M4maths Previous Puzzles

20 Dec 2017 Probability

What is the probability of getting a product of 72 from three throws of a dice?

OPtion

1) 8/216
2) 6/216
3) 10/216
4) 12/216
5) 15/216
6) 16/216
7) 1/23
8) 1/25
9) 1/27
10)None of these

Solution

Total Number of possible outcomes = 6C1*6C1*6C1 = 6*6*6 = 216
Positive outcomes must satisfy D1*D2*D3= 36
Below are such values of D1, D2 and D3:
2, 6, 6
3, 6, 4
3, 4, 6
4, 6, 3
4, 3, 6
6, 6, 2
6, 4, 3
6, 3, 4
6, 2, 6



Count of positive outcome = 9
Probability = Positive outcome/Total Possible Outcomes = 9/216 = 1/24
Option 10)

Correct Option: 10 Best Solution (7)

19 Dec 2017 Direction Sense

Bhola started from his house towards west. After covering a distance of 13 km. he turned towards left and covered a distance of 7 km. Then he turned left and covered a distance of 3 km. What is the shortest distance between where he is now and his house?

OPtion

1) 11.91
2) 21.12
3) 12.21
4) 21.29
5) 12.31
6) 12.81.
7) 22.69
8) 11.99
9) 12.59
10) None of these

Solution

As per question Bhola starts from Point A and moves to Point B in west by travelling 13 KM. Then he turns left and travels 7KM to reach point C. Then he turns left again and travels 3 KMs to reach point D. We need to find shortest distance between D and A

13
B-----------------A
|
| 7
|
C----D
3

Horizontal distance betwween AD = 13-3 =10
Vertical distance between AD = 7
We need to find shortest distance between A and D = Sq. root (10^2 + 7^2 ) = ~12.21 KMS

Correct Option: 3 Best Solution (7)

18 Dec 2017 Arrangement

How many unique ways are there to arrange the letters in the word Chimpanzee?

OPtion

1) 907200
2) 1814490
3) 3628800
4) 5189184
5) 1814400
6) 7018012
7) 6918910
8) 8456890
9) 2289100
10) None of these

Solution

Total number of letters in the word Chimpanzee = 10
Total number of repeated letters = 2 (e is appearing twice)
So total unique ways to arrange the letters of the word Chimpanzee = 10!/(2!) = 1814400
Option 5)

Correct Option: 5 Best Solution (3)

15 Dec 2017 Time and Work

P can do a work in 9.5 days. Q can do the same work in 19 days and R can do the same in 28.5 days. Q and R start the work and leave after 6 days. P finishes the remaining work in X days. What is the value of 2X?

OPtion

1) 5 days
2) 3 days
3) 4 days
4) 5.5 days
5) 4.5 days
6) 2 days
7) 9 days
8) 7 days
9) 1 day
10) None of these

Solution

Amount of work done by Q and R in 6 days = 6*(1/19 + 1/28.5) = 6*((1.5+1)/28.5) = 15/28.5 = 150/285 = 10/19
Amount of work remaining after 6 days = 9/19

Amount of work done by P in 1 day = 1/9.5
So for 1/9.5 work P takes 1 day
Hence for 9/19 work P would take (1/(1/9.5))*9/19 = 4.5 days
So 2X = 4.5*2 = 9

Option 7)

Correct Option: 7 Best Solution (5)

14 Dec 2017 LCM

Two numbers are in the ratio 3 : 7. If their L.C.M. is 252. what is sum of the numbers?

OPtion

1) 110
2) 105
3) 125
4) 120
5) 90
6) 220
7) 135
8) 115
9) 100
10) None of these

Solution

Let the numbers be 3x and 7x

LCM of 3x and 7x is 21x


So as per question 21x = 252

=> x= 12
3x = 3*12 = 36 and 7x = 7*12 = 84


Sum of the numbers = 36+84 = 120

Correct Option: 4 Best Solution (7)

13 Dec 2017 Bankers Discount

The banker's discount on a bill due 12 months hence at 13% is Rs. 2017. What is the true discount?

