Triumphant Institute of Management Education Pvt. Ltd.
The No.1 coaching institute in India INTRODUCTION TO DATA INTERPRETATION
Data, represented in various forms, is something that a manager has to constantly work with. Hence, it is very rare to find any managem ententrance exam that does not emphasise the area of Data Interpretation. Data Interpretation (DI) is an integral part of the CAT exam and has always carried considerable weightage in terms of the number of questions asked. (A) Number of questions asked in this area over the previous few years: TABLE (I) gives an illustration of the number of questions asked from this area over the past four years. TABLE (I) Year
Number of questions
Marks
26 (Section A) 12 (Section B)
2004 (Nov)
Sec-A: each question of 1 mark Sec-B: each question of 2 marks
(Retest)
31
Each question of 1 mark
(Nov)
30
Each question of 1 mark
2002
32
Each question of 1 mark
2001
23
Each question of 1 mark
2003
(B) Break up of the types of DI questions asked in CAT over the past four years: Table (II) gives a clasification of the types of questions asked in this area over the past four years. TABLE (II) 2004 (Nov)
2003 (Retest)
2003 (Nov)
Sets
Qs.
Sets
Qs.
Sets
Qs.
Sets
Qs.
Sets
Qs.
Only Table
4
16
5
19
7
20
5
24
3
11
Only Bar Graph
1
4
2
5
0
0
1
6
2
9
Only Pie chart
0
0
0
0
0
0
1
2
1
3
Only Line Graph
1
4
1
3
1
4
0
0
0
0
Combination
0
0
1
4
0
0
0
0
0
0
Other Type
0
0
0
0
1
3
0
0
0
0
Type
2002
2001
(C) Descriptions of types of questions asked: (1) TABLE: This is the most basic as well as commonly used format for data representation. Usually the data in a simple table consists of two dimensions only. However more complex tables can be used to represent data having more than two dimentions. Tables (I) and (II), and the three dimensional chart given below are a couple of such examples.The data represented in any other format can always be converted into the table format. Hence a certain level of familarity with this format defnitely helps in tackling questions on any other formats of data representation. Some other formats of data representation usually encountered are shown below. (2) Line Graph (3) Bar Graph (4) Pie Chart y
•
Sales
Productions
•
•
Product B
•
Product A Product B
Product D
•
Product C
• Year
x
Year
→
Total Prodution
(5) Spiderweb
(6) Stacked Graph
(7) Three Dimensional Chart
•
Product E •
Y ea rI II
Product B •
Y ea rI I
• •
Expenditure
• •
•
•
•
I ar Ye
Z of ge nta rce Pe
Pe rce nta ge of X
Product C Product D
· · ·
• •
Product F
Product A
Year
Percentage of Y
(8) Caselet Based: Questions asked in CAT can also be of caselet (information given in verbal / para format) type where a caselet of length 100-150 words (approximately) could be given. (D) Types of questions asked in other management entrance exams: Different types of questions related to Data Interpretation have been asked in management entrance exams other t h a n CAT. For example questions on “Spider Web” have been asked in JMET. (E) Different ways of attempting questions in DI: The questions in DI can be solved by (i) direct calculation (ii) observation (iii) elimination (iv) a combination of more than one of the above mentioned techniques. DIRECTIONS for question 1: Answer the question on the basis of the following charts. Per Capita Availability of Te a (gms) in Chaidesh 600
487
464
1995
1996
510
544
566
1997 Ye ar
1998
1999
400 200 0
(Note: Availability is defined as production less export.)
Production and export of Tea (C haidesh) 207
1995
421 189
1996
561
209
1997
587
215
1998
645
220
1999 0
100
200
660 300
Production (million Kg)
400
500
600
700
Export (million Kg)
1. If the land area under tea cultivation in Chaidesh continuously decreased in all four years from 1996 to 1999, by 10%, 7% , 4% and 1%, respectively, in which year was tea productivity (production per unit of area) the highest? (1) 1999 (2) 1998 (3) 1997 (4) 1996 Sol.Tea productivity =
production Area
When production is maximum and area is minimum, we can say that tea productivity is the maximum. In such case, calculation of tea productivity for each of the year is not required. Area is the least in year 1999 as
compared to that in the year 1996, 1997, and 1998. Also, by observation, production is maximum for year 1999. Hence tea productivity is maximum for year 1999. Choice (1) DIRECTIONS for question 2: Answer the question on the basis of the information given below: Each point in the graph below shows the profit and turnover data for 12 different companies. Each company belongs to one of the three industries: textile, cement and steel.
