M4maths Previous Puzzles

11 Jan 2017 Radius of Sphere

2 solid spheres of radius 2 m and a solid cone of radius 2 m, height 2 m are melted to form a bigger solid sphere. What is the radius of this bigger solid sphere?

Please note that symbol ^ denotes power of

OPtion

1) 72^(1/3)
2) 54^(1/3)
3) 36^(1/3)
4) 18^(1/3)
5) (45/4)^(1/3)
6) (45/2)^(1/3)
7) (45/8)^(1/3)
8) 45^(1/3)
9) 18^(2/3)
10)36^(2/3)

Solution

Answer: 18^(1/3)
Volume of 2 smaller sphere's = 2*(4/3)*Pi*r^3
Volume of Cone = (1/3)*Pi*r^2*h
Volume of Larger Sphere = (4/3)*Pi*R^3
Here r=h=2m and R=?
Volume of Larger Sphere = Volume of 2 smaller sphere's + Volume of Cone
(4/3)*Pi*R^3 = 2*(4/3)*Pi*r^3 + (1/3)*Pi*r^2*h
=> 4*R^3 = (8*2^3 + 2^3) = 8*9
=> R^3 = 18
R = 18^(1/3)

Correct Option: 4 Best Solution (8)

10 Jan 2017 Sequence

What is the next number of the following sequence
15, 60, 135, 240, ?

OPtion

1) 550
2) 500
3) 480
4) 440
5) 425
6) 400
7) 375
8) 350
9) 325
10)300

Solution

Nth term of Series is formed by (3*n)*(5*n) where n = 1, 2, 3, 4, 5
So for n = 5 i.e. 5th term = 3*5*5*5 = 375

Correct Option: 7 Best Solution (22)

09 Jan 2017 Rate of Interest

A sum of Rs. 12,000 amounts to Rs. 15,000 in 4 years at the rate of simple interest. What is the rate of interest?

OPtion

1) 5.75 %
2) 5.8 %
3) 5.85 %
4) 5.9 %
5) 6.0 %
6) 6.05 %
7) 6.15 %
8) 6.25 %
9) 6.5 %
10)None of these

Solution

S.I. = Rs. (15000 - 12000) = Rs. 3000.
Rate = (SI*100)/(P*T)
Rate = (3000*100)/(12000*4) = 6.25%

Option 8)

Correct Option: 8 Best Solution (29)

06 Jan 2017 Profit

Seema bought more mangoes than guavas. She sells mangoes at Rs.23 apiece and makes 15% profit. She sells guavas at Rs.10 apiece and makes 25% profit. If she gets Rs.653 after selling all the mangoes and guavas, find her profit percentage.

OPtion

1) 15.4%
2) 15.9%
3) 16.4%
4) 16.9%
5) 17.4%
6) 17.9%
7) 18.2%
8) 18.4%
9) 18.6%
10) 18.8%

Solution

Assume Seema Sells X mangoes and Y guavas, where X > Y
Then, 23X + 10Y = 653 ---(i)
Try putting X = 1, 11, 21, 31…
(Why are we trying X =1,11,21? because as per equation (i) last digit of 23*X needs to be3 )
X=1 cannot be true as X>Y
When X=11, Y = 40 so this also cannot be true as X >Y
Next we find X = 21 and Y = 17 is the only solution where X > Y

Cost of aMango = 23/1.15 and cost of aGuava = 10/1.25
Overall cost = 483/1.15 + 170/1.25 = 556
Then profit = 653 – 556=97
Profit percentage = (97/556)×100=17.4%
Option 5)

Correct Option: 5 Best Solution (8)

05 Jan 2017 Probability

Two numbers are randomly selected from following set {3, 4,7,8,and 9}. What is the probability that product of these 2 selected numbers is an even number?

