M4maths Previous Puzzles

14 Oct 2011 board

There are 5 switches in a board. In these 5 switches 1 is attached with the fan. A person has to start the fan in 2 attempts only. Probability of success will be

OPtion

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

Solution

Probability of success in first attempt = 1/5
Probability of success in second attempt after first unsuccessful attempt = (4/5)*(1/4) = 1/5
so total probability = 1/5 + 1/5 = 2/5

Correct Option: 2 Best Solution (6)

13 Oct 2011 well

A square shaped well has to be dug. Cost of the land is 1800 rupee per square feet and cost of digging (based on depth) is 500 rupee per feet. The cost of digging is not based on area of the plot. We have to make a well of 1000 cubic feet volume. What will be its dimensions (in feet) for minimum cost.

OPtion

1) (50/9)^1/2, (50/9)^1/2, 180
2) 20, 20, 2.5
3) 10, 10, 10
4) (50/3)^1/2, (50/3)^1/2, 60
5) (100/3)^1/2, (100/3)^1/2, 30
6) (25/6)^1/2, (25/6)^1/2, 240
7) 5, 5, 40
8) (25/3)^1/2, (25/3)^1/2, 120
9) 12, 12, 125/18
10) none of these

Solution

According to given condition cost = 1800*(x^2)+500*h, and (x^2)*h=1000
cost will be minimum if 1800*(x^2) = 500*h
so 1800*(1000/h)=500*h so h^2=1800*1000/500=3600 so h^2=3600 or h=60feet
so 4th option is correct

Correct Option: 4 Best Solution (0)

12 Oct 2011 age

The sum of ages of three children is 15 years. The age of the eldest one is twice that of the younger one and the age of the youngest is one less than half the age of eldest.Calculate the product of ages?

OPtion

1) 90
2) 96
3) 102
4) 105
5) 80
6) 78
7) 110
8) 120
9) 150
10) none of these

Solution

According to the given condition
x+y+z = 15
x = 2y
z = (x/2)-1
on solving we will get
x = 8, y = 4, z = 3
so product = 96

Correct Option: 2 Best Solution (0)

11 Oct 2011 integers

How many integers between 5000 and 10000 can be formed by using the digits 5,6,7,9 and 4 ( You can use as many digits as you desire and repetition is not allowed.)

OPtion

1) 120
2) 60
3) 24
4) 6
5) 2500
6) 124
7) 96
8) 108
9) 12
10) none of these

Solution

Methods for filling first place = 4
for other places methods = 4, 3, 2
so total methods = 4*4*3*2 = 96

Correct Option: 7 Best Solution (1)

10 Oct 2011 sequence

Fill the blank space
1, 8, 9, 64, 25, ....., 49, 512 will be

OPtion

1) 4
2) 36
3) 27
4) 16
5) 125
6) 216
7) 243
8) 1024
9) Data are insufficient
10) none of these

Solution

There are two sequence
1^2, 3^2, 5^2, 7^2
2^3, 4^3, 6^3, 8^3

Correct Option: 6 Best Solution (0)

07 Oct 2011 sphere

A sphere of radius 10.4 cm. is melted to form spheres of radius 2.75 cm. Calculate the number of spheres of small size

OPtion

1) 40
2) 44
3) 45
4) 48
5) 54
6) 60
7) 62
8) 64
9) 66
10) none of these

Solution

volume of bigger sphere is proportional to (10.4)^3
volume of smaller sphere is proportional to (2.75)^3
so no. of smaller spheres = (10.4)^3/(2.75)^3 = 54

Correct Option: 5 Best Solution (4)

06 Oct 2011 work

10 men & 15 women complete half of the work in 12 days and 6 men & 15 women complete one third of the work in 10 days. How many days are required to complete the same full work by taking 10 men and 30 women?

OPtion

1) 12
2) 16
3) 18
4) 20
5) 21
6) 24
7) 27
8) 30
9) data are insufficient
10) none of these

Solution

10 men & 15 women complete half of the work in 12 days
so 20 men and 30 women complete the work in 12 days
so 240 men and 360 women complete the work in 1 day
similarly 6 men & 15 women complete one third of the work in 10 days
so 18 men and 45 women complete the work in 10 days
so 180 men and 450 women complete the work in 1 day
on comparing 240 men 360 women = 180 men 450 women
or 60 men = 90 women
so 2 men = 3 women
now 10 men 15 women = 20 men
and 10 men 30 women = 30 men
it is given that 20 men complete the work in 24 days
so 30 men will do the same work in 24*20/30 = 16 days

Correct Option: 2 Best Solution (9)

05 Oct 2011 Find the probability

What will be the probability to form word NOTEBOOK by using letters B,E,K,N,O,O,O and T. If you have to make arrangement of E,N,O and T first, after then you have to arrange B,K,O and O.

OPtion

1) 1/122
2) 1/266
3) 1/288
4) 1/166
5) 3/322
6) 1/323
7) 1/12
8) 1/222
9) 1/322
10) none of these

Solution

In the first Case Probability = 1/24
similarly probability for second case = 1/12

so total probability will be = 1/24*1/12 = 1/288

Correct Option: 3 Best Solution (7)

04 Oct 2011 Percentage

6% of x is root of equation x^2-6x+9=0, then x = ?

OPtion

1) 10
2) 20
3) 30
4) 40
5) 50
6) 60
7) 70
8) 80
9) 90
10) 100

Solution

Root of the given equation = 3
according to the given condition 6x/100 = 3
or x = 50

Correct Option: 5 Best Solution (14)

03 Oct 2011 sequence

Fill the blank space
4, 5, 12, 15, ...., 45, 108, 135

OPtion

1) 30
2) 35
3) 36
4) 40
5) 45
6) 48
7) 55
8) 58
9) 60
10)none of these

Solution

Two different sequences are included in this sequence
4,12,36,108
5,15,45,135

Correct Option: 3 Best Solution (10)