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Modern Math Version 1.1


Hi,

I am glad to see that you have started your preparation for CAT 2015. Work hard and you shall

succeed. Remember the key to success in an exam like CAT has little to with intelligence or to

do with hard work. It is about discipline. Even if you study couple of hours a day regularly, rest

assured you will do well in CAT.

In this PDF, you will find questions on Modern Math. These questions were sent as doubts by

students. Some of these questions might be harder than the actual CAT questions. The idea

behind these solved examples is to build your concepts.

Below every question, you will find a link to the video solution of the question. Before watching

the video solution, please try to solve the questions on your own first. Hope you learn from it.

In case you face a problem or have some doubts, please post them on the course feed.

Alternatively, you can also mail your doubts on [email protected]

I look forward to hearing from you.

Cheers,

Ravi Handa

09765142632

PS: If you got this PDF from a friend of yours and are not enrolled in our course, please check

out our course here: http://handakafunda.com/online


1. Data of 450 candidates, who took an examination in Social Science,

Mathematics, and Science, is given below:

Number of candidates who passed in all the subjects - 167

Number of candidates who failed in all the subjects - 60

Number of candidates who failed in Social science - 175

Number of candidates who failed in Mathematics - 199

Number of candidates who failed in Science - 191

Number of candidates who passed in only Social Sciences - 62

Number of candidates who passed in only Mathematics - 48

Number of candidates who passed in only Science - 52

1) How many students failed in Social sciences only ?

(a) 15 (b) 21 (c) 30 (d) 42

2) How many students failed in one subject only?

(a) 152 (b) 144 (c) 61 (d) 56

3) How many students passed in Mathematics and at least one more subject?

(a) 210 (b) 203 (c) 170 (d) 194

4) How many students failed in two subjects only?

(a) 56 (b) 61 (c) 152 (d) 162

5) How many students passed at least in one subject?

(a) 450 (b) 390 (c) 304 (d) 167

Video Solution : https://www.wiziq.com/tutorial/729714-Solved-Example-Modern-Math-01-

Set-Theory


2. 70 percent of the employees in a multinational corporation have VCD players, 75

percent have microwave ovens, 80 percent have AC's and 85 percent have washing

machines. At least what percentage of employees has all four gadgets?

(a) 15% (b) 5%

(c) 10% (d) Cannot be determined


Set-Theory

3. Two packs of 52playing cards are shuffled together. Find the number of ways in which a

man can be dealt 26 cards such that he doesnt get two cards which have the same suit

and the same denomination.


Permutation-and-Combination

4. 1/(2)(3)(4) + 1/(3)(4)(5) . + 1/(19)(20)(21) . What is the sum of the series?


Progressions


5. A Survey was conducted among 175 people. Each person among them likes at least one

among Shahrukh Khan, Salman Khan, Akshay Kumar and Abhishek Bachan. Among them

90 people like Shahrukh Khan, 95 people like Salman Khan, 85 people like Akshay

Kumarand 75 people like Abhishek Bachan, 20 people like all of them and 25 people like

Shahrukh Khan only. The number of people who like any one combination of three

heroes is the same as those who like any other combination of three heroes. Also the

number of peoplewho like any one combination of two heroes is the same as those who

like any othercombination of two heroes.

1) How many people like Shahrukh Khan and Abhishek Bachan only ?

a) 5 b) 10 c)20 d) 15 e) 25

2) How many people like Salman Khan and Akshay Kumar ?

a) 50 b) 60 c) 45 d) 40 e) 55

3) How many people like either only Salman Khan or only Abhishek Bachan ?

a) 45 b) 35 c) 40 d) 30 e) 50

Video Solution : https://www.wiziq.com/tutorial/869054-solveed-example-set-theory-4-sets

6) The following data pertains to the profiles of 100 students who have appeared for

the 'Selection Process' of a B-School, ISW College in the year 2009.

1. Each student has written exactly one of the two tests LAT or BAT, and every one

of them has at least one of the two features - Good Academic Record (GAR) or Extra

Curricular Activities (ECA).

2. No student who has written LAT has both GAR and ECA.

3. Sixty percent (60%) of the students who have appeared for the Selection Process

have written LAT, of which 40% have Work Experience.

4. Fifty percent (50%) of the students who have appeared for the Selection Process

have Work Experience, of which 30 students have GAR.

