M4maths Previous Puzzles

10 Oct 2018 Probability

What is the probability of getting a product of 8 from three throws of a dice?

OPtion

1) 8/216
2) 10/216
3) 6/216
4) 5/216
5) 4/216
6) 9/216
7) 7/216
8) 11/216
9) 12/216
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, 4, 2
1, 2, 4
2, 4, 1
2, 2, 2
2, 1, 4
4, 2, 1
4, 1, 2

Count of positive outcome = 7
Probability = Positive outcome/Total Possible Outcomes = 7/216
Option 7)

Correct Option: 7 Best Solution (2)

09 Oct 2018 Perfect Square

How many factors of 2027229039 are perfect squares?

OPtion

1) 60
2) 18
3) 12
4) 9
5) 15
6) 16
7) 6
8) 24
9) 27
10) None of these

Solution

2027229039 = 23^3 * 17^1 * 11^2 * 3^4

Any factor of this number should be of the form 23^a * 17^b * 11^c * 3^d

For the factor to be a perfect square a,b,c,d have to be even.

a can take values 0,2
b can take values 0,
c can take values 0, 2
d can take values 0, 2, 4



Total number of perfect squares = 2*1*2*3 = 12

Option 3)

Correct Option: 3 Best Solution (0)

08 Oct 2018 Series

What is the seventh term of following series:
2, 9, 28, 65, 126

OPtion

1) 216
2) 217
3) 330
4) 236
5) 335
6) 344
7) 345
8) 239
9) 234
10) None of these

Solution

nth term = n^3 + 1
n=1, 2, 3, 4, 5, 6, and so on

So 7th term = 7^3 + 1 = 344

Option 6)

Correct Option: 6 Best Solution (4)

05 Oct 2018 Age

A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 45 years now, what was the son's age three and half years years back?

OPtion

1) 19
2) 16
3) 18
4) 17
5) 15
6) 14
7) 13
8) 20
9) 21
10) None of these

Solution

Let the sons current age be x
So fathers age x years back when son was born => 45-x = x
Solving we get x = 22.5
3.5 Years back son's age = 22.5-3.5 = 19 years

Option 1)

Correct Option: 1 Best Solution (7)

04 Oct 2018 Fraction

If a/b = 21/34, b/c = 121/120, c/d = 17/77, e/f = 11/15 and d/e = 14/17 then what is the value of (abc/def)*2 ?

OPtion

1) 100
2) 200
3) 1/3
4) 2/595
5) 110/360
6) 77/180
7) 121/360
8) 121/260
9) 19/60
10) None of these

Solution

a/d = (a/b)*(b/c)*(c/d) = 11/80
b/e = (b/c)*(c/d)*(d/e) = 11/60
c/f = (c/d)*(d/e)*(e/f) = 2/15

So 100*abc/def = 100*(a/d)*(b/e)*(c/f) = 100*(11/80) *(11/60) * (2/15) = 121/18000

Option 10)

Correct Option: 7 Best Solution (3)

03 Oct 2018 Earthquake

The tremors of earthquake are felt at interval of 25 seconds.The first tremor was felt at 02:54:57 and the last tremor was felt at 10:45:22 am. How many times were the tremors felt?

OPtion

1) 441
2) 2361
3) 1417
4) 1119
5) 2360
6) 1416
7) 1179
8) 440
9) 1219
10) None of these

Solution

The time duration of earthquake = Duration Between first and last tremor = 10:45:22 - 02:54:57

For ease of calculation, let's assume that first tremor was at 02:45:22
Number of hours between 02:45:22 and 10:45:22 = 8 Hours = 8 * 60 *60 seconds = 28800 seconds

But in reality, its less than 8 hours as tremors started at 02:54:57 instead of 02:45:22
So time duration between 02:54:57 and 02:45:22 = 9 minutes 35 seconds = 575 seconds

The total duration of the earthquake in seconds = 28800 - 575 = 28225
The tremor was felt every 25 seconds so the number of times tremor was felt in 28225 seconds = 28225/25 = 1129

1129+1 = 1130 (Note: +1 for the first tremor)

Option 10

Correct Option: 10 Best Solution (3)

02 Oct 2018 Probability

Following is one of the quotes by Mahatama Gandhi:
"Strength does not come
from physical capacity.
It comes from an indomitable will."

An alphanumeric character is randomy picked from this quote, what is the probability that it would contain one of the following letters: G or A or N or D or H or I?
Note: Alphanumeric character means alphabet or number. Space and other characters should be ignored.

OPtion

1) 1/3
2) 10/33
3) 19/67
4) 7/22
5) 3/11
6) 20/67
7) 3/10
8) 18/67
9) 19/66
10) None of these

Solution

Count of total letters = 67
Count of G's = 1
Count of A's = 5
Count of N's = 4
Count of D's = 2
Count of H's = 2
Count of I's = 6

Total count of positive outcomes = 20

Probability = 20/67

Option 6)

Correct Option: 6 Best Solution (2)

01 Oct 2018 Profit and Loss

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

OPtion

1) 12.04
2) 12.036
3) 13.36
4) 12.36
5) 21.36
6) 12.63
7) 17.86
8) 11.12
9) 14.02
10) None of these

Solution

Let the CP of 1000 gm (1 kg) be Rs. 1000
Then CP of 890 gm = Rs 890
SP of 890gm = Rs 100

Profit = (1000-890)*100/890 = (110/890)*100 = 12.36
Option 4)

Correct Option: 4 Best Solution (6)

28 Sep 2018 Profit and Loss

250 Mangoes are bought for Rs. 4500 and sold at the rate of Rs. 250 per dozen. The percentage of profit or loss is:

OPtion

1) 15.55 % Profit
2) 15.16 % Loss
3) 16.41 % Profit
4) 15.74 % Profit
5) 16.667 % Profit
6) 16.14 % Profit
7) 18.00 % Profit
8) 16.67 % Profit
9) 15.5 % Profit
10) None of these

Solution

Cost of 1 Mango = 4500/250 = 18
Selling price of 1 Mango = 250/12 = Rs. 20.8333

As SP > CP so its profit
So Profit % = (20.8333- 18 )*100/18 = 15.74074 = ~15.74 %

Option 4)

Correct Option: 4 Best Solution (0)

27 Sep 2018 Bankers Discount

The banker's discount on a bill due 6 months hence at 9% is Rs. 5700. What is the true discount?

OPtion

1) 5401.66
2) 5404.96
3) 5494.54
4) 5445.65
5) 5418.88
6) 5429.41
7) 5478.88
8) 5407.23
9) 5411.26
10) None of these

Solution

T.D.=B.D. x 100 /(100 + (R x T))
=> 5700*100/(100+(9*6/12))
=> ~5454.54

Option 10)

Correct Option: 10 Best Solution (3)