OPtion

1) 1781.66
2) 1784.96
3) 1785.23
4) 1782.78
5) 1783.36
6) 1788.06
7) 1789.92
8) 1786.23
9) 1787.26
10) None of these

Solution

T.D.=B.D. x 100 /(100 + (R x T))
=> 2017*100/(100+(13*12/12))
=> ~1784.96

Option 2)

Correct Option: 2 Best Solution (7)

12 Dec 2017 Probability

With Dhoni and Bumrah at the crease Cricket Team of India needs to score 5 runs in last 2 balls to win the match. What is the probability that the India wins the match? Assume that:
-There were no wide balls or no balls bowled in these 2 balls.

-No Wicket has fallen in these 2 balls

-No Overthrows or extra runs were scored in these 2 balls

-In case if run(s) are scored on any of these 2 balls it can only be one of these values: 1, 2, 3, 4 & 6

This also implies that it’s quite possible that zero runs are scored on a particular ball

OPtion

1) 17/36
2) 17/31
3) 16/36
4) 14/31
5) 5/12
6) 2/9
7) 15/31
8) 16/31
9) 7/12
10) None of these

Solution

On any of these 2 balls the possible runs which can be scored are: 0,1,2,3,4,6
India would win the match if India manages to score 5 or more runs in these 2 balls.

In other words India would not win the the match if India manages to score 4 or less runs in these 2 balls.
So possible pair of runs in 2 balls which will result in India losing :
(0,0), (0,1), (0,2), (0,3), (0,4), (1,0), (1,1), (1,2), (1,3), (2,0), (2,1), (2,2), (3,0), (3,1), (4,0) => count of pairs = 15

While calculating total possible outcomes, we need to take care of the fact that if 6 is hit on first ball then then second ball would not come into picture.
So total possible outcome = 6*6 - 6 + 1 = 31
Note: - 6 +1 because outcomes like (6,0), (6,1), (6,2), (6,3), (6,4), (6,6) are not valid due the fact that if 6 is scored in first ball second ball would not be bowled.
So all these 6 outcomes could be represented as 1 single outcome (6,N/A)

Probability that India would lose= 15/31
Probability that India would win= 1 - 15/31 = 16/31

Correct Option: 8 Best Solution (1)

11 Dec 2017 Age

A is 5 years older than B who is three times as old as C. The total of the ages of A, B and C is 54 years. What is the product of ages of A and C?

OPtion

1) 147
2) 546
3) 182
4) 123
5) 144
6) 150
7) 120
8) 160
9) 180
10)None of these

Solution

Let’s assume Age of B be B years
Age of A = B+5
Age of C = B/3

Total age = B + 5 + B + B/3 = 54
Solving 7B/3 = 49
B = 21
C = B/3 = 21/3 = 7 years
A = 21+5 = 26 years
Product = 26*7 = 182

Option 3)

Correct Option: 3 Best Solution (0)

08 Dec 2017 Ratio

If a/b = 39/7, b/c = 4/11, c/d = 7/26, e/f = 49/77 and d/e = 44/56 then what is the value of 13*abc/def ?

OPtion

1) 1
2) 1/177
3) 21/286
4) 3/286
5) 14/169
6) 7/3718
7) 8/5
8) 21/3718
9) 14/143
10) None of these

Solution

a/d = (a/b)*(b/c)*(c/d) = (39/7)*(4/11)*(7/26) = 6/11
b/e = (b/c)*(c/d)*(d/e) = (4/11)*(7/26)*(44/56) = 1/13
c/f = (c/d)*(d/e)*(e/f) = (7/26)*(44/56)*(49/77) = 7/52

So 13*abc/def = 13*(a/d)*(b/e)*(c/f) = 13*(6/11)*(1/13)*(7/52) = 21/286

Correct Option: 3 Best Solution (1)

07 Dec 2017 Simple Interest

Divide Rs. 16653 into 3 parts so that their amount after 2,3 and 4 years respectively may be equal, the rate of interest being 5% per annum at simple interest. The third part is

OPtion

1) 5539
2) 5544
3) 5796
4) 5323
5) 5313
6) 5791
7) 5315
8) 5545
9) 5792
10) None of these

Solution

Let the parts be x, y and z
x + (x * 2 * 5/100) = y + (y * 3 * 5/100) = z + (z * 4 * 5/100)
11x/10 = 23y/20 = 6z/5 = k
x = 10k/11, y = 20k/23, z = 5k/6
But x + y + z = 16653
10k/11 + 20k/23 + 5k/6 = 16653
k = 6375.6
z = (5/6)*6375.6 = 5313
Hence, the third part is Rs. 5313

Correct Option: 5 Best Solution (1)