5. The no. of students who have written BAT and also have both Workex and GAR is

20.

6. The no. of students who have written LAT and also have GAR is 25.

7. The no. of students who have ECA but have no Work Experience is 35.

Note: The questions that follow are for the year 2009 only.


Q1. Out of all the students who have appeared for the Selection Process of ISW

College, how many have written BAT and have Work Experience and GAR, but no

ECA?

(a) 10 (b) 15 (c) 20 (d) Cannot be determined


College, what is the maximum possible number of students who have GAR and who

have also written BAT but have no Work Experience?



College, what is the total number of students who have written LAT and have ECA?


Video Solution: https://www.wiziq.com/tutorial/967364-solved-example-modern-maths-06-

set-theory-multiple-venn-diag

7) 880 students appeared in an exam. 224 passed in Physics, 240 passed in Chemistry

and 336 passed in Maths. 64 passed in Chemistry & Maths, 80 passed in Physics &

Maths, 40 passed in Physics & Chemistry. 24 passed in all three.

1. What is the % of students who did not pass in any of the subjects?

2. What is the % of students who passed in only 1 subject?

3. What is the number of students who passed in at least 2 subjects?


set-theory-3-sets-easy

8) In a colony there are 200 people. Each one of them reads at least one out of three

newspapers TOI. Telegraph and Hindu. 80 people dont read TOI. 30 people read

only Telegraph. 70 people read both TOI and Hindu. 20 people read all three

newspapers. 80 people read exactly two newspapers.

1. What is the maximum number of people reading only TOI & Telegraph?

A) 20


B) 30

C) 40

D) 50

2. What is the least number of people reading only Hindu & Telegraph?

A) 0 B)10 C)15 D)20

3. How many people read only TOI & Hindu?

A) 20 B)30 C)40 D)50

4. If 30 people read only Hindu, how many read only TOI?

A) 20 B)30 C)40 D)50

5. How many people read only one newspaper?

A) 60 B)80 C)90 D)100


set-theory-3-sets

9) The sum of the first 20 terms of the sequence 0.7, 0.77, 0.777 . Is

A) 7/81 (179-10^-20)

B) 7/9 (99-10^-20)

C) 7/81 (179+10^-20)

D) 7/9 (99+10^-20)


progressions

10) An eight-digit telephone number consists of exactly two zeroes. One of the digits is

repeated thrice. Remaining three digits are all distinct. If the first three digits (from

left to right) are 987, then find the probability of having only one 9, one 8 and one 7

in the telephone number.

A. 1/18

B. 1/20

C. 1/10

D. 5/47



probability1

11) The game 'Chunk-a-Luck' is played at carnivals in some parts of Europe. Its rules are

You pick a number from 1 to 6 and the operator rolls three dice. If the number you

picked comes up on all three dice, the operator pays you Rs. 3 If it comes up on two

dice, you are paid Rs. 2 And it comes up on just one dice, you are paid Rs. 1 Only if

the number you picked does not come up at all, you pay the operator Rs. 1 The

probability that you will win money playing in this game is:

A. 0.52

B. 0.753

C. 0.42

D. None of the above


probability-2

12) Two squares are chosen at random on a chessboard. What is the probability that

they have a side in common?

(1) 1 / 18

(2) 64 / 4032

(3) 63 / 64

(4) 1 / 9


probability-3

13) Five boys and four girls are to be seated on 9 adjacent seats in cinema hall. It is

desired that no two girls sit together. Find the number of way in which they can be

arranged?

a) 43000

b) 43200

c) 43300

d) 43340

e) 43500


Video Solution: https://www.wiziq.com/tutorial/967668-permutation-and-combination-

alternating-arrangement-in-a-row

14) What is the number of permutations of the letters of the word LUMINARY?

(Such that neither the pattern LURY nor MINA occurs)

A. 46800

B. 24600

C. 40086

D. 40082

E. None of the following

Video Solution: https://www.wiziq.com/tutorial/968658-solved-example-permutation-and-

combination-letter-arrangement-in-a

15) The maximum possible sum of the series (20+(1/4))+(18+(2/4))+(16+(3/4))+. . . is

A) 255/2

B) 495/4

C) 253/2

D) 495/2

E) 257/2

Video Solution: https://www.wiziq.com/tutorial/973320-solved-example-modern-maths-

sequence-and-series-progressions


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