Profit
400
o o
300 200 100
o D D o D o D 1000
Textile D Cement o Steel
2000 3000 4000
Turnover
2. For how many companies does the profit exceed 10% of turnover? (1) 8 (2) 7 (3) 6
(4) 5
Sol.Profit > 10% of turnover. Here a diagonal line can be drawn which divides the region into two parts. All the points on to the left of the line indicate the relevant companies.Thus, for such a question, there is no need to find the profit for each of the companies. (F) Pitfalls to look out for: These could be categorized as follows: (i) Units: It may be required to find an amount in Rs. lakh, but some of the choices may have the same amount in Rs. crore. Even though the numerical figures may match, the answer will not be correct unless the final denomination is also correct. (ii) Rows columns in table: One needs to be alert as to when the numbers have to be taken from a row and when from a column. (G) SURPRISES: Data interpretation in the past has typically seen questions in the form of tables, pie charts, bar graphs etc., which involved calculations. In recent years, DI has been more reasoning based rather than calculations based. For example in CAT 2004, most of the questions in DI were reasoning based while some of the questions needed to be solved by observation. (H) Tips on how to prepare for DI: (1) One must regularly go through different types of newspapers, and magazines and become familiar with different types of data representations frequently appearing in them. (2) Enhance speed of calculations: This can be done by becoming conversant with the following: (i) Multiplication tables upto 20 (ii) Reciprocals of numbers upto 12 (iii) Complements of 100 (iv) Comparison of fractions and other techniques to improve speed and accuracy of calculations. (3) Speed Tests: Since speed and accuracy play a significant role in CAT, one must pay special attention to developing calculation skills. For the development of such skills, practising every day (atleast 5 days per week) for at least 20 minutes is essential. One can distribute the time slots in four different sessions (each session of 5 minute duration) – one each in the morning, afternoon, evening, and night.
One must mentally practise basic operations like adding, subtracting, multiplying and dividing two numbers. Also, one must practice converting fractional values into percentage values and vice-versa. One can take any two random numbers and carry out these operations. One must also practise various approximation techniques.The following examples suggest a couple of such techniques. 1234 . Find the approximate decimal equivalent of x. 4781 (1) 0.55 (2) 0.85 (3) 0.75
1. x =
(4) 0.25
Sol.Here, since the answer choices are not very close to each other one can go ahead with the basic approximation
1234 1200 1 ~ = = 0.25 Choice (4) 4781 4800 4 In some cases, the answer choices are quite close to each other, as in the following question. 1243 , find x rounded off to two decimal places. 4781 (1) 0.27 (2) 0.23 (3) 0.25
2. If x =
(4) 0.26
Sol.Here, 1/4th of 4781 ~ 1195 1243 - 1195 ~ 48 ~ 1/100 x 4781 = 0.01 of 4781 Therefore
1243 ~ 0.25 + 0.01 i.e. 0.26 4781
The above problem can also be solved by a convenient and accurate method commonly known as the “Tenpercentage” method. For this one must know how to caluclate 10% and 1% of any given number. We can arrive at 10% of any given number simply by moving the decimal to the left by one place and 1% by moving the decimal by two places. After this, the given numerator must be written as a multiple of (10% of denominator) + a multiple of (1% of denominator). In this case: 10% of 4781 ~ 478.1 ~ 480, 1% of 4781 ~ 47.8 ~ 50 Note: The level of approximations will depend on the question and the corresponding answer choices. The final answers must usually compensate for errors in the approximations while selecting the correct answer choice. Now approximating 1234 as 1240, we get 2 x (480) + 6 x (50)= 1260 and 2 x (480) + 5 x (50) = 1210. Since our approximations above were on the higher side, it is clear that our answer must be 26% (as 25% i.e. 1210 < 1234, despite an approximation on the higher side). Hence the correct answer must be 26% i.e. 0.26. Choice (4) Finally, the student must bear in mind that practice makes one perfect. Hence one must constantly work on this area in order to excel in it.
