Data Interpretation Previous Year Questions (CAT) - Set 01
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Previous years CAT questions: Data Interpretation
Share your solutions to the questions below.
For admission to various affiliated colleges, a university conducts a written test with four different sections, each with a maximum of 50 marks. The following table gives the aggregate as well as the sectional cut-off marks fixed by six different colleges affiliated to the university. A student will get admission only if he/she gets marks greater than or equal to the cut-off marks in each of the sections and his/her aggregate marks are at least equal to the aggregate cut-off marks as specified by the college.
1. Aditya did not get a call from even a single college. What could be the maximum aggregate marks obtained by him ?
(1) 181 (2) 176 (3) 184 (4) 196 (5) 190
2. Bhama got calls from all colleges. What could be the minimum aggregate marks obtained by her ?
(1) 180 (2) 181 (3) 196 (4) 176 (5) 184
3. Charlie got calls from two colleges. What could be the minimum marks obtained by him in a section ?
(1) 0 (2) 21 (3) 25 (4) 35 (5) 41
( CAT 2008 )
Answer: Option 3 Option 2 Option 3
The bar chart below shows the revenue received, in million US Dollars (USD), from subscribers to a particular Internet service. The data covers the period 2003 to 2007 for the United States (US) and Europe. The bar chart also shows the estimated revenues from subscription to this service for the period 2008 to 2010.
1. While the subscription in Europe has been growing steadily towards that of the US, the growth rate in Europe seems to be declining. Which of the following is closest to the percent change in growth rate of 2007 (over 2006) relative to the growth rate of 2005 (over 2004)?
(1) 17 (2) 20 (3) 35 (4) 60 (5) 100
2. The difference between the estimated subscription in Europe in 2008 and what it would have been if it were computed using the percentage growth rate of 2007 (over 2006), is closest to :
(1) 50 (2) 80 (3) 20 (4) 10 (5) 0
3. In 2003, sixty percent of subscribers in Europe were men. Given that woman subscribers increase at the rate of 10 percent per annum and men at the rate of 5 percent per annum, what is the approximate percentage growth of subscribers between 2003 and 2010 in Europe? The subscription prices are volatile and may change each year.
(1) 62 (2) 15 (3) 78 (4) 84 (5) 50
4. Consider the annual percent change in the gap between subscription revenues in the US and Europe. What is the year in which the absolute value of this change is the highest?
(1) 03-04 (2) 05-06 (3) 06-07 (4) 08-09 (5) 09-10
(CAT 2008 )
Answer: Option 3 Option 1 Option 1 Option 4
There are 100 employees in an organization across five departments. The following table gives the department-wise distribution of average age, average basic pay and allowances. The gross pay of an employee is the sum of his/her basic pay and allowances.
There are limited numbers of employees considered for transfer/promotion across departments. Whenever a person is transferred/promoted from a department of lower average age to a department of higher average age, he/she will get an additional allowance of 10% of basic pay over and above his/her current allowance. There will not be any change in pay structure if a person is transferred/promoted from a department with higher average age to a department with lower average age.
Questions below are independent of each other.
1. There was a mutual transfer of an employee between Marketing and Finance departments and transfer of one employee from Marketing to HR. As a result, the average age of Finance department increased by one year and that of marketing department remained the same. What is the new average age of HR department?
(1) 30 (2) 35 (3) 40 (4) 45 (5) cannot be determined
2. What is the approximate percentage change in the average gross pay of the HR department due to transfer of a 40-yr old person with basic pay of Rs. 8000 from the Marketing department?
(1) 9% (2) 11% (3) 13% (4) 15% (5) 17%
3. If two employees (each with a basic pay of Rs. 6000) are transferred from Maintenance department to HR department and one person (with a basic pay of Rs. 8000) was transferred from Marketing department to HR department, what will be the percentage change in average basic pay of HR department?