OPtion

1) 3/10
2) 7/20
3) 2/5
4) 7/10
5) 3/20
6) 1/8
7) 9/20
8) 11/20
9) 13/20
10)9/10

Solution

For faster solution let’s find out probability of Product of 2 number being odd
Product of 2 numbers a and b would be odd only if both a and b are odd
Odd numbers in given set {3,7,9}
Number of such numbers where product of 2 selected number is odd = 3C2 = 3*2/2 = 3
Total Number of possible ways to select 2 numbers from set {3,4,7,8,9} = 5C2 = 5*4/2 = 10
Probability that product of these 2 selected numbers is odd = 3/10
Probability that product of these 2 selected numbers is even = 1-
(3/10) = 7/10

Option 4)]

Correct Option: 4 Best Solution (16)

04 Jan 2017 Percentage

5 kg of adulterated rice has 2.72% stones in it and the rest is rice. Half of the stone content was removed. Now the percentage of stone content in it is

OPtion

1) 1.3517%
2) 1.3587%
3) 1.3600 %
4) 1.3617%%
5) 1.3687%
6) 1.3717%
7) 1.3737%
8) 1.3787%
9) 1.3827%
10)1.3887%

Solution

Weight of stones in 5 KG of adulterated rice = (2.72/100)*5000 = 136 gm
Weight of rice = 5000 - 136 = 4864 gm
Weight of Half of the stones which are removed = 136/2 = 68 gm
Total weight of remaining adulterated rice = 4932 gm
Percentage of Stones = 68/(4932) = 1.3787%

Option 8)

Correct Option: 8 Best Solution (14)

03 Jan 2017 Coding Decoding

If in coded language
CHINA = 351
JAPAN = 554
NEPAL = 622
Then
EGYPT = ?

OPtion

1) 355
2) 395
3) 755
4) 795
5) 955
6) 995
7) 1155
8) 1195
9) 1355
10)1395

Solution

A=1, B=2, C=3, D=4, E=5, F=6, G=7, H=8, I=9......
Each string is coded as: Sum of (Square of Position of each letter in string)
CHINA = 3^3+8^2+9^2+14^2+1^2 = 351
JAPAN = 10^2+1^2+16^2+1^2+14^2 = 554
NEPAL = 14^2+5^2+16^2+1^2+12^2 = 622
EGYPT = 5^2+7^2+25^2+16^2+20^2 = 1355

Option 9)

Correct Option: 9 Best Solution (14)

02 Jan 2017 Sequence

What is the next number of the following sequence
2, 6, 15, 28, 55, ?

OPtion

1) 63
2) 78
3) 66
4) 72
5) 84
6) 98
7) 104
8) 106
9) 108
10)110

Solution

Series is formed by Multiplying Prime number with its position in prime number list
1*2 = 2
2*3 =6
3*5 = 15
4*7 = 28
5*11 = 55
6*13 = 78

Option 2)

Correct Option: 2 Best Solution (0)

30 Dec 2016 Time, Distance & Speed

Pradeep could either walk or drive to office. The time taken to walk to the office is 8 times the driving time. One day, his wife took the car making him walk to office. After walking 1 km, he reached a temple when his wife called to say that he can now take the car. Pradeep figured that continuing to walk to the office will take as long as walking back home and then driving to the office. Calculate the distance between the temple and the office.

OPtion

1) 13/7
2) 7/3
3) 9/7
4) 16/7
5) 16/9
6) 24/7
7) 17/7
8) 23/14
9) 25/14
10)27/14

Solution

Suppose the distance between his home and office is x km. Then, distance between his office and temple is (x - 1) km.
If he walks at a speed of y km/hr. Then his driving speed = 8y km/hour, as he is 8 times faster in car.

Then,
1/y + x/8y = (x - 1)/y
Or, 1 + x/8 = x - 1
or 7x/8 = 2
Or, x = 16/7
Finally, x - 1 = 16/7 - 1 = 9/7
Option 3)

Correct Option: 10 Best Solution (6)

29 Dec 2016 Runs Scored

In a cricket match, Team A scored 223 runs without losing a wicket. The score consisted of byes, wides and runs scored by two opening batsmen: Ram and Shyam. The runs scored by the two batsmen are 27 times wides. There are 20 more byes than wides. If the ratio of the runs scored by Ram and Shyam is 8:6, then the runs scored by Ram is

OPtion

1) 81
2) 88
3) 90
4) 96
5) 100
6) 102
7) 104
8) 108
9) 112
10)116

Solution

Let Runs Scored by Ram+Shyam be x, byes be y and wides be z
As per question
x = 27z and y = 20+z

So Total runs = 27z+20+z+z = 223
=> 29z = 223 - 20
=> z = 7

Runs Scored by Ram+Shyam = 27*7
Runs scored by Ram = 27*7*8/14 = 108
Option 8)

Correct Option: 8 Best Solution (0)