Test Ref: TEP0502
Time: 60 minutes
DIRECTIONS for questions 1 to 5: These questions are based on the graphs given below. Pe rce n tage wise Bre ak-up of the share h olding patte rn of Unite d Le ve r. (for the pe riod 20th Nov to 20th De c 2003) Mutual Funds / Banks 38%
GDR 2%
General Motors (GM) 42%
Others 14%
FII 4%
GDR = Global Depository Receipts FII = Foreign Institutional Investors Market value of a Unite d Le ver share from 20th Nov to 20th Dec of 2003 (in $) 370 350
Marke t value of a Ge ne ral Motors share from 20th Nov to 20th De c of 2003 (in $) 450 400
330 310
350
290
300
270 250
250 230 20th Nov 27th Nov
4th Dec 12th Dec 20th Dec
200 20th Nov
27th Nov
4th Dec 12th Dec
20th Dec
1. What is the percentage increase in the value of GM’s holding in United Lever from 10 December 2002 to 10th December 2003, given that the value of GM’s holding in United Lever as on 10th December 2002 was 124.88 million dollars and the difference between the value of the shares of United Lever held in the form of GDRs and that of those held by FIIs as on 10th December 2003 was 17.84 million dollars? (1) 100% (2) 200% (3) 300% (4) Cannot be determined th
2. What is the number of shares of United Lever held by ‘Others’ as on 20th December 2003, given that the difference between the value of the shares of United Lever held by GM and that held by Mutual Funds/Banks as on 20th December 2003 was 250 million dollars? (1) 2.75 million (2) 3 million (3) 3.5 million (4) Cannot be determined 3. Which of the following statements is true as per the graphs given? (1) The market value of a United Lever share is directly proportional to the market value of a General Motors hare. (2) The peak value attained by the United Lever share is exactly 80% of the peak value of the General Motors share during the period 20th November to 20th December 2003. (3) The percentage decrease in the value of the United Lever share from 12th December to 20th December 2003 is less than the percentage decrease in the value of the GM share from 27th November to 20th December 2003. (4) None of these 4. If the value of shares held by Mutual funds / banks and ‘others’ together on 27th November 2003 in United Lever 260.4 million dollars, find the approximate value of shares (in mn$) held by FII on 20th November 2003 in United Lever. (1)15 (2) 16 (3) 18 (4) 20 5. What is the percentage increase in the value of shares held by General Motors in United Lever from 4th December 2003 to 12th December 2003, given that the total number of shares held by ‘Others’ is 84,350? (1) 10.6% (2) 11.8% (3) 12.7% (4) 13.8%
DIRECTIONS for questions 6 to 10: These questions are based on the table given above in next column. 6. If Cylinder Size (in cc.) =
Engine displacemnet (in cc.) , what is the maximum Cylinder Size Number of Clinders
among the vehicles having a maximum power of less than 100 BHP? (1) 124.6 (2) 237.5 (3) 182.1
(4) 287.5
A B C D E F G H I J K L M N O P Q R S
H = Hydraulic;
Kerb Weight
Fuel Consump-
Price on Road (Rs.
