M4maths Previous Puzzles

07 Jun 2017 Standard Deviation

Raghav scored below runs in his last 7 innings
13 ; 38 ; 3 ; 29 ; 14 ; 68 ; 17
Find population standard deviation for his score in last 7 innings?

OPtion

1) 21.76
2) 24.39
3) 24.89
4) 25.14
5) 25.39
6) 20.14
7) 24.81
8) 23.51
9) 25.81
10)None of these

Solution

Mean of 7 score = (13+38+3+29+14+68+17)/7 = 182/7 = 26
Sum of squared difference from mean for each number = (26-13)^2 + (26-38)^2 + (26-3)^2 + (26-29)^2 + (26-14)^2 + (26-68)^2 + (26-17)^2
= 2840

Average of Squared difference (Variance) = 2840/7 = 405.71
Standard Deviation = Square root of variance = 405.71^1/2 = 20.14

Correct Option: 6 Best Solution (10)

06 Jun 2017 Clock

An accurate clock shows 4 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2:45 PM?

OPtion

1) 350 degree
2) 355 degree
3) 340 degree
4) 310 degree
5) 320.5 degree
6) 320.0 degree
7) 322.5 degree
8) 322 degree
9) 325 degree
10) None of these

Solution

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

From 4 to 2:45, there are 10.75 hours (10 hour 45 mins).

Angle traced by the hour hand in 10.75 hours = 10.75×360/12
=322.5 degree

Correct Option: 7 Best Solution (29)

05 Jun 2017 Age

The present ages of two persons differ by 35 years. 3 years later, the elder one would be 4.5 times as old as the younger one. What is the present age of the elder person?

OPtion

1) 37 years
2) 38 Years
3) 39 years
4) 45 years
5) 44 years
6) 41 years
7) 40 years
8) 42 years
9) 48 years
10) None of these

Solution

Let the present age of elder one be x and younger one be y
So x-y = 35 ----(i)
3 year later
(x+3) =4.5(y+3)
=> x = 4.5y + 10.5

Putting x value in (i)
4.5y + 10.5 - y = 35
=>3.5y = 24.5
=> y = 7 and x = 35+7 = 42

Correct Option: 8 Best Solution (29)

02 Jun 2017 Work Remaining

A can do a work in 6 days and B in 15 days. If they work on it together for 3 days, then the fraction of the work that is left after 3 days is :

OPtion

1) 3/10
2) 2/10
3) 4/10
4) 6/10
5) 7/9
6) 7/11
7) 5/12
8) 7/30
9) 7/9
10) None of these

Solution

A's 1 day's work = 1/6
B's 1 day's work = 1/15
(A + B)'s 1 day's work = 1/6 + 1/15 = (5+2)/30 = 7/30
(A + B)'s 3 day's work = (7/30)*3 = 7/10

Therefore, Remaining work = (1 - 7/10) = 3/10

Correct Option: 1 Best Solution (23)

01 Jun 2017 Find the value

If m and n are whole numbers and m^n = 841, what is the value of (m - 23)^(n+1) ?

OPtion

1) 27
2) 8
3) 64
4) 216
5) 144
6) 196
7) 81
8) 128
9) 243
10) None of these

Solution

m^n = 841

We know that 29^2 = 841

Hence we can take m = 29 and n = 2
So (m - 23)^(n+1) = (29-23)^2+1 = 6^3 = 216

Correct Option: 4 Best Solution (7)

31 May 2017 Profit and Loss

96 mangoes are bought for Rs. 1440 and sold at the rate of Rs. 72 per half dozen. The percentage of profit or loss is:

OPtion

1) 28% Profit
2) 22% Profit
3) 25% Loss
4) 33% Profit
5) 20% Loss
6) 28% Profit
7) 20% Profit
8) 25% Profit
9) 30% Profit
10) None of these

Solution

Cost of 1 mango = 1440/96 = 15
Selling price of 1 mango = 72/6 = Rs. 12

As SP < CP so its loss
So Loss % = (15 - 12)*100/15 = 20%
Option 5)

Correct Option: 5 Best Solution (0)

30 May 2017 Series

What is the sixth term of following series:

5+7i, 7+14i, 11+55i, 19+110i, 35+121i, ....

OPtion

1) 56 + 256i
2) 67 + 222i
3) 67 + 242i
4) 68 + 226i
5) 67 + 227i
6) 67 + 221i
7) 56 + 227i
8) 56 + 243i
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
nth term is 2^n+3 = 2^6+3 = 67

Imaginary part:
7, 14, 55, 110, 121, 242
Sum of previous number and its reverse = 7+7 = 14
Similarly 14+41 = 55
55+55 = 110
110+011 = 121
121+121 = 242

Correct Option: 3 Best Solution (22)

29 May 2017 Age

A is 9 years older than B who is four times as old as C. The total of the ages of A, B and C is 49 years. What is the product of ages of A and C?

OPtion

1) 240
2) 360
3) 60
4) 100
5) 480
6) 2400
7) 120
8) 180
9) 150
10)None of these

Solution

Let’s assume Age of B be B years
Age of A = B+9
Age of C = B/4

Total age = B + 9 + B + B/4 = 49
Solving 9B/4 = 40
B = 160/9
C = B/4 = 40/9 years
A = B+9 = 160/9 + 9 = 241/9 years
Product = 241/9*40/9 = 9640/81 = ~119

Option 10)

Correct Option: 10 Best Solution (8)

26 May 2017 Probability

There are 12 boys and 9 girls in a class. If three students are selected at random, what is the probability that 1 girl and 2 boys are selected?

OPtion

1) 3/21
2) 7/36
3) 1/4
4) 7/23
5) 297/656
6) 291/665
7) 8/25
8) 297/665
9) 1/3
10) None of these

Solution

Total number of ways of selecting 3 students = 21C3
Total number of selecting 2 boys = 12 C2
Total number of selecting 1 Girl = 9C1

Probability = (12C2 * 9C1)/21C3 = ((12*11/2)*9)/(21*20*19/3*2)
= 6*11*9/7*10*19 = 297/665

Correct Option: 8 Best Solution (9)

25 May 2017 Speed and Time

A boatman goes 4 km against the current of the stream in 2 hour and goes 7.5 kms along the current in 90 minutes. How long will it take to go 7 km in stationary water?

OPtion

1) 2 hours 33 minutes
2) 2.23 hours
3) 2 hours 20 minutes
4) 2.5 Hours
5) 2 hours 15 minutes
6) 2.03 hours
7) 2 hours 20 minutes
8) 2 hours 25 minutes
9) 2.0 hours
10)None of these

Solution

Speed (upstream) =4/2 = 2 km/hr
Speed (downstream)= 7.5/1.5= 5 km/hr

Speed in still water = 1/2 (5+2) = 3.5 km/hr

Time taken in stationary water to go 7 KM = 7/3.5 = 2 hr

Option 9)

Correct Option: 9 Best Solution (12)