(1) 10.5% (2) 12.5% (3) 15% (4) 30% (5) 40%
(CAT 2008 )
Answer: Option 3 Option 3 Option 2
Abdul, Bikram and Chetan are three professional traders who trade in shares of a company XYZ Ltd. Abdul follows the strategy of buying at the opening of the day at 10 am and selling the whole lot at the close of the day at 3 pm. Bikram follows the strategy of buying at hourly intervals: 10 am, 11 am, 12 noon, 1 pm and 2 pm, and selling the whole lot at the close of the day. Further, he buys an equal number of shares in each purchase. Chetan follows a similar pattern as Bikram but his strategy is somewhat different. Chetan‟s total investment amount is divided equally among his purchases. The profit or loss made by each investor is the difference between the sale value at the close of the day less the investment in purchase. The “return” for each investor is defined as the ratio of the profit or loss to the investment amount expressed as a percentage.
1. On a “boom” day the price of XYZ Ltd. keeps rising throughout the day and peaks at the close of the day. Which trader got the minimum return on that day?
(1) Bikram (2) Chetan (3) Abdul (4) Abdul or Chetan (5) cannot be determined
2. On a day of fluctuating market prices, the share price of XYZ Ltd. ends with a gain, i.e., it is higher at the close of the day compared to the opening value. Which trader got the maximum return on that day?
(1) Bikram (2) Chetan (3) Abdul (4) Bikram or Chetan (5) cannot be determined
3. Which one of the following statements is always true?
(1) Abdul will not be the one with the minimum return
(2) Return for Chetan will be higher than that of Bikram
(3) Return for Bikram will be higher than that of Chetan
(4) Return for Chetan cannot be higher than that of Abdul
(5) none of the above
One day, two other traders, Dane and Emily joined Abdul, Bikram and Chetan for trading in the shares of XYZ Ltd. Dane followed a strategy of buying equal numbers of shares at 10 am, 11 am and 12 noon, and selling the same numbers at 1 pm, 2 pm and 3 pm. Emily, on the other hand, followed the strategy of buying shares using all her money at 10 am and selling all of them at 12 noon and again buying the shares for all the money at 1 pm and again selling all of them at the close of the day at 3 pm. At the close of the day the following was observed:
- Abdul lost money in the transactions.
- Both Dane and Emily made profits.
- There was an increase in share price during the closing hour compared to the price at 2 pm.
- Share price at 12 noon was lower than the opening price.
4. Which of the following is necessarily false?
(1) Share price was at its lowest at 2 pm
(2) Share price was at its lowest at 11 am
(3) Share price at 1 pm was higher than the share price at 2 pm
(4) Share price at 1 pm was higher than the share price at 12 noon
(5) none of the above
5. Share price was at its highest at
(1) 10 am (2) 11 am (3) 12 noon (4) 1 pm (5) cannot be determined
(CAT 2008 )
Answer: Option 1 Option 5 Option 5 Option 5 Option 1
Telecom operators get revenue from transfer of data and voice. Average revenue received from transfer of each unit of data is known as ARDT. In the diagram below, the revenue received from data transfer as percentage of total revenue received and the ARDT in US Dollars (USD) are given for various countries.Â
1.Â If the total revenue received is the same for the pairs of countries listed in the choices below, choose the pair that has approximately the same volume of data transfer.
(1) Philippines and Austria
(2) Canada and Poland
(3) Germany and USA
(4) UK and Spain
(5) Denmark and Mexico
2. It was found that the volume of data transfer in India is the same as that of Singapore. Then which of the following statements are true?
(1) Total revenue is the same in both countries.
(2) Total revenue in India is about 2 times that of Singapore
(3) Total revenue in India is about 4 times that of Singapore
(4) Total revenue in Singapore is about 2 times that of India
(5) Total revenue in Singapore is about 4 times that of India
3. It is expected that by 2010, revenue from the data transfer as a percentage of total revenue will triple for India and double for Sweden. Assume that in 2010, the total revenue in India is twice that of Sweden and that the volume of data transfer is the same in both the countries. What is the percentage increase of ARDT in India if there is no change in ARDT in Sweden?
(5) cannot be determined
(CAT 2008 )
Answer: Option 4 Option 5 Option 3
Q1: We need to find Max Aggregate marks of Aditya and our Clue is that he didnt get ANY call. Means he should not clear the cutoff of one/more section or the aggregate cutoff or both.. Now the trick is that no college has cutoff for the all the sections. Means if Aditya missed only one sectional cutoff he can still get some calls.. say Aditya scored less in Section A, he may still get calls from College 2,3 and 6 as they are not considering Section A cutoff. So in order to ensure that he is not getting any calls he need to miss the cut off of two section..now million $ question.. which two sections ? :)
See the table and check for two sections so that at least one is always present in the selection criteria of any college we choose.