Tyre Size
Boot Space
Rear
Front
Fuel Tank Capacity
Maximum
Engine Displacement
Model
Number of
7. Approximately what percentage of the cars given in the table cannot finish a rally race which involves 2 legs each of length 900 km, given that each car is allowed to refuel only once during the rally after the start (all cars start the rally with a full tank of fuel)? (1) 25% (2) 26% (3) 27% (4) 20%
8 16 8
796 997 997
39 55 45
60 50 50
H LS LS
LS MS MS
120 150 90
90 90 80
1.8 3.4 3
20 15 10
740 900 850
8 8 8 8 16 16 16 16 16 16 8 16 16 16 16 8
1016 1457 796 980 1600 1392 1810 2600 2600 2400 1900 3800 3500 2500 2200 2300
60 60 58 62 100 70 80 120 120 90 65 220 140 90 130 170
30 80 100 120 140 200 300 100 250 170 290 420 300 250 200 175
LS LS LS LS MS MS H H MS H MS MS LS ITA LS MS
H ITA LS MS ITA ITA MS MS ITA MS MS LS LS ITA MS ITA
140 160 100 140 250 230 300 600 750 750 800 1100 1600 1800 800 900
100 100 80 80 90 110 110 120 120 100 90 140 150 160 120 110
3.3 3.7 3.4 3 4.5 4.8 5.2 9.6 13.5 6.2 7.5 35 5.3 7 18.6 12.1
25 10 10 35 10 10 15 6 8 12 10 5 8 14 15 12
950 1200 1000 1400 1500 1400 1500 1750 2200 1300 1750 3000 3500 2200 1800 2000
LS = Leaf Spring;
MS = Mcpherson Struts; ITA = Independent Trailing Arm
8. How many cars here have a boot space to fuel tank capacity ratio of more than 2.9 and whose price is less than Rs.8 lacs? (1) 9 (2) 8 (3) 7 (4) 5 9. If all the cars are ranked in the ascending order of the number of revolutions of the tyre required to cover a distance of 1 km, then find the average fuel consumption for the top six ranked cars? (1) 11.66 km/litre (2) 9.33 km/litre (3) 10.20 km/litre (4) 6.54 km/litre 10. What is the ratio of the number of vehicles which have a Kerb Weight of less than 1200 kg and also use a leaf spring in their suspension to the number of vehicles whose Engine Displacement (in cc.) is more than their Kerb Weight (in kgs)? (1) 5 : 14 (2) 1 : 3 (3) 2 : 5 (4) 6 : 13 80% 70%
60%
60%
65%
62%
67%
50% Ratio
DIRECTIONS for the questions 11 to 15: These questions are based on the following chart which expresses the ratio of the cumulative deposits over different time horizons mentioned to the total asset base of the bank (the asset base of the bank remaining constant for the entire period). The chart gives the ratios for five time horizons for two banks, PNB and BOB.
40% 30% 20% 10%
25% 10%
15%
13%
18%
17%
0% < 3 M onths
< 6 M onths
PNB
< 1 Yr T im e H orizons
< 3 Y rs
BOB
< 5 Y rs
11. During which of the following time period is the absolute value of deposits the maximum for BOB? (1) 3 to 6 months (2) 6 months to 1 yr (3) 1 yr to 3 yrs (4) 3 yrs to 5 yrs 12. Based on the data provided it can, be concluded that: (1) The deposits in the ‘3 to 5 years’ time period is minimum in terms of absolute values for both PNB and BOB. (2) The total asset base of PNB is more than that of BOB. (3) The cumulative deposits in the time horizon of ‘less than 5 years’ is lower for PNB than BOB. (4) None of the above can be inferred. 13. If the total asset base of BOB is Rs.500 crore and that of PNB is Rs.750 crore, then the difference between the cumulative deposits of the two banks for the ‘less than 6 months’ time horizon is: (1) Rs.12.50 crore (2) Rs.7.50 crore (3) Rs.15 crore (4) Cannot be determined 14. The total asset base of PNB is 10% higher than that of BOB for the current year. Also, the growth rate of the total asset base this year is 15% for BOB while the total asset base of PNB fell by 5% in this year. If the ratios for the given time horizons in the next year are same as that in this year, then which of the following statements is/are true? I. The cumulative deposits of BOB in the current year for the ‘less than 5 years’ time horizon are higher than the cumulative deposits of PNB for the next year for the same time horizon. II. In the next year, the total asset base of BOB is higher than that of PNB by approximately 10%. III. The cumulative deposits of PNB for the ‘less than 3 months’ time horizon in the current year are higher than that of PNB for the ‘less than 6 months’ time horizon in the next year. (1) I and II (2) I only (3) I, II only (4) I and III only 15. By what percent do the deposits of BOB during the ‘1 to 3 years’ time period exceed its cumulative deposits for the less than 1 year’ time horizon? (1) 60% (2) 55% (3) 30% (4) None of these DIRECTIONS for questions 16 to 20: These questions are based on the line graph given below which gives the number of graduates passing out of Indian Universities (X), the number of graduates getting U.S. visa (Y) and the number of students applying to Indian Management Institutes (Z). X (in 000's)
