M4maths Previous Puzzles

20 Jun 2018 Probability

An alphanumeric character is randomly selected from following sentence:
"Everybody is a genius.

But if you judge a fish by its ability to climb a tree,

it will live its whole life believing that it is stupid."

What is the probability that picked character is one of the following letters K or I or T or Y?
Note: Alphanumeric character means alphabet or number. Space and other characters should be ignored.

OPtion

1) 33/105
2) 32/103
3) 34/103
4) 34/104
5) 32/102
6) 31/104
7) 33/103
8) 34/105
9) 32/105
10) None of these

Solution

Sentence = "Everybody is a genius. But if you judge a fish by its ability to climb a tree, it will live its whole life believing that it is stupid."


Total number of alphanumeric character in the sentence = 105
Total Number of K = 0, I = 18, T= 11, Y =5
Total = 34

Probability = (34)/105
Option 8)

Correct Option: 8 Best Solution (5)

19 Jun 2018 Clock

A clock is started at noon. By 20 minutes past 4, the hour hand has turned through how many degrees?

OPtion

1) 90°
2) 120°
3) 130°
4) 125°
5) 105°
6) 110°
7) 115°
8) 100°
9) 135°
10) None of these

Solution

We know that angle traced by hour hand in 12 hrs = 360°
So angle traced in 1 hours = 360/12 = 30°

Time duration from noon to 20 minutes past 4 = 4 hours 20 minutes = 4 hour + 20/60 hours = 13/3 hours

Angle traced in 1 hours = 360/12 = 30°
Hence the angle traced by hour hand in 13/3 hours = 130°

Correct Option: 3 Best Solution (3)

18 Jun 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 42 years now, what was the son's age five 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 => 42-x = x
Solving we get x = 21
5 Years back son's age = 21-5 = 16 years

Option 2)

Correct Option: 2 Best Solution (6)

15 Jun 2018 Time and Work

P can do a work in 20 days. Q can do the same work in 12 days and R can do the same in 16 days. Q and R start the work and leave after 6 days. P finishes the remaining work in X days. What is the value of X?

OPtion

1) 5.0 days
2) 1.5 days
3) 1.75 days
4) 2.0 days
5) 2.25 days
6) 4.5 days
7) 2.5 days
8) 5.5 days
9) 6.0 days
10) None of these

Solution

Amount of work done by Q and R in 6 days = 6*(1/12 + 1/16) = 42/48 = 7/8
Amount of work remaining after 6 days = 1/8

Amount of work done by P in 1 day = 1/20
So for 1/20 work P takes 1 day
Hence for 1/8 work P would take (1/(1/20))*1/8 = 20/8 = 2.5 days

Correct Option: 7 Best Solution (10)

14 Jun 2018 Code Decode

IF TWINKLE TWINKLE LITTLE STAR is coded as 211514 then what is the code for "LONDON BRIDGE IS FALLING"

OPtion

1) 7826
2) 78254
3) 78054
4) 71754
5) 788264
6) 78874
7) 728224
8) 728814
9) 72834
10) None of these

Solution

Each lettter is coded as A=1, B=2. C=3 ....Z=26

Code is formed by: multiplication of highest number of each word - (Sum of highest number of each word)

So for TWINKLE TWINKLE LITTLE STAR = 23*23*20*19 - (23+23+20+20) = 211600 - 86

Similarly for LONDON BRIDGE IS FALLING = (15*18*19*14) - (15+18+19+14) = 71820 - 66 = 71754

Option 4)

Correct Option: 4 Best Solution (0)

13 Jun 2018 Cost Price

Simran went to buy 13 chocolates worth Rs. x. She gave Rs.500 rupee note to the shopkeeper to buy the chocolates then shopkeeper gave rest of the money in the denominations of 50 paise, 5 rupee, and 10 rupees. If the ratio of the number of coins is 16:19:15 respectively. Then what is the price of three chocolates?

OPtion

1) 247
2) 19
3) 17
4) 51
5) 224
6) 18
7) 57
8) 20
9) 260
10) None of these

Solution

Possible coins = (16, 19, 15) & (32, 38, 30)
If (16, 19, 15) = 0.50*16+ 5*19 + 10*15 = 253

Chocolate cost = 500 - 253 = 247

Case 2: (32, 38, 30) = 0.50*32+ 5*38 + 10*30 = 506 which is more than 200 rupees so wrong

So cost of 13 chocolates = Rs 247

Cost of 3 Chocolates = (247/13)*3 = Rs 57

Option 7)

Correct Option: 7 Best Solution (7)

12 Jun 2018 Probability

A prime number is randomly picked from list of prime numbers less than 70 , what is probability that one of its digit will be 7?

OPtion

1) 5/17
2) 5/18
3) 4/19
4) 5/19
5) 6/19
6) 7/18
7) 7/17
8) 7/19
9) 6/17
10) None of these

Solution

Total number of prime numbers less than 70 = 19 => 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67
Number of positive outcomes i.e. number where at least one of its digit is 7 = 5

Probability = 5/19

Correct Option: 4 Best Solution (6)

11 Jun 2018 Discount

Arun bought a mobile with 25% discount on the labeled price. He sold the mobile for Rs.3200 with 20% profit on the labeled price. At what price did he buy the mobile?

OPtion

1) 2000
2) 2100
3) 2200
4) 2666.67
5) 2300
6) 2400.33
7) 2500
8) 2700
9) 2800
10) None of these

Solution

Let labelled price be x
CP = 0.75x
SP = 1.20x

As per question SP = 3200
So 1.2x = 3200
Hence CP = 0.75x = 3200 *(0.75/1.2) = 2000

Correct Option: 1 Best Solution (5)

08 Jun 2018 Mean, Median and Mode

Find the product of half of mean, twice of median and three times of mode (i.e. you need to find (1/2)*mean* 2*median * 3*mode) for the following list of values?
67 17 37
27 27 87
17 57
47 17

OPtion

1) 49860
2) 149860
3) 74520
4) 48954
5) 65820
6) 49070
7) 24840
8) 49680
9) 17820
10) None of these

Solution

Mean = Sum of nos. / Count of numbers = 400/10 = 40
Median = Middle term when number are arranged in ascending order = 32
Mode = Number which is present maximum number of times = 17
Product = 1/2*40*2*32*17*3 = 65280

Option 10)

Correct Option: 10 Best Solution (4)

07 Jun 2018 Even Number

How many factors of 1907980272 are even numbers?

OPtion

1) 360
2) 300
3) 120
4) 90
5) 150
6) 160
7) 180
8) 240
9) 125
10) None of these

Solution

1907980272 = 23^3 * 11^2 * 3^4 * 2^4

Any factor of this number should be of the form 23^a *11^b * 3^c * 2^d

For the factors of this number to be an even number d should be non 0

a can take values 0, 1, 2, 3
b can take values 0, 1, 2
c can take values 0, 1, 2, 3, 4
d can take values 1, 2, 3, 4

Total number of odd factors = 4*3*5*4= 240

Option 8)

Correct Option: 8 Best Solution (0)