A & B - Not an option as College 3 is not interested in both
A & C - Nopes.. as College 6 is not interested in both..
similarly quickly check for other pairs.. its easy.. visual inspection will suffice :)
we can get that Section C & D are the only two sections which satisfies the condition. Every college is interested in either C or D.
So coming back to our question to miss all the calls Aditya has two options
- miss the aggregate cutoff of all colleges - he can score 170 as the least aggregate cutoff is 171 for college 3.
- miss the cut off of C and D - In this case he can score 41 in C and 43 in D ( as least cutoff for Section C is 42 for College 1 and for section D least cutoff score is 44 for College 6). Now remember we need max score. so he is free to score full marks in other two sections (A & B).
so this case he can score a max aggregate of 50 + 50 + 41 + 43 = 184
Q2: We need to find the min score of bhama and clue is that she got calls from all the colleges. Means she should clear all sectional cutoffs and the aggregate cutoff.
She should score min 180 as that is the highest cutoff for college5. Otherwise she wont get call from there.
Now she should score at least the highest sectional cutoff for each sections to get calls from all colleges. She should score min 45 in section A (Otherwise no calls from College5), 45 in Section B (Otherwise no calls from College2), 46 in SectionC (otherwise no calls from College3) and 45 in sectionD (otherwise no calls from College4).
so she should score min 45 + 45 + 46 + 45 = 181 ( easy to solve as 45 * 4 + 1)
now this is already higher than the min aggregate cutoff so bhama should score min of 181 to get calls from all colleges.
Q3. we need to find the min score of charlie in a section. clue is he got only 2 calls.
to score min in a section charlie should score maximum in other sections. we can solve this question through options. As we need the min marks we will start with the option with least value. and good thing is options are already in ascending order.. :)
Option 1 - 0: not possible. if charlie score 0 in a section he can score max aggregate of 150 only (50+50+50) wont get call from any college.
Option 2 - 21: Charlie can score max of 171 ( 21 + 50 + 50 + 50 ). can get call from only one college. (college3)
Option 3 - 25: He can score max 175 (25 + 50 + 50 + 50). can get call from only 2 colleges (College 2 & 3). College 2 and 3 are not interested in cutoffs of section A and D. so charlie is free to score 25 in Section A or D !!!
our answer is option 3 :)
for 2007 : 500
for 2006 : 380
for 2005 : 270
for 2004 : 180
Growth rate for the period 2006-2007 : ( 500 - 380 ) / 380 = 120/380 = 6/19
Growth rate for the period 2004-2005 : ( 270 - 180 ) / 180 = 90/180 = 1/2
% change = [( 1/2 - 6/19 ) / 1/2] * 100
~ ( 1 - 2/3 ) * 100 ~ 33.33
Safe to go with Option 3
for 2008 = 610
we already know the growth rate for 2006-2007 from Q1 ( 6/19)
so if we use this growth rate to calculate 2008 subscriptions,
500 ( 1 + 6/19) > 500 + 150 > 650. difference is greater than 40 ( 650 - 610 )
Will go with Option 1
we have 100 subscribers for 2003.
we have 60 men and 40 women
2010 we will have 60 * (1.05)7 men and 40 * (1.1)7 women
using binomial series, ( 1 + n )x = 1 + nx + n (n - 1 )/2! x2 + ...
60 * (1.05)7 ~ 60 * ( 1 + 0.35 + 0.05 + ... ) ~ 84
40 * (1.1)7 ~ 40 * ( 1 + 0.7 + 0.21 + ... ) ~ 76
total number of subscribers by 2010 = 84 + 76 = 160
% growth = (160 - 100) / 100 = 60
actual value will be little greater than 60 as we avoided the terms from x3 in binomial series.
