Post on 07-Jan-2016
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Modern Math Version 1.1
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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 handakafunda@gmail.com
I look forward to hearing from you.
Cheers,
Ravi Handa
09765142632
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out our course here: http://handakafunda.com/online
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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
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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
Video Solution : https://www.wiziq.com/tutorial/730372-Solved-Example-Modern-Math-02-
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.
Video Solution : https://www.wiziq.com/tutorial/731148-Solved-Example-Modern-Math-03-
Permutation-and-Combination
4. 1/(2)(3)(4) + 1/(3)(4)(5) . + 1/(19)(20)(21) . What is the sum of the series?
Video Solution : https://www.wiziq.com/tutorial/748951-Solved-Example-Modern-Math-04-
Progressions
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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.
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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
Q2. Out of all the students who have appeared for the Selection Process of ISW
College, what is the maximum possible number of students who have GAR and who
have also written BAT but have no Work Experience?
(a) 10 (b) 12 (c) 14 (d) Cannot be determined
Q3. Out of all the students who have appeared for the Selection Process of ISW
College, what is the total number of students who have written LAT and have ECA?
(a) 31 (b) 35 (c) 28 (d) Cannot be determined
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?
Video Solution: https://www.wiziq.com/tutorial/967648-solved-example-modern-maths-07-
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
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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
Video Solution: https://www.wiziq.com/tutorial/962407-solved-example-modern-maths-07-
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)
Video Solution: https://www.wiziq.com/tutorial/962409-solved-example-modern-maths-07-
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
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Video Solution: https://www.wiziq.com/tutorial/963494-solved-example-modern-maths-09-
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
Video Solution: https://www.wiziq.com/tutorial/963497-solved-example-modern-maths-09-
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
Video Solution: https://www.wiziq.com/tutorial/963500-solved-example-modern-maths-09-
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
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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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