Y, Z (in 000's) 50 45 40 35 30 25 20 15 10 5 0 1989
1990
Y
1991
1992
1993
Z
1994
160 155 150 145 140 135 130 125 120 115 110 105 100
1995
X
16. If it is expected that Z will vary directly with Y, then in how many years is contradictory data noticed? (1) 4 (2) 3 (3) 2 (4) 1 17. If it is believed that in any year compared to its previous year Z increases or decreases respectively as X increases or decreases, and it decreases or increases respectively as Y increases or decreases, then in which of the following years is the belief proved completely wrong? (1) 1992 (2) 1991 (3) 1995 (4) 1993
18. If it is believed that the relationship between X, Y and Z is best expressed by Z = X - 4Y for any year, the data for which of the following years best satisfies this relationship? (1) 1990 (2) 1993 (3) 1989 (4) 1994 19. If it is believed that the relationship between X, Y and Z is best expressed by Z = 0.4X - Y for any year, the data for which of the following years best satisfies this relationship? (1) 1989 (2) 1991 (3) 1990 (4) 1994 20. If out of the total number of graduates passing out of Indian universities, those who neither get U.S visas nor apply to Indian Management Institutes take up “other careers”, then in which of the following years was the number of graduates taking up “other careers” the least? (1) 1990 (2) 1989 (3) 1994 (4) Cannot be determined DIRECTIONS for questions 21 to 25: These questions are based on the table given below which gives the details of the performance of eight students - S1 to S8 - in examination consisting of four sections - Verbal Ability, Quantitative Ability, Reading Comprehension, and Data Interpretation. Student Code
Quantitative Ability
Verbal Ability
Data Interpretation
Reading Comprehension
=
x
net
=
x
net
x
net
=
x
net
S1
20
4
19
32
12
29
35
10
32.5
14
8
12
S2
42
8
40
17
4
16
40
10
37.5
20
5
18.75
S3
36
14
32.5
30
12
27
34
16
30
18
4
17
S4
7
4
6
12
8
10
32
12
29
14
4
13
S5
20
30
12.5
11
12
8
18
4
17
10
12
7
S6
40
10
37.5
30
20
25
30
20
25
15
10
12.5
S7
34
10
31.5
24
4
23
35
12
32
18
6
16.5
S8
28
20
2
32
16
28
30
16
26
20
4
19
= → Number of questions correct net → Net score in the section
=
x → Number of questions wrong Cut-off Marks Total number of questions in
Cut off
Verbal Ability
50
23
Quantitative Ability
50
18
Reading Comprehension
50
22
Data Interpretation
50
10
Section
Note: Students qualify in the test if they score more than or equal to the cut off mark in all the sections. The sum of the net scores in all four sections together is called Grand Total. 21. Among the students who have qualified what is the maximum Grand Total? (1) 106.5 (2) 108.5 (3) 100
(4) 103
22. What is the least Grand Total among the students who have qualified? (1) 100 (2) 96 (3) 94
(4) 96.5
23. Who among the following committed the maximum number of mistakes? (2) S2 (3) S3 (1) S1
(4) S7
24. Which of the following statements is/are true? I. The person who scored the maximum mark in Reading Comprehension did not qualify in the test. II. The person who had the maximum Grand Total did not get maximum in any of the individual sections. III. S8 attempted maximum number of questions among all the students. (1) Only I (2) Only I and III (3) All the three statements (4) Only I and II 25. Who among the following answered maximum number of questions correctly? (1) S8 (2) S7 (3) S5
(4) S6
DIRECTIONS for questions 26 to 30: These questions are based on the diagram and information given below. B
400
1000
100 600
A
200
E
C
100
G
200
100
J
H
F
100