Option 1, 62%
This one we will solve visually. We are asked to find the year in which the absolute value for annual percent change in the gap between subscription revenues in the US and Europe. We need to find the year where the the height difference between black and white bars increased/decreased (as we are taking absolute) the most.
for 2003 we can see the difference between white/black bars are 3 blocks and for 2004 it is 3.5 blocks. given below is a rough diagram plotting all the values ( interms of blocks.. dont go and find the values.. its a trap :D ). We can see that max difference ( in terms of % ) happened during 2008 - 2009 ( 1.75 -> 1.25 ). Hence Answer d
The person who joined finance from marketing is 20 years elder to the person who joined marketing from finance. ( As the average age increased by 1 for 20 people ). Avg age of marketing department remains the same. Marketing dept's net loss is one person so there should be a total reduction of 35 years. 20 years Marketing department "lost" to fin. which means the guy who moved to HR is 15 years old. so HR dept's ( now 5 + 1 ) avg age = ( 45 * 5 + 15 ) / 6 = 40 years.
HR dept's avg age is 45 and marketing dept's avg age is 35. Transfer from lower avg age to higher avg age means 10% additional allowance of basic pay.
Guy from marketing has an allowance of 80% of 8000 = 6400,
new allowance = 6400 * ( 1 + 10/100) = 7040
new gross pay of the transferred person = 8000 + 7040 = 15040
initial avg gross pay of HR = 5000 + 70/100 * 5000 = 8500
new avg gross pay of HR (after transfer) = ( 8500 * 5 + 15040 ) / 6 = 9590
% change = (9590 - 8500)/8500 ~ 13
new avg basic pay after the transfer,
(5 * 5000 + 2 * 6000 + 8000)/8 = 5625
% change = (5625 - 5000/5000) * 100 = 12.5%
share price is rising through out, so abdul will make the max returns as he buys @ the least price and sells @ max price.
Let's say share price was as below for various time slots
Bikram brought say 20 shares in all slots.
So he spent 100 + 200 + 400 + 500 + 1000 = 2200 rupees
he recieved 5000 rupees @ 3 PM
Chetan brought shares for say 100 rs in all slots.
so he spent 500 rupees.
Total shares he bought = 100/5 + 100/10 + 100/20 + 100/25 + 100/50 = 41
he recieved 41 * 50 = 2050 rupees.
Chetan's returns is higher than Bikram's. So Bikram got the minimum returns.
Question 2 :
Cannot say anything about Chetan and Bikram as their return depends on the variation of the price in each hour slot. Option 5
Question 3 :
On a day when the price starts @ peak and ends at the least, Abdul will have the minimum returns. So option 1 ruled out. Option 2 and Option 3 are not always true. if the share price doesn't change then all three of them can have the same returns. Option 4 is also not always true as if the least price happens to be @ 11 AM and then rises to max @ 3PM Chetan can have better returns than Abdul. so none of the given options are always true.
Question 4 :
Abdul lost money => [email protected] > [email protected]
[email protected] > [email protected] (given)
[email protected] < [email protected] (given)
Emiley made profit
=> [email protected] > [email protected]
[email protected] < [email protected]
Dane made profit
=> [email protected] + [email protected] + [email protected] < [email protected] + [email protected] + [email protected]
=> [email protected] < [email protected] ( [email protected] > [email protected] & [email protected] > [email protected] )
we will try to list the price in decreasing order
Question 5 :
From the order we got above [email protected] is the highest, hence Option 1
( % revenue from data transfer/100 ) = X
ARDT = Y
Question 1 :
X * total revenue = Y * volume
as total revenue is same volume = X / Y
we need to find countries with same volume. if X/Y = const then the plot will be a straight line passing through the origin. so in this case we are looking for pair of countries that will fall in the line that can pass through the origin, only pair that can form the line passing through origin is UK and Spain.
Question 2 :
X * total revenue = Y * volume
total revenue = Y * volume / X
as volume is same, the ratio of total revenues of India and singapore will be
(totat revenue - India)/(total revenue singapore) = (Y/X) - India / (Y/X)-Singapore
(Y/X) - India = 1/9
(Y/X)-Singapore = 9/20
(totat revenue - India)/(total revenue singapore) = (1/9)/(9/20) = 20/81 ~ 1/4
(total revenue singapore) = 4 * (totat revenue - India)
Question 3 :
27 * 2R = ARDT (India) * V
36 * R = 6 * V
ARDT(India) = (27 * 2 * 6) / 36 = 27/3 = 9
Current value of ARDT(India) = 1
so % change = [ ( 9 - 1 ) / 1 ] * 100 = 800%