Question Bank  Modern Math  Shashank Prabhu  CAT 100 Percentiler

Set 1
Answer the questions on the basis of the information given below:
The annual sugarcane production (in million tonnes) in Meethagaon for the period 20002006 is shown in the bar graph given below.What is the approximate average annual sugarcane production (in million tonnes) in Meethagaon for the period 20002005?
(a) 281.4
(b) 326.5
(c) 272.1
(d) 328.3The sugarcane production in Meethagaon in the year 2007 increases by 15% over the year 2006. What is the approximate compounded annual growth rate of sugarcane production in Meethagaon over the period 20042007?
(a) 19%
(b) 17%
(c) 16%
(d) 18%Out of the following, which year has shown the highest percentage increase in sugarcane production in Meethagaon compared to the previous year?
(a) 2001
(b) 2004
(c) 2005
(d) 2006Solution
(1) is very easy.. probably the shortest way is to take some base value and study the deviation around it. Take 280 for example. +15+17+74743+1=50 divided by 6 will be 8.33. So approximately 272.
(2) 2007 produce will be 337+33.7+16.8=387.5 approx.
CAGR over 3 years will be cube root of (387.5/237.09) which will be 1.178 or 17.8% which will be 18%. Heavy approximations plus calculation is required for this. Unless you have a calculator, doesnt make sense attempting this question.(3) Compare 1.3/296, 1.25/234, 44/237 and 56/281. The doubt should be between c and d, but d is almost 20% while c is short of 20% by a fair bit. So, d is correct.
Set 2
The following tables show the batting performance of the Australian Cricket Team in a match. Table 1indicates the score of the team at the fall of each wicket (from 1 to 10). Table 2 gives the runs scored by the 11 batsmen and the order in which they appeared in the batting line up.
Additional Information:
 At any point there are two batsmen on the field, till the fall of the 10th wicket. Whenever the team loses a wicket, the new batsman comes as per the batting order. E.g. If one of the openers gets out, the no. 3 batsman takes the field.
 A partnership between any two batsmen is the number of runs scored while both of them are batting.
How many batsmen lost their wicket between Haydens and Husseys dismissal?
(a) 0 (b) 1 (c) 2 (d) More than 2How many runs were scored by the batsman who was the 9th to be dismissed?
(a) 11 (b) 18 (c) 0 (d) Cannot be determinedWhat was the percentage contribution to the second highest partnership of the batsman to be dismissed first in that partnership?
(a) 33.33% (b) 61.53%(c) 71.43% (d) None of theseThe Australian total comprised only Singles and Fours. The number of Fours scored cannot exceed
(a) 27 (b) 24 (c) 21 (d) 20Solution
The sequence would look as follows:
Outcontributionnot outcontribution
Gil7Hay18
Pon8Hay1
Sym4Hay4
Hay5Hus10
Hod3Hus2
Hus8Lee5
Joh5Lee2
Whi0Lee4
Lee/Cla7/11Cla/Lee6/2Last partnership of 11 runs. Williams and whoever was left scored 5 runs. The last one is tricky and we need to see the runs scored in individual partnerships. So, although Hussey scored 20 in total, he could not have scored 5 fours as his contribution in the fifth wicket partnership is 2 and so, they could have been a couple of singles only.
Set 3
A team of 5 players Arpit, Bimal, Chatur, Dinu and Elan participated in a ‘Freaket’ tournament and played four matches (1 to 4). The following table gives partial information about their individual scores and the total runs scored by the team in each match. Each column has two values missing. These are the runs scored by the two lowest scorers in that match. None of the two missing values is more than 10% of the total runs scored in that match.
What is the maximum possible percentage contribution of Arpit in the total runs scored in the four matches?
(a) 19.7% (b) 19.9% (c) 20.1% (d) 20.2%If the absolute difference between the total runs scored by Arpit and Chatur in the four matches is minimum possible then what is the absolute difference between total runs scored by Bimal and Elan in the four matches?
(a) 32 (b) 37 (c) 27 (d) Cannot be determinedThe players are ranked 1 to 5 on the basis of the total runs scored by them in the four matches, with the highest scorer getting Rank 1. If it is known that no two players scored the same number of total runs, how many players are there whose rank can be exactly determined?
(a) 0 (b) 1 (c) 3 (d) 5Solution
Arpit in match one varies from 23 to 27. Chatur in match one varies from 27 to 23. Similarly, Arpit in match 3 will vary from 13 to 19 and Bimal from 19 to 13. In match 5, Chatur will vary from 19 to 20 and Elan from 20 to 19. In match 2, both the missing values will be 30 each. Now we are good to go for all the questions:
(1) 27+100+19+53=199 which is 19.7%
(2) This one is a bit tricky especially if you are going for absolute values for each match. Arpit's total will vary from 189 to 199 and Chatur's total will vary from 182 to 187. We can see that 189 and 187 is simultaneously possible and so, minimum difference is 2. The corresponding value for BE will be 28+3559+33=37
(3) Arpit is 189199, Bimal is 218224, Chatur is 182187, Dinu is 223 and Elan is 187188. Chatur is rank 5, Dinu is 4, Arpit is 3 for sure. So, 3 ranks can be uniquely determined.