300 100
100
D
300 I
300
Given above is the pipeline network of ‘XYZ Water Works’ that manages the drinking water supply for a certain city. Each of the pipeline segments has a maximum capacity of 1000 litres per minute. The slack in any pipeline is defined as the extra flow required in it to bring it to full capacity. The magnitudes of the flow in some of the pipelines, along with the directions, and the requirements at some of the hubs are given (both in litres per minute i.e., lpm). The magnitude and the direction of flow in certain pipelines and the requirements at certain hubs are to be found. Note: Every hub except A, which is the only source, has a certain minimum requirement, which for some of the hubs, is indicated in the rectangles next to the respective hubs. The flow through the pipe line is indicated on the top of the line. 26. What is the maximum possible requirement (in lpm) that can be met at the hub I? (1) 1000 (2) 900 (3) 800 (4) 700 27. Find the requirement (in lpm) at the hubs H and B put together. (1) 200 (2) 300 (3) 500
(4) 600
28. Find the slack (in lpm) in the pipeline joining A to D. (1) 0 (2) 300 (3) 400
(4) Cannot be determined
29. Find the requirement (in lpm) at hub E. (1) 200 (2) 300
(4) 400
(3) 100
30. Find the total supply (in lpm) from A if the pipeline connecting D to I has a slack of 400 lpm. (1) 2400 (2) 2500 (3) 2600 (4) 2700
DIRECTIONS for questions 31 to 35: These questions are based on the pie-charts given below which give the country-wise breakup of the world oil trade by value, for the year 1999. Exports
Imports
Iran 14%
Russia 13%
Iraq 6%
USA 10%
Iran 22%
Russia 7%
Japan 17%
India 16%
Others 16%
Others 9%
USA 25%
Iraq 45%
All trade transactions are carried out at a constant international price. Total production of oil in 1999 is worth $1350 billion. Total exports = 40% of total production (by value). Total world exports = Total world imports. Revenue surplus from oil trade for a country = Value of Exports − Value of Imports 31. If 10% of Iran’s exports and 40% of Others’ exports go to India, with India’s remaining imports coming from Iraq, then approximately what is the worth of the oil that Iraq exports to India? (1) $3 bn (2) $30 bn (3) $40 bn (4) Data insufficient 32. Among the following countries, which country gets the maximum revenue surplus from oil trade? (1) India (2) Russia (3) Iran (4) USA 33. If 10% of Iran’s exports and 12.5% of Russia’s exports go to Japan, what percentage of Japan’s imports come from Iraq? (1) 3.17% (2) 7.02% (3) 13% (4) Cannot be determined 34. Which country has the highest revenue surplus to exports ratio? (1) Iraq (2) Iran (3) Russia
(4) Others
35. If Iraq exports an additional $123 billion worth of oil, which is exported (by value) to the various countries in the ratio of their present shares of world oil imports, then Japan’s oil imports will bear what ratio to that of India (approximately) ? (1) 1.06 : 1 (2) 1.10 : 1 (3) 1.15 : 1 (4) Cannot be determined DIRECTIONS for questions 36 to 40: These questions are based on the data given below.
Capital
Debt
Promoters Ä 25%
D 30%
Ä 75%
Ä 60%
D 70%
D Ä 70% 25%
Revenue Interest on Investment
Sales Ä 80%
D 70%
Ä 5%
D Ä 20% 15%
D 10%
Expenditur e Other Income
Salaries D 20%
Ä D 10% 15%
Head
Ä 35%
Interest on Debt
D Ä 40% 15%
⊗
∆
Capital
10
15
Debt
30
20
Revenue
20
25
Expenditure
15
20
⊗ → Actual amounts for the year ending 31/03/03 ∆
Other
Banks
Fll s
Others
→ Proposed / Estimated for the year ending 31/03/04
Others Ä D 20% 50%
D 40%
