M4maths Previous Puzzles

05 Jul 2017 Standard Deviation

Age of 6 members in a family are 17 years, 36 years, 12 years, 16 years, 63 Years and 39 years.
What is the population standard deviation of their ages?

OPtion

1) 17.76
2) 15.23
3) 18.37
4) 16.69
5) 17.67
6) 16.96
7) 15.32
8) 18.03
9) 17.86
10)None of these

Solution

Mean of 6 ages = (12+16+17+36+39+63)/6 = 30.5
Sum of squared difference from mean for each number = (30.5-12)^2 + (30.5-16)^2 + (30.5-17)^2 + (30.5-36)^2 + (30.5-39)^2 + (30.5-63)^2
=1893.5

Average of Squared difference (Variance) = 1893.5/6 = 315.58
Population Standard Deviation = Square root of variance = 315.58^1/2 = 17.76

Correct Option: 1 Best Solution (11)

04 Jul 2017 Root and Power

5^x * 2^3 = 36.
Find 5^(x+1) =?

OPtion

1) 2.25
2) 22
3) 21.5
4) 225
5) 23
6) 32.5
7) 45/2
8) 21
9) 24
10) None of these

Solution

5^x * 2^3 = 36
5^x = 36/8
5^x = 9/2

5^(x+1) = (5^x) * (5) = (9/2)*5 = 22.5 = 45/2

Correct Option: 7 Best Solution (20)

03 Jul 2017 Profit and Loss

Robert buys an old scooter for Rs. 14650 and spends Rs. 2184 on its repairs. If he sells the scooter for Rs. 18850, his gain percent is:

OPtion

1) 10.58 %
2) 11.097 %
3) 10.48 %
4) 11.85 %
5) 11.90 %
6) 11.58 %
7) 10.98 %
8) 11.93 %
9) 11.98 %
10) None of these

Solution

Cost Price (C.P.) = Rs. (14650 + 2184) = Rs. 16834

Selling Price (S.P.) = Rs. 18850

Gain = (S.P.) - (C.P.) = Rs.(18850 - 16834) = Rs. 2016

Gain % = (2016/16834)*100 = 11.9757 = ~ 11.98%

Correct Option: 9 Best Solution (27)

30 Jun 2017 Clock

An accurate clock shows 6 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 3:30 PM?

OPtion

1) 250 degree
2) 210 degree
3) 240 degree
4) 255 degree
5) 280 degree
6) 205 degree
7) 245 degree
8) 230 degree
9) 260 degree
10) None of these

Solution

We know that angle traced by hour hand in 12 hrs = 360°

From 6 to 3:30, there are 9.5 hours (9 hour 30 mins).

Angle traced by the hour hand in 9.5 hours = 9.5×360/12
=285 degree

Correct Option: 10 Best Solution (17)

29 Jun 2017 Profit and Loss

100 oranges are bought for Rs. 380 and sold at the rate of Rs. 48 per dozen. The percentage of profit or loss is:

OPtion

1) 2.8% Loss
2) 5.26% Loss
3) 5.7% Loss
4) 5.39% Loss
5) 2.5% Loss
6) 2.8% Profit
7) 5.26% Profit
8) 5.7% Profit
9) 5.39% Profit
10) 2.5% Profit

Solution

Cost of 1 orange= 380/100 = 3.8
Selling price of 1 orange = 48/12 = Rs. 4

As SP > CP so its profit
So Profit % = (4 - 3.8)*100/3.8 = 5.26%
Option 7)

Correct Option: 7 Best Solution (29)

28 Jun 2017 Probability

There are 8 boys and 5 girls in a class. If four students are selected at random, what is the probability that 2 girls and 2 boy are selected?

