All business consists of processing data and making decisions. It checks the ability of a person to calculate fast and comprehend relevant information which is essential for potential managers.
Normally D.I. combined with Logical Reasoning forms a separate section. The number of questions vary from 25‐40. It has an overall weightage of 20% and is given in combination with Logical Reasoning or Data Sufficiency.
Numerical data pertaining to any situation can be presented in the following ways.
 Numerical data table
ii.  Line Graphs  * Single line, Single axis 

 * Multiple line, Single axis 

 * Multiple line, Double axis 
iii.  Bar Chart  * Vertical 

 * Horizontal 
 Pie Chart
 Case‐lets
 Combination graph Line + Bar / Line + Pie/Bar + Pie
 Venn diagram (Set theory)
 Directional graphs
 Geometrical diagram
 Network diagram
Data Interpretation problems judge the person’s ability to analyze data quickly. Graphs, charts and tables are given and a person has to find out the relevant data which is required in a question and then do a calculation on it. Good observation coupled with speedier calculation helps in cracking DI problems. In the case of difficult problems, it becomes imperative to read the problem along with the options. The approach to DI problems lies in understanding:
 “What is given” – See the given data carefully to see the time period, the units and the trend. Each data tells a story. See whether it is a rising or declining trend.
 “What is asked” – Look at the questions and locate which is the relevant data that is required for the question.
 “What are the approximations and calculations required” – Sometimes an increase between two years may be asked, or the percentage growth, or a ratio. Look at the desired values and do quick calculations to get the answer. Choices are a big help in selecting answers.
The student must ignore superfluous information. Sometimes large tables are given and not all the data is useful to answer the questions. Sometimes there is a combination of tables and graphs. One must correlate the graphs provided and understand the relationship between the graphs, before actually attempting the question. Intelligent guessing can reduce calculations and in turn saves time.
Some quick approximation techniques are illustrated below:
Example: Study the following table and answer the questions that follow:
Number of Items (in lakhs) produced by six companies over the years
Year →  1997  1998  1999  2000  2001 
Company ↓ 





