M4maths Previous Puzzles

27 Sep 2019 Solve

The tickets numbered from 1 to 30 are mixed up and then a ticket is drawn at random. What is the probability that the ticket has a number which is a multiple of 3 or 5?

OPtion

1) 9/20
2) 8/30
3) 8/30
4) 9/30
5) 8/15
6) 7/150
7) 14/30
8) 1/4
9) 1/2
10) None of these

Solution

The sample space, S= (1, 2, 3, 4, 5 ...28, 29, 30) or n(S) = 30

The event "E" of getting a multiple of 3 or 5 = (3, 6, 9, 12, 15, 18, 21, 24, 27, 5, 10, 20, 25, 30) or n (E) = 14

Probability = 14/30 = 7/15

Correct Option: 7 Best Solution (4)

26 Sep 2019 Solve

The HCF of 2/3, 8/9, 64/81, and 10/27 is:

OPtion

1) 2/27
2) 2/9
3) 3/49
4) 2/81
5) 5/49
6) 4/81
7) 4/27
8) 4/49
9) 2/243
10) None of these

Solution

HCF = HCF of Numerator/LCM of denominator

HCF of 2, 8, 64 and 10 = 2
LCM of 3, 9, 81, 27 = 81

Hence HCF = HCF/LCM = 2/81

Correct Option: 4 Best Solution (3)

25 Sep 2019 Solve

A train moving at speed of 180 km/hr crosses a pole in 7 seconds. Find the length of the train.

OPtion

1) 250
2) 300
3) 350
4) 175
5) 700
6) 150
7) 125
8) 375
9) 325
10) None of these

Solution

Length of the train is equal to the distance covered by train to cross the pole. So, we will find the distance traveled by the train in 7 seconds by applying the following formula:

Distance= Speed x Time

Speed is given in Km/hr so we will convert it into m/s as answers are given in meters.

Speed=180*5/18 = 50 m/s
Time = 7 seconds

Distance = 50 * 7= 350 meters

Correct Option: 3 Best Solution (0)

24 Sep 2019 Solve

The value of 5 ^ (1/8) x (625) ^ 0.25 is

OPtion

1) 6.22
2) 6.41
3) 6.011
4) 5.911
5) 6.19
6) 5^(8/7)
7) 5^(7/6)
8) 5^(9/8)
9) 5^(8/9)
10) None of these

Solution

5^(1/8) x (625)^0.25
=> 5^(1/8) x (5^4)^1/4
=> 5^(1/8) x (5)
=> 5^(1/8 + 1)
=> 5^(9/8)

Correct Option: 8 Best Solution (2)

23 Sep 2019 Profit and Loss

A shopkeeper sells his goods at cost price but uses a weight of
910 gm instead of kilogram weight. What is his profit percentage?

OPtion

1) 9.98%
2) 9.89%
3) 9.063%
4) 9.089%
5) 9.49%
6) 9.08%
7) 9.71%
8) 9.53%
9) 9.77%
10) None of these

Solution

Let the CP of 1000 gm item be Rs. 1000
CP of 910 GM item = Rs 910
SP of 910 gm item = Rs 1000

Profit %= (1000 - 910)*100/880 = 120*100/910 = 9.89%

Correct Option: 2 Best Solution (1)

20 Sep 2019 Series

Find the twelfth term of below series is:
-1, 7, 5, 21, 19, 43, 41, .....

OPtion

1) 167
2) 169
3) 171
4) 121
5) 109
6) 177
7) 157
8) 110
9) 144
10)None of these

Solution

1^2 - 2 = -1
2^2 + 3 = 7
3^2 - 4 = 5
4^2 + 5 = 21
5^2 - 6 = 19
6^2 + 7 = 43
7^2 - 8 = 41
8^2 + 9 = 73
9^2 - 10 = 71
10^2 + 11 = 111
11^2 - 12 = 109
12^2 + 13 = 157

Correct Option: 7 Best Solution (4)

19 Sep 2019 Logarithm

If log2 + log(3x+1) = log(2x-9) + 2, then value of x is ?
Note: Assume all log represented above is to the base of 10.

OPtion

1) 441/94
2) 451/94
3) 461/94
4) 441/97
5) 461/97
6) 451/97
7) 431/97
8) 451/91
9) 451/93
10)None of these

Solution

Considering base is 10, so 1 could be represented as Log10
=> log2 + log(3x+1) = log(2x-9) + log100

Let’s revise the formula for Logs
Log(XY) = LogX+LogY
Applying the formula we get:
Log[2*(3x+1)] = Log[100*(2x-9)]
Solving
=> 6x + 2 = 200x - 900
=> 194x= 902
=> x = 451/97

Correct Option: 6 Best Solution (1)

18 Sep 2019 Mode

Find the mode of following list of values:
86 69 77
68 85 97
85 68
96 83 69 68

OPtion

1) 69
2) 97
3) 77
4) 68
5) 85
6) 86
7) 85
8) 83
9) 96
10) None of these

Solution

Mode = Number which is present maximum number of times = 68

Correct Option: 4 Best Solution (0)

17 Sep 2019 Volume

44 cubic centimeters of silver is drawn into a wire 4 mm in diameter. The length if the wire in meters will be:

OPtion

1) 3.5cm
2) 35cm
3) 35cm
4) 3500m
5) 35000cm
6) 3.5m
7) 0.35m
8) 35m
9) 350m
10) None of these

Solution

Let the length of the wire be h
Radius=4/2 mm = 1/5 cm
Volume = πr^2h= 44
=> (22/7)∗(1/5)∗(1/5)∗h = 44
=>h = (44∗5∗5∗7)/22 = 350cm = 3.5m

Correct Option: 6 Best Solution (0)

16 Sep 2019 Interest

At what rate of compound interest per annum will a sum of Rs. 5000 become Rs. 10068 in 10 years?

OPtion

1) 6.5%
2) 7.5%
3) 7.75%
4) 8.5%
5) 7.25%
6) 7.0%
7) 8.0%
8) 6.75%
9) 8.25%
10) None of these

Solution

A = P (1 + r/n)^t 
Solving for R, we get R= 7.25%

Correct Option: 5 Best Solution (1)