OPtion

1) 4/13
2) 56/286
3) 56/143
4) 1/10
5) 290/715
6) 56/288
7) 55/143
8) 56/134
9) 40/143
10) None of these

Solution

Total number of ways of selecting 4 students = 13C4
Total number of selecting 2 boys = 8C2
Total number of selecting 2 Girl = 5C2

Probability = (8C2 * 5C2)/13C4 = ((8*7/2)*(5*4/2))/(13*12*11*10/4*3*2)
=> 28*10/715 = 56/143

Correct Option: 3 Best Solution (14)

27 Jun 2017 Mixture

A merchant has 70 kg of sugar, part of which he sells at 3.5% profit and the rest at 10.5% profit. He gains 8% on the whole. The quantity sold at 3.5% profit is:

OPtion

1) 35 kg
2) 25 kg
3) 15 kg
4) 22.5 kg
5) 27.5 kg
6) 20 kg
7) 45 kg
8) 40 kg
9) 60 kg
10)None of these

Solution

(Quantity of Cheaper)/(Quantity of Dearer) = (Price of Dearer - Mean Price)/(Mean Price - Price of Cheaper)

(Quantity of Cheaper)/(Quantity of Dearer) = (110.5 - 108)/(108-103.5) = 2.5/4.5 = 5/9

Total Quantity = 70 KG

The quantity sold at 3.5% profit is = (5/14) * 70 = 25 Kgs

Option 2)

Correct Option: 2 Best Solution (18)

26 Jun 2017 Series

What is the seventh term of following series:

5+6i, 7+13i, 11+32i, 19+69i, 35+130i, ....

OPtion

1) 56 + 256i
2) 67 + 121i
3) 56 + 221i
4) 68 + 216i
5) 67 + 227i
6) 67 + 221i
7) 56 + 227i
8) 131 + 248i
9) 68 + 221i
10) None of these

Solution

The complex number is formed by two series:
Real part series is:
5, 7, 11, 19, 35, 67, 131
nth term is 2^n+3 = 2^7+3 = 131

Imaginary part is:
6, 13, 32, 69, 130, 221
nth term = n^3+5
7th term = 7^3+5 = 343+5 = 348

Hence 6th term 131+348i

Correct Option: 10 Best Solution (5)

23 Jun 2017 Age

Simran's father was 24 years of age when she was born while her mother was 24 years old when her brother six years younger to her was born. What is the difference between the ages of her parents?

OPtion

1) 3 Year
2) 2.5 Years
3) 4 Years
4) 0 Years
5) 6 Years
6) 5 Years
7) 5.5 Years
8) 6.5 Years
9) 7 Years
10)None of these

Solution

Age of Simran's father when Simran was born = 24
Age of Simran's mother when Simran was born = 24−6 =18
Required difference of age =24−18= 6 Years

Correct Option: 5 Best Solution (7)

22 Jun 2017 Radius and Volume

5 solid spheres of radius 2 m, 7 solid cylinder of radius 3 m, height 7 meter and 4 solid cones of radius 5 m, height 8 m are melted to form a bigger solid sphere. What is the radius of this bigger solid sphere in meters?

OPtion

1) 7.22
2) 9.14
3) 8.29
4) 9.01
5) 8.89
6) 7.99
7) 8.09
8) 8.66
9) 9.58
10)None of these

Solution

Volume of 5 smaller sphere's = 5*(4/3)*Pi*r1^3
Volume of 7 Cylinder = 7*(Pi*r2^2*h1)
Volume of 4 Cones = 4*(1/3)*Pi*r3^2*h2
Volume of Larger Sphere = (4/3)*Pi*R^3

Here r1=2m, r2=3m, r3=5m, h1=7m, h2=8m, and R=?
Volume of Larger Sphere = Volume of 5 smaller sphere's + Volume of 7 Cylinder +Volume of 4 Cones
=> (4/3)*Pi*R^3 = 5*(4/3)*Pi*r1^3 + 7*P1*r2^2*h1 + 4*(1/3)*Pi*r2^2*h2

=> 4/3*R^3 = 5*8*4/3 + 7*63 + 4/3*200 = 2283/3
=> R^3 = 570.75
R = 570.75^(1/3) = 8.29 m

Option 3)

Correct Option: 3 Best Solution (12)