M4maths Previous Puzzles

01 Aug 2013 Probability

In a single throw of two dice, what is the probability of getting an odd number on one and a multiple of 3 on the other.

OPtion

1) 1/36
2) 1/6
3) 1/12
4) 5/18
5) 11/36
6) 2/13
7) 5/36
8) 2/3
9) 1/2
10)None of these

Solution

An odd number on one and a multiple of 3 on the other:
Total number of favourable outcomes = 11
(1,3),(1,6),(3,3),(3,6),(5,3),(5,6),(3,1),(3,5),(6,1),(6,3),(6,5)
Required probability = 11/36

Correct Option: 5 Best Solution (5)

31 Jul 2013 Problem

A takes 10 days less than the time taken by B to finish a piece of work, if both A and B together finish a work in 12 days. Find the time taken by B to finish the work.

OPtion

1) 1
2) 11
3) 15
4) 25
5) 30
6) 20
7) 35
8) 40
9) 50
10)None of these

Solution

Le A can finish the work in x days
B can finish the work in x+10 days
So the work done by A in one day = 1/x times the total work
and the work done by B in one day = 1/x+10 times the total work
In 12 days, then can do the work together
(12/x)+(12/x+10)=1
solve
x=20
Hence A complete the work in 20 days and B in 20+10 = 30 days
option 5

Correct Option: 5 Best Solution (31)

30 Jul 2013 Problem

A Shopkeeper buys a number of books for Rs.80. If he had bought four more books for the same amount, each book would have cost him Rs.1 less. How many books did he buy?

OPtion

1) 12
2) 15
3) 16
4) 20
5) 21
6) 24
7) 26
8) 28
9) 32
10)None of these

Solution

Let the number of books purchased for Rs.80 = x
Then cost of each books = 80/x
If he buys for more books, the number of books = x+4
Cost of each book = 80/x+4
(80/x)-[80/(x+4)]=1
Solve x=-20 and x = 16
Rejecting x = -20
The number of books purchased = 16
option 3

Correct Option: 3 Best Solution (26)

29 Jul 2013 Sequence

What is the next no of the following sequence
5,31,283,3381,.....

OPtion

1) 19432
2) 28456
3) 30100
4) 36987
5) 42446
6) 45676
7) 49781
8) 56256
9) 62345
10)None of these

Solution

1^1+2^2 = 5
2^2+3^3 = 31
3^3+4^4 = 283
4^4+5^5 = 3381
5^5+6^6 = 49781
option 7

Correct Option: 7 Best Solution (0)

26 Jul 2013 Probability

If there are 3 children in a family, find the probability that there is one girl in the family.

OPtion

1) 1/3
2) 1/8
3) 2/3
4) 2/7
5) 3/8
6) 3/7
7) 2/5
8) 3/4
9) 1/7
10) None of these

Solution

Let us denote a boy by b and girl by g.
Then same space = (bbb,bbg,bgb,gbb,gbg,ggb,bgg,ggg)=8
Total number of possible outcomes = 8
Total number of favorable outcomes =3(bbg,bgb,gbb)
p(a girl) = 3/8

Correct Option: 5 Best Solution (5)

25 Jul 2013 HCF

If (x^2-x-2) is HCF of the polynomials (x-2)(2x^2+ax+1) and (x+1)(3x^2+bx+2), find the value of a.

OPtion

1) 1
2) 2
3) 3
4) 4
5) 5
6) 6
7) 7
8) 8
9) 9
10)None of these

Solution

Let P(x)=(x-2)(2x^2+ax+1) and Q(x)=(x+1)(3x^2+bx+2)
Factorize (x^2-x-2)=(x-2)(x+1)
As (x-2)(x+1) is the HCF of P(x) and Q(x), both (x-2) and (x+1) must be factor of P(x) and Q(x)
Solve
a=3
option

Correct Option: 3 Best Solution (16)

24 Jul 2013 Problem

Two trains leave a railway station at the same time. The first train travels due west and the second train travels due north. The first train travels 5 km/hr faster than the second train. If after two hours, they are 50 km apart, find the speed of first train.

OPtion

1) 10 km/hr
2) 15 km/hr
3) 20 km/hr
4) 25 km/hr
5) 30 km/hr
6) 35 km/hr
7) 40 km/hr
8) 45 km/hr
9) 50 km/hr
10) None of these

Solution

Let the speed of the second train = x km/hr
The speed of the first train = x+5 km/hr
Distance covered after two hours by the first train is 2(x+5) km.
Distance covered by the second train after two hours is 2x km.
(2x)^2 + 4(x+5)^2=(50)^2 (Using pythagoras theorem)
Solve
We get x=-20 and x=15
The speed of the first train = 15+5=20km/hr
option 3

Correct Option: 3 Best Solution (0)

23 Jul 2013 Work

A man is engaged for 70 days. He is to receive Rs.24 per day, when he works, but has to pay a fine of Rs.6 for every day that he is absent. He receive altogether Rs.1230. How many days did he work?

OPtion

1) 30
2) 35
3) 45
4) 48
5) 53
6) 55
7) 62
8) 68
9) 70
10)None of these

Solution

Let us consider that he worked for x days.
The number of days on which he is absent = 70-x
Wages for x days = 24x (i)
Find for the days he is absent = 6(70-x) (ii)
Wages for x days - fine for (70-x) days = Amount Received
24x - 6(70-x)= 1230
Solve
therefore He worked for 55 days
option 6

Correct Option: 6 Best Solution (44)

22 Jul 2013 What will be next number

2, 12, 1112, 3112, 132112, 1113122112, ?

OPtion

1) 131311212211
2) 111331221221
3) 111133212212
4) 311321221212
5) 311311222112
6) 313111222212
7) 131321221211
8) 311131222121
9) 112223123121
10) none of these

Solution

2
now read this
this is 1 times 2
so next number = 12
now read this
this is 1 times 1 and 1 times 2
so next number = 1112
now read this
this is 3 times 1 and 1 times 2
so next number = 3112
now read similarly for the others and make the numbers

Correct Option: 5 Best Solution (38)

19 Jul 2013 Line

B is a point in the line segment AC such that it lies between A and C if AB = 9cm and AB*AC=12(BC)^2, find BC.

OPtion

1) 9 cm
2) 5 cm
3) 16 cm
4) 15 cm
5) 6 cm
6) 3 cm
7) 8 cm
8) 12 cm
9) 4 cm
10)None of these

Solution

Let BC = x
9*(9+x)=12x^2
solve
x=-27/12 (Not Possible) and x = 3
option 6

Correct Option: 6 Best Solution (23)