledge of ratios which help in comparisonsÂ  of fractions
• Make approximations mentally and keep eliminating the choices instead of calculating the answers going all the way, which will be time consuming.

In this edition let us look at one of the other variations of data interpretation called caselet, which most of the aspirants are very vary of attempting.

Before I look at it, I would like to bring to your notice the approximation methods that will be used here. We discussed them in the last article on DI. Many readers I believe, called the HT office seeking clarifications on the method used. You should keep in mind that you are working on approximations.Â  For your benefit I am discussing in detail here –

 Â Approximations through method of DIVIDE and RULEEg. Find out 64.41% of 12275 ?Â  How to calculate mentally and faster â€“ 64.41% is close to 66.67% or 2/3rdÂ  of 12275. Therefore calculate 2/3 ofÂ  (12000 + 275); which is approximately 8000 + 180. Now look at the choices and eliminate. You will realize that couple choices would vanish. But what we need is approximately 2% less than 2/3rd.Â  Hence next step of approximation will be as follows. 1% of 12275 is 123, hence 2% is 246. Therefore we have 8180 â€“ 250 + 4 = 7934. Again you can eliminate choices.Â  Hence we have got 64.67%. Further proceeding, if 2% is 246,Â  .2% will be approximately 25.Â  Now subtract the 7934 – 25 = 7909.Â  Now we have got 64.47 and we needed 64.41%. We can go on and on approximating and find the value to the last decimal, as you have seen that is what we are doing. Every step of approximation will lead us closer to the exact value. CAT is not about calculation to the last decimal place. It is about approximations and eliminations.If you have observed this calculation carefully, you can do any calculation faster. Any given decimal value could be approximated to the nearest decimal value which can be easily calculated. Say 1.79% of a number, is nothing but 1% of the number,Â  plus .75% or Â¾ of the number with decimal corrections, plus .01% of the number * 4;Â  also other way of doing is 1% of the number + 80% or 4/5 of the numberÂ  with decimal corrections, minus .01% of the number.  If you have understood this. You can do any calculation by approximating with the help of the popular fractions like 1/5, Â¼. 1/3, 2/5, Â½, 2/3, Â¾, 4/5, which over the years you have become familiar with and the computation of these fractional values of any number should not be difficult. Then in each step of approximation move either side of these computed values according to whether the required value is greater or lesser than the fractional value so computed.   This method demands a change in your outlook towards calculations.Â  But, once you starting thinking on this plane, you will realize that computations could be done mentally without resorting to pencil and paper.

## Food Processing: The fruits of growth

Significantly there were 253 foreign collaborations which accounted for 7.3 percent of total foreign direct investment â€“ Rs. 27,300 crores â€“ in 1993-94. And processed food exports at Rs. 5509 crores in 1994-95 constituted 6.7% of the exports from the country during that year; the 28% growth over the previous year was substantially more than the 18% growth in exports as a whole. Two third of processed food exports in 1994-95 comprised of marine products. Spices accounted for 11% while exports of fruits and vegetables accounted for 8.9% in the same year.

Questions â€“

1. What was the value of total exports in 1994-95 ?
2. What was the value of total exports in 1993-94 ?
3. If the marine products, spices, fruits and vegetable and frozen meat comprise the processed food exports, then what is the % contribution of frozen meat to the total exports in 1994-95.
4. What was the % of processed food exports to the total exports in 1993-94
5. What is the amount of total foreign direct investment in the area of processed foods in the period 1993-94.

If you try answering the questions right away your efficiency will be low.Â  For answering every question you will be looking at the paragraph again and again to ascertain what the numbers signify.Â  A manager will solve any unstructured situation by first converting it into a situation which is structured so as to make the problem on hand easier. This is what you, as a manager aspirant, are supposed to do. Therefore convert this stream of words into a structured form â€“ a table.

Now, let us see how you have to go about.Â  You will build the table as you go along reading the passage with your knowledge of reciprocals, percentage equivalents and approximations. You will do all the computations illustrated mentally.

• Food processing industry accountedÂ  for 7.3% of total FDI, Rs 27,300 crores in â€˜93-94.

Given 7.3%,Â  is approximately equivalent to 1/14 of 27,300 crÂ  or little less than 2000 cr.

 FDI (FDI in Processed foods) â€˜93-94 27,300Â  ( ~ 2000)

• Processed foodÂ  (PF) exports at Rs 5509 in 1994-95 constituted 6.7% of the exports from the country during that year.