Q1) Four stacks containing equal number of chips are to be made from 11 orange, 9 white, 13 black and 7 yellow chips. If all of these chips are used and each stack contains at least one chip of each color, what is the maximum number of white chips in any one stack?
a. 3
b. 4
c. 5
d. 6[OA: Option d]

Q2) For a scholarship, at most n candidates out of (2n + 1) can be selected. If the number of different ways of selection of at least one candidate is 63, the maximum number of candidates that can be selected for the scholarship is:
a. 3
b. 4
c. 2
d. 5[OA: Option a]

Q3) From a group of 7 men and 6 women 5 persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many different ways can it be done?
(1) 756
(2) 735
(3) 564
(4) 645
(5) None of these

Q4) In a row at a bus stop, A is 7th from the left and B is 9th from the right. They both interchange their positions. A becomes 11th from the left. How many people are there in the row?
a. 18
b. 19
c. 20
d. 21

Q5) Rajan has 30 toys in three different colours  green, pink and yellow. Each toy is of a single colour. He has not more than 13 green toys and not more than 7 pink toys. Which of the following is necessarily false?
I. More than half his toys are yellow.
II. He has three pink toys more than green toys.a. I alone
b. II alone
c. Both I and II
d. Neither I nor II

Q6) A, B, C, D, E, F, G and H are 8 students in a school. The class teacher wants to send 4 students each for a quiz competition and drawing competition such that each student goes for exactly one competition. Assuming that each student is capable of participating in either of the two competitions, in how many ways can the class teacher create the two teams?

Q7) A playschool contains 4 boys and y girls. On every Wednesday during winter, five students, of which at least three are boys, go to Zoological Garden, a different group being sent every week. At the Zoological Garden, each boy in the group is given a ball. If the total number of balls distributed is 368, then the value of y is

Q8) The Carson family will purchase three used cars. There are two models of cars available, Model A and Model B, each of which is available in four colors: blue, black, red, and green. How many different combinations of three cars can the Carsons select if all the cars are to be different colors?
A. 24
B. 32
C. 48
D. 60
E. 192

Q9) Four boxes are labeled as A, B, C and D. Each box contains three balls  one red, one blue and one green. In how many ways can a person pick 2 red and 3 blue balls?
(a) 48
(b) 24
(c) 8
(d) 16

Q10) A watch salesman started his day with 11 identical watches. During the first hour of the day, he visited exactly four people and sold at least one watch. In how many ways could he have sold the watches during the first hour of the day?

Q11) Probability that three missiles A, B and C hitting a target are P(A) = 0.3, P(B) = 0.4, P(C) = 0.8. Find the probability that at least two missiles hit the target.

Q12) 4 identical Buzz Lightyear action figures have to be distributed among 4 boys. Considering all possible arrangements, what would be the probability that none of the boys will get more than 2 action figures.

Q13) A bag contains 2 red, 3 green, 4 blue and 5 white balls. Two balls are drawn at random from the bag without replacement. X is defined as the event that at least one of the two balls drawn is white and Y is defined as the event that none of the two balls drawn is white. Then,
a. P(X) = P(Y)
b. P(X) > P(Y)
c. P(X) > 1.5P(Y)
d. More than one of the above

Q14) A survey revealed that 800 people owned shares of company X, 1000 owned shares of company Y and 600 owned shares of company Z. It was found that 325 people owned shares of companies X and Z and 300 owned shares of companies Y and Z. 150 people owned shares of all three companies. If S represents the total number of people who own shares of any of these 3 companies, then what is the difference between the maximum and minimum value of S?

Q15) Each of the 100 people surveyed by the Baratheons support one or more of the 3 communities viz. the Targaryens, the Starks and the Lannisters. Ten of them support both the Targaryens and the Starks. 30 of them support both the Lannisters and the Targaryens. 15 of them support both the Lannisters and the Starks. 35 of them support the Lannisters.
a. How many of them support all the 3 houses?
b. How many of them support exactly one of the 3 houses?

Q16) In a locality, there are ten houses in a row. On a particular night a thief planned to steal from three houses of the locality. In how many ways can he plan such that no two of the houses are next to each other?

Q17) N is a natural number of at the most 6 digits and sum of the digits is at the most 5. How many such numbers are there?

Q18) Abel, Mabel, and Caleb went bird watching. Each of them saw one bird that none of the others did. Each pair saw one bird that the third did not. And one bird was seen by all three. Of the birds Abel saw, two were yellow. Of the birds Mabel saw, three were yellow. Of the birds Caleb saw, four were yellow. How many yellow birds were seen in all?

Q19) A ten – digit number is to be formed using all the digits from 0 to 9 such that the number is odd and all the even digits in the number are at the 1st, 3rd, 5th, 7th and 9th positions from the left. How many such numbers can be formed (Repetition is not allowed)?