M4maths Previous Puzzles

03 Jan 2018 Probability

What is the probability of getting a product of 12 from three throws of a dice?

OPtion

1) 8/216
2) 6/216
3) 10/216
4) 12/216
5) 15/216
6) 16/216
7) 1/26
8) 1/24
9) 1/27
10)None of these

Solution

Total Number of possible outcomes = 6C1*6C1*6C1 = 6*6*6 = 216
Positive outcomes must satisfy D1*D2*D3= 12
Below are such values of D1, D2 and D3:
1, 6, 2
1, 4, 3
1, 3, 4
1, 2, 6
2, 6, 1
2, 3, 2
2, 2, 3
2, 1, 6
3, 4, 1
3, 2, 2
3, 1, 4
4, 3, 1
4, 1, 3
6, 2, 1
6, 1, 2

Count of positive outcome = 15
Probability = Positive outcome/Total Possible Outcomes = 15/216
Option 5)

Correct Option: 5 Best Solution (0)

02 Jan 2018 Find the Value

If a^2−b^2=2640 and a^2+b^2=6338 then what is the value of 23ab?

OPtion

1) 32491
2) 64013
3) 66263
4) 63097
5) 63079
6) 28813
7) 28816
8) 32491
9) 60263
10) None of these

Solution

As per question
a^2 - b^2 = 2640 ...(1)
a^2 + b^2 = 6338...(2)

Adding (1) and (2), we get
2a^2 = 8978
=> a^2 = 4489
=> a = 67

Substracting (1) from (2), we get
2b^2 = 3698
=> b^2 = 1849
=> b = 43

23*a*b= 23*67*43 = 66263

Correct Option: 3 Best Solution (7)

01 Jan 2018 Probability

An alphanumeric character is randomly selected from following sentence:
"A very happy new year to all m4maths users"

What is the probability that its an vowel?
Note: Alphanumeric character means alphabet or number. Space and other characters should be ignored.

OPtion

1) 1/3
2) 11/35
3) 10/33
4) 5/17
5) 2/7
6) 11/36
7) 4/15
8) 11/34
9) 6/13
10) None of these

Solution

Total number of alphanumeric character in the sentence = 34
Total Number of vowels = 11

Probability = 11/34

Correct Option: 8 Best Solution (2)

29 Dec 2017 Profit and Loss

Ramadheer buys an old car for Rs. 113750 and spends Rs. 19275 on its repairs. If he sells the car for Rs. 149000, his gain percent is:

OPtion

1) 12.01 %
2) 12.06 %
3) 12.09 %
4) 12.05 %
5) 12.90 %
6) 12.60 %
7) 12.80 %
8) 12.30 %
9) 12.62 %
10) None of these

Solution

Cost Price (C.P.) = Rs. ( 113750 + 19275 ) = Rs. 133025

Selling Price (S.P.) = Rs. 149000

Gain = (S.P.) - (C.P.) = Rs.(149000 - 133025) = Rs. 15975

Gain % = (15975/133025)*100 = 12.0090 = ~12.01 %

Option 1)

Correct Option: 1 Best Solution (0)

28 Dec 2017 Length of wire

198 cubic centimeters of silver is drawn into a wire 1 mm in diameter. The length of the wire will be:

OPtion

1) 25200 mm
2) 6300 cm
3) 25000 cm
4) 25000 mm
5) 252 m
6) 2520 cm
7) 6300 mm
8) 630 cm
9) 63 m
10) None of these

Solution

Radius in cm = (1/2)*(1/10) = 1/20 cm

Volume of Cylinder = Pi*r^2*l

So, Length l = 198/(Pi*r^2)
=> 198/(22/7 * 1/20 *1/20)
=> 25200 cm = 252 m

Correct Option: 5 Best Solution (0)

27 Dec 2017 Find the Value

If a^2−b^2=848 and a^2+b^2=5650 then what is the value of 11ab?

OPtion

1) 3249
2) 2401
3) 30123
4) 3097
5) 3079
6) 30273
7) 30723
8) 32499
9) 34299
10) None of these

Solution

As per question
a^2 - b^2 = 848 ...(1)
a^2 + b^2 = 5650...(2)

Adding (1) and (2), we get
2a^2 = 6498
=> a^2 = 3249
=> a = 57

Substracting (1) from (2), we get
2b^2 = 4802
=> b^2 = 2401
=> b = 49

11*a*b= 11*57*49 = 30723

Correct Option: 7 Best Solution (0)

26 Dec 2017 LCM

Two numbers are in the ratio 3 : 4. If their L.C.M. is 192. what is sum of the numbers?

OPtion

1) 110
2) 105
3) 108
4) 121
5) 109
6) 120
7) 115
8) 112
9) 100
10) None of these

Solution

Let the numbers be 3x and 4x

LCM of 3x and 4x is 12x


So as per question 12x = 192

=> x= 16
3x = 3*16 = 48 and 4x = 4*16 = 64


Sum of the numbers = 48+64 = 112

Correct Option: 8 Best Solution (1)

25 Dec 2017 Work & Time

Bakers are needed to prepare for a Christmas party. Each baker can make either 7 large cakes per hour, or 45 small cakes per hour. The kitchen is available for 3 hours and 140 large cakes and 990 small cakes are needed. How many bakers are required?

OPtion

1) 13.33
2) 12.5
3) 13
4) 14.33
5) 15
6) 14
7) 16
8) 12
9) 12.33
10) None of these

Solution

Lets find out person hours required to prepare the required cakes for the celebration:
Time taken to cook 140 large cakes by 1 baker =140/7 =20 hours
Time taken to cook 990 small cakes by 1 baker = 990/45= 22 hours
Total hours required by 1 baker = 20+22 = 42 hours

As we have kitchen available only for 3 hours, so we need to have more bakers to finish the work in 3 hours

1 baker * 42 hours = X baker * 3 hours
So X = 42/3 = 14

Correct Option: 6 Best Solution (1)

22 Dec 2017 Number

AB is a 2 digit odd number. If you subtract it from the number formed by reversing the digits(BA), you get 18 as result. What is the product of A and B?
Please note that A and B both are odd numbers greater than 5.

OPtion

1) 57
2) 15
3) 03
4) 63
5) 35
6) 53
7) 75
8) 39
9) 57
10) None of these

Solution

As per question
BA-AB = 18
So
10B+A-10A-B = 18
9B-9A = 18
B-A=2

As A and B both are odd numbers greater than 5 so only possible values of A and B which satisfy B-A=2 are:
A=7 and B=9

So Product of A and B = 7*9 =63

Correct Option: 4 Best Solution (4)

21 Dec 2017 Percentage

In a shop, the profit is 125% of the cost. If the cost increases by 35% but the selling price remains constant, find out approximately what percentage of the selling price is the profit?

OPtion

1) 66.66
2) 75.00
3) 40.88
4) 80.00
5) 153.00
6) 125.00
7) 135.00
8) 130.00
9) 40.00
10) None of these

Solution

Let the CP be Rs. 100
SP considering 150% of profit = 100+125 = Rs. 225
CP after 35% increase = Rs. 135

Profit = 225 – 135 = Rs. 90
Profit % on SP = (90/225)*100 = 40

Option 9)

Correct Option: 9 Best Solution (4)