P  38.5  53.4  48.6  76.4  56.5 
Q 





10.6  68.6  62.7  98.9  72.8  
R 





65.4  72.8  63.5  82.5  86.4  
S 





48.5  96.5  78.6  91.5  92.8  
T 





52.6  99.8  82.2  102.8  89.5  
U 





78.4  103.4  88.9  110.7  98.4  






 What was the percentage of numbers produced by Company P in 2000 to that produced by Company U in 2001?
Solution:
First, see what figures we need. Look at row P and continue till you hit column 2000. The figure is 76.4 Then look at row U and look under the column 2001.
The rest of the data is not required for this question.
So the fraction required to find percentage is (76.4/98.4) × 100. If we do the calculation, we find it is not very easy.
Using approximation, we first round off the figures to 77/100. (Increasing the numerator and denominator by just a little bit to get around figures)
We now visually see that the answer is close to 77%. So in this way we have avoided a calculation.
Important: While approximation, either increase both quantities or decrease both quantities, otherwise the error will be high.
 What is the percentage increase in production for Company P from 1997 to 2001?
Solution: To find percentage increase, we need the figures of P in 1997 and in 2001. We see that the percentage increase required is from 38.5 to 56.5.
The formula for percentage increase is: [New value – Old value]/[Old value] × 100 The figure required in this case is: [56.5 – 38.5]/[38.5] × 100 = 18/38.5 × 100.
We again see that it is a somewhat lengthy calculation. So we try approximation.
Rounding off by increasing both numerator and denominator, we can reduce the fraction to 20/40.
We then get the answer as 50%, but since we have increased the numerator more (compared to 18), we need to reduce the answer somewhat. So the answer would be around 47‐48%. After getting this figure, the choices will tell us the choice that we need to tick. Note again that we have avoided a calculation.
Important: Do the increase/decrease judiciously. Also, take a look at the choices. If the choices are close, wide approximation cannot be done. However, if the answer choices are far apart, one can make good use of this technique.
What was the share of production of Company Q in total production in 2001?
Solution: Share of Company Q is given by (Q’s Production/Total Production) × 100 = (72.8/496.4) × 100. Using approximation, we can make this fraction as 70/490 [by reducing both numerator and denominator]. We see that 70/490 = 1/7 = 14% approximately.
 Which company has shown the maximum increase in production between 1997 to 2001
Solution: No calculation is required in such sums. See the figures for each company. We see that the maximum increase happens for Company Q, which goes from 10.6 to 72.8, which is about 7 times, which is not matched by any other company
The above can be done quickly if one has a familiarity with numbers.
Thus, tables, squares, cubes, fractions, and percentages must be learned by heart.
Tables from 1‐10:
Table  2  3  4  5  6  7  8  9  10 
1  2  3  4  5  6  7  8  9  10 
2  4  6  8  10  12  14  16  18  20 
3  6  9  12  15  18  21  24  27  30 
4  8  12  16  20  24  28  32  36  40 
5  10  15  20  25  30  35  40  45  50 
6  12  18  24  30  36  42  48  54  60 
7  14  21  28  35  42  49  56  63  70 
8  16  24  32  40  48  56  64  72  80 
9  18  27  36  45  54  63  72  81  90 
10  20  30  40  50  60  70  80  90  100 
11  22  33  44  55  66  77  88  99  110 
12  24  36  48  60  72  84  96  108  120 
13  26  39  52  65  78  91  104  117  130 
14  28  42  56  70  84  98  112  126  140 
15  30  45  60  75  90  105  120  135  150 
16  32  48  64  80  96  112  128  144  160 
17  34  51  68  85  102  119  136  153  170 
18  36  54  72  90  108  126  144  162  180 
19  38  57  76  95  114  133  152  171  190 
20  40  60  80  100  120  140  160  180  200 
Tables from 11‐20: 










Table  11  12  13  14  15  16  17  18  19  20 
1  11  12  13  14  15  16  17  18  19  20 
2  22  24  26  28  30  32  34  36  38  40 
3  33  36  39  42  45  48  51  54  57  60 
4  44  48  52  56  60  64  68  72  76  80 
5  55  60  65  70  75  80  85  90  95  100 
6  66  72  78  84  90  96  102  108  114  120 
7  77  84  91  98  105  112  119  126  133  140 
8  88  96  104  112  120  128  136  144  152  160 
9  99  108  117  126  135  144  153  162  171  180 
10  110  120  130  140  150  160  170  180  190  200 
11  121  132  143  154  165  176  187  198  209  220 
12  132  144  156  168  180  192  204  216  228  240 
13  143  156  169  182  195  208  221  234  247  260 
14  154  168  182  196  210  224  238  252  266  280 
15  165  180  195  210  225  240  255  270  285  300 
16  176  192  208  224  240  256  272  288  304  320 
17  187  204  221  238  255  272  289  306  323  340 
18  198  216  234  252  270  288  306  324  342  360 
19  209  228  247  266  285  304  323  342  361  380 
20  220  240  260  280  300  320  340  360  380  400 
Squares and Cubes:
Students should learn the squares of numbers up to 32 and cubes up to 12 so that they do not waste time in the exam. Square roots of numbers up to 16 should also be learnt.
Squares 



 
2^{2}  = 4  10^{2}  = 100  18^{2} = 324  26^{2} = 676  
3^{2}  = 9  11^{2}  = 121  19^{2} = 361  27^{2}  = 729 
_{4}2  = 16 12^{2}  = 144  20^{2} = 400  28^{2}  = 784  
5^{2}  = 25 13^{2}  = 169  21^{2} = 441  29^{2}  = 841  
6^{2}  = 36 14^{2}  = 196  22^{2} = 484  30^{2}  = 900  
7^{2}  = 49 15^{2}  = 225  23^{2} = 529  31^{2}  = 961  
8^{2}  = 64  16^{2}  = 256  24^{2} = 576  32^{2}  = 1024 
9^{2}  = 81  17^{2}  = 289  25^{2} = 625 


Square Roots 


 
√2 = 1.414  √6 = 2.449 √10 = 3.162  √14 = 3.741  
√3 = 1.732  √7 = 2.646  √11 = 3.316  √15 = 3.873  
√4 = 2  √8 = 2.828  √12 = 3.464  √16 = 4  
√5 = 2.236  √9 = 3  √13 = 3.605 
 