36. During the year ending 31/03/03, what is the rate of interest paid on the debt taken from FIIs, if the average rate of interest paid on the debt taken from Banks and Others is 61/4%? (1) 71/2% (2) 77/9% (3) 81/3% (4) 88/9% 37. If the sales were Rs.100 crores and the interest paid was Rs.10.5 crores, what would be the profit (in Rs. Crore) earned for the year ending on 31/3/2003 ? (Profit = Revenue – Expenditure). (1) 35 (2) 55 (3) 70 (4) 80 38. Which of the following statements is correct? (1) During the year ending 31/03/04 the promoters propose to increase the capital by 5%. (2) The proposed sales is Rs.2.50 crore more than the actual sales. (3) The average rate of interest on debt is expected to decrease by 5 percentage points. (4) The other income is proposed to be increased by Rs.2 crore. 39. If 40% of the profit for the year 31/3/2003 is earmarked to pay dividend to 25,000 shareholders holding 100 shares of Rs.10 each, what are the earnings per share? (1) Rs.1.20 (2) Rs.0.80 (3) Rs.8.00 (4) Rs.2.40 40. For which of the following is the proposed value for the year ending 31/03/04, as a percentage of the actual value for the year ending 31/03/03 the highest? (1) Capital by ‘Others’ (2) Debt from ‘Others’ (3) Expenditure on Salaries (4) Revenue from interest on investment DIRECTIONS for questions 41 to 45: These questions are based on the diagram given below which represents the distribution of the number of students from a well known institute of CAT coaching in India getting admissions at five prestigious Institutes of Management in India. 24
→ IIMA
6
→ IIMB → IIMC → IIML
12
8
6 6
5 1
17
15 2
7
4 7
16 8
11 5 4
14
→ IIMI 22
41. Of the students who did not get admission into IIMA but did get admission into IIMC, how many did not get admission into IIMB or did not get admission into IIML? (1) 34 (2) 35 (3) 37 (4) None of these 42. How many students are there who got admission into at least one among IIMA and IIMI and also got admission into at least one among IIMB and IIMC but definitely did not get admission into IIML? (1) 35 (2) 34 (3) 33 (4) None of these 43. How many students got admission into at least two of the given colleges? (1) 199 (2) 188 (3) 119
(4) None of these
44. How many students got admission into exactly four of the given colleges? (1) 25 (2) 30 (3) 32
(4) None of these
45. How many students got admission into exactly two or exactly three of the given colleges? (1) 87 (2) 90 (3) 91 (4) None of these
DIRECTIONS for questions 46 to 50: These questions are based on the following table. The table shows a schedule of 20 topics across three areas, Quantitative Aptitude (Q), Logic (L) and English (E), to be covered by a student appearing for the SITE exam. In the schedule, any number of topics can be done simultaneously subject to the only condition that the prerequisite/s for that topic is/are already done. SCHEDULE OF PREPARATION FOR SITE EXAM Sl.No.
Names of the topics
Time for preparation (in days)
Topics to be necessarily learnt before this.
1
Logic Basics (L)
2
Nil
2
Numbers (Q)
3
Nil
3
Number Series (L)
1
Numbers
4
Letter Series (L)
1
Nil
5
Equations (Q)
2
Numbers
6
Progressions (Q)
1
Mixtures
7
Grammar (E)
4
Nil
8
Time and Work (Q)
3
Numbers, Ratios, Equations
9
Analogies (L)
2
Nil
10
Mixtures (Q)
1
Averages, Ratios, Percentages, Profit and Loss
11
Vocabulary (E)
6
Nil
12
Ratios (Q)
2
Equations
13
Time and Distance (Q)
3
Ratios, Equations
14
Reading Comprehension (E)
5
Nil
15
Venn Diagrams (L)
2
Nil
16
Averages (Q)
1
Numbers, Equations
17
Deductions (L)
2
Nil
18
Percentages (Q)
2
Ratios
19
Paragraph Forming (E)
4
Nil
20
Profit and Loss (Q)
2
Percentages, Ratios
46. What is the minimum number of days required for the complete preparation? (1) 13 (2) 14 (3) 19
(4) 49
47. How many topics cannot be covered within the first five days of preparation? (1) 10 (2) 12 (3) 13
(4) None of these
48. Manish and Vittal start preparing for Quantitative Aptitude and English respectively on the same day. If Vittal continues with Quantitative Aptitude after English and Manish continues with Logic after Quantitative Aptitude, then the person who completes his preparation of the two topics first will do so by how many days? (Assume that each prepares topics of only one area at a time.) (1) 0 (2) 1 (3) 2 (4) 3 49. For which of the following topics/set of topics is the minimum number of days required for completion the maximum? (1) Time and Work (2) Vocabulary, Grammar and Reading Comprehension (3) All the Logic topics (4) Profit and Loss 50. What is the average number of days per topic required at the minimum? (1) 7/10 (2) 4/5 (3) 9/10
(4) None of these