Given 6.7% is approximately equivalent to 1/15 of the total exports. Or total exports is 15 times that of PF exports i.e., 15 * 5509 orÂ  15 * 5 thousand + 15 * 5 hundreds + 15 * 9 or 75000 + 7500 + 105; approximately equivalent to 83,000.

 FDI (FDI in Processed foods) PF exports Total exports â€˜93-94 27,300Â  ( ~ 2000) â€˜94-95 5,509 83,000

• PF exports growth of 28% over the previous year in â€˜94-95 is substantially higher than the total exports growth of 18%.

Given growth of PF exports is 28% over the previous year. It means if 1.28 is the exports in â€˜94-95, it was 1.00 in â€˜93-94.Â  Given 1.28 is 5,509 you have to find 1.0.Â  Now look at the figures 1.28 is little greater than 1.25. Therefore you have to find out the approximated fraction value ofÂ  1/1.25 or 4/5 of 5509 to find out the FP exports in ’93-94. If 5 parts is 5509, 4 parts will be approximately, 4400. But correcting for the approximation the actual value will be less than 4400 since the denominator has to be 1.28 instead of 1.25. Let us take it as 4300.

 FDI (FDI in Processed foods) PF exports Total exports â€˜93-94 27,300Â  ( ~ 2000) ~ 4,300 â€˜94-95 Â Â  5,509 ~ 83,000

Given growth of total exports is 18% over the previous year. It means if 1.18 is the exports in â€˜94-95, it was 1.00 in â€˜93-94.Â  Given 1.18 is 83,000 you have to find 1.0.Â  Now look at the figures 1.18 is little less than 1.20. Therefore you have to find out the approximated fraction value ofÂ  1/1.2 or 5/6 of 83,000 to find out the total exports in ’93-94. If 6 parts is 83,000, 5 parts will be approximately, 70,000 ( 14 *5 = 70, 14 * 6 = 84 ).Â  But correcting for the approximations we had taken â€“ 1.2 instead of 1.18 and 84,000 instead of 83,000 -Â  the actual value will be little less than 70,000.

 FDI (FDI in Processed foods) PF exports Total exports â€˜93-94 27,300Â  ( ~ 2000) ~ 4,300 ~ 70,000 â€˜94-95 Â Â  5,509 ~ 83,000

• Two third of processed food exports in 1994-95 comprised of marine products. Spices accounted for 11% while exports of fruits and vegetables accounted for 8.9% in the same year.

Adding all these percentages â€“ 86.57% and subtracting from 100 we get â€“ Rest of PF 13.43%

 FDI (FDI in Processed foods) PF exports Total exports â€˜93-94 27,300Â  ( ~ 2000) ~ 4,300 ~ 70,000 â€˜94-95 Â Â  5,509 ~ 83,000 Marine prodÂ Â Â  66.67%SpicesÂ Â Â Â Â Â Â Â Â Â Â Â Â  11.00%Fruits & VegÂ Â Â Â Â  8.90%REST OF PFÂ Â  13.43%

Now we have converted the unstructured problem into structured one and answering the questions will be childâ€™s play.

1. What was the value of value of total exports in 1994-95 ?Â Â Â Â Â Â Â  Little less thanÂ  83,000Cr
2. What was the value of value of total exports in 1993-94 ?Â Â Â Â Â Â Â  Little less than 70,000Cr
3. If the marine products, spices, fruits and vegetable and frozen meat comprise the processed food exports, then what is the % contribution of frozen meat to the total exports in 1994-95 ?

Rest of PF 13.43% is nothing but frozen meat. PF constitutes 6.67% of total exports, hence frozen meat as percentage of total exports will be 13.43% * 6.67% or approximately equal to 13% * 7% i.e. .9%

1. What was the % of processed food exports to the total exports in 1993-94 ?

PF exports percentage of total exports is approximately 4300/70000 or little greater than 3/50 or little greater than 6%

1. What is the amount of total foreign direct investment in the area of processed foods in the period 1993-94 ?Â Â Â Â Â Â Â Â Â  Little less than 2000Cr

By now you must have realised that the only way to run faster in DI is to work with reciprocals, ratios, their percentage equivalents, quicker approximations and elimination of choices. Every stage of approximation will help you in eliminating one or more of the given choices. Try and practise the methods discussed here in. It isÂ  a question of sheer practise and you will start identifying the faster methods you could adopt to run faster.

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