Cubes 



 
2^{3}  = 8  6^{3} = 216 
 10^{3} = 1000  
3^{3}  = 27  7^{3} = 343 
 11^{3} = 1331  
_{4}3  = 64  8^{3} = 512 
 12^{3} = 1728  
5^{3}  = 125  9^{3} = 729 



Equivalent Percentages of some commonly used Fractions 
 
It is useful to learn these by heart 


 
Fraction  Equivalent  Fraction  Equivalent  Fraction  Equivalent 
 % 
 % 
 % 
1  50%  3  75%  2  22.22% 
2 
 4 
 9 

1  33.33%  4  80%  1  6.67% 
3 
 5 
 15 

1  25%  1  12.5%  1  5% 
4 
 8 
 20 

1  20%  1  8.33%  1  4% 
5 
 12 
 25 

1  16.67%  3  37.5%  1  2% 
6 
 8 
 50 

2  40%  5  62.5%  4  133.33% 
5 
 8 
 3 

3  60%  7  87.5%  5  125% 
5 
 8 
 4 

2  66.67%  1  11.11%  6  120% 
3 
 9 
 5 

Units 

1 Lakh = 1,00,000 = 10^{5}  
1 Crore = 1,00,00,000 = 10^{7}  
1  Million = 1,000,000 = 10^{6} 
1  Billion = 1,000,000,000 = 10^{9} 
⇒ 1 Billion = 10 Crores = 1000 Million  
1  Million = 10 Lakhs 
1 Km = 1000 m.  
1 m = 100 cms.  
1 inch = 2.54 cms.  
1 Foot = 12 inch = 30.48 cms.  
1 Yard = 3 foot = 36 inch = 91.44 cms.  
1 Mile = 1760 yards = 1.6 kms. 
STRATEGY FOR DI:
In DI, read the data and questions very carefully. You can't solve questions correctly if you haven't understood the questions. Many students read the questions very fast in order to save time. They find that they either have to read the questions again or they leave those questions for lack of understanding. Read the question slowly and carefully. Concentrate and make it a point that you understand the question in one single reading. Similarly, you should spend some time on the data and understand it. There is no point in trying to solve questions if you haven't understood the data.
 First spend 15 to 30 seconds in having a look at and analyzing the graph. Spending this time once would necessarily reduce the 12‐18 seconds you will otherwise spend in solving every question in the block.
 Read all the information carefully, specifically the minor details (which you consider minor) given, like
 data in ’000
 in tons of
 lakh bales of 150 kg each
 profit = revenue – cost
 last nine months/for the first quarter
 If any * or like symbol is given, carefully read the information next to the symbol in the footnote and relate it with the graph.
 Read every question without missing even a single word from the statement. Be cautious where the information given in the graph denotes in ‘000 or in lakhs. In such cases either the questions should also include ‘000 or lakhs respectively or the options should have ‘000 or lakhs in them respectively. A very common error is to solve the question correctly but mark the choice with the wrong units. For example, if your answer is 234(000) a common mistake is to mark the choice as 234 units, whereas the answer should be 2.34 lakh units.
 After reading the question relate the question to the graph and then see what is required to be calculated.
 Keep the choices in focus. How far away they are from each other and what kind of guesses can take you closer to the answer.
 After seeing the choices you can calculate the approximate answer, e.g. in order to multiply 122 and 179 you can multiply 12 with 18 along with 2 zeroes, in the end, this would give you an approximation. In 95% of the cases there would be only one option close to the approximation and that would be the right answer.
 Remember that a question on “increase” and the “percentage increase” are toe different things. The former represents the absolute increase that can be calculated as the final minus initial figure. The percentage increase represents the relative increase that is calculated as: (Final – initial figure)/(initial figure) × 100.
 See what is required: is it “X is what percent of Y” or “X is how much percent more than Y.” In the former case (X ÷ Y)× 100 will give you the answer and in the latter case [(X – Y) ÷ Y] × 100 will give you the answer.
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