M4maths Previous Puzzles

31 Jan 2018 Probability

An alphanumeric character is randomly selected from following sentence:
"Toleration and liberty are the foundations of a great republic."

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

OPtion

1) 1/2
2) 23/50
3) 23/51
4) 21/52
5) 23/52
6) 23/53
7) 21/53
8) 24/53
9) 24/55
10) None of these

Solution

Sentence = Toleration and liberty are the foundations of a great republic.

Total number of alphanumeric character in the sentence = 53
Total Number of vowels = 23 (OEAIOAIEYAEEOUAIOOAEAEUI)

Probability = 23/53

Correct Option: 6 Best Solution (4)

30 Jan 2018 Find the Value

If a^2−b^2=2352 and a^2+b^2=5090 then what is the value of 29ab?

OPtion

1) 65253
2) 65353
3) 65463
4) 65653
5) 65453
6) 65853
7) 65353
8) 63253
9) 65293
10) None of these

Solution

As per question
a^2 - b^2 = 2352 ...(1)
a^2 + b^2 = 5090...(2)

Adding (1) and (2), we get
2a^2 = 7442
=> a^2 = 3721
=> a = 61

Subtracting (1) from (2), we get
2b^2 = 2738
=> b^2 = 1369
=> b = 37

29*a*b= 13*61*37 = 65453

Correct Option: 5 Best Solution (1)

29 Jan 2018 Arrangement

How many unique ways are there to arrange the letters in the word PRETTIER?

OPtion

1) 630
2) 1260
3) 2520
4) 840
5) 420
6) 1680
7) 660
8) 5040
9) 880
10) None of these

Solution

Total number of letters in the word PRETTIER = 8
Total number of repeated letters = 6 (E, R and T are repeated twice )
So total unique ways to arrnage the letters of the word PRETTIER = 8!/(2!*2!*2) = 5040
Option 8)

Correct Option: 8 Best Solution (8)

26 Jan 2018 ODD Number

How many factors of 48886966800 are odd numbers?

OPtion

1) 120
2) 80
3) 160
4) 180
5) 210
6) 240
7) 125
8) 144
9) 150
10) None of these

Solution

48886966800 = 53^1 * 83^1 * 7^3 * 5^2 * 2^4 * 3^4

Any factor of this number should be of the form 53^a * 83^b * 7^c * 5^d * 2^e * 3^f.

For the factor to be an odd number e should be 0.

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

Total number of odd factors = 2*2*4*3*1*5 = 240

Option 6)

Correct Option: 6 Best Solution (0)

25 Jan 2018 Percentage

In a shop, the profit is 100% of the cost. If the cost increases by 75% but the selling price remains constant, find out approximately what percentage of the selling price is the profit?

OPtion

1) 14.29
2) 86.71
3) 25.00
4) 90.00
5) 15.00
6) 12.50
7) 87.50
8) 12.00
9) 88.00
10) None of these

Solution

Let the CP be Rs. 100
SP considering 100% of profit = 100+100 = Rs. 200
CP after 75 increase = Rs. 175

Profit = 200 – 175 = Rs. 25
Profit % on SP = (25/200)*100 = 12.5

Option 6)

Correct Option: 6 Best Solution (0)

24 Jan 2018 Divisibility

How many numbers between 1 and 100 (inclusive) are divisible by 5 or 3?

OPtion

1) 53
2) 54
3) 51
4) 52
5) 48
6) 50
7) 49
8) 47
9) 46
10) None of these

Solution

There are 20 numbers divisible by 5 between 1 and 100, and 33 numbers divisible by 3 between 1 and 100.

So there are 20 + 33 = 53, so 53 numbers divisible by one or the other, but this also includes every number which is divisible by both 5 and 3 twice.
Such numbers are 15, 30 and so on multiples of 15 between 1 to 100
There are 6 numbers divisible by 15 between 1 and 100 (i.e divisible by both 3 and 5)


So answer is 20+33-6 = 47

Correct Option: 8 Best Solution (0)

23 Jan 2018 Find the Value

If a^2−b^2=2352 and a^2+b^2=14210 then what is the value of 13ab?

OPtion

1) 19091
2) 91019
3) 91891
4) 91091
5) 19019
6) 91191
7) 91691
8) 91391
9) 91819
10) None of these

Solution

As per question
a^2 - b^2 = 2352 ...(1)
a^2 + b^2 = 14210...(2)

Adding (1) and (2), we get
2a^2 = 16562
=> a^2 = 8281
=> a = 91

Substracting (1) from (2), we get
2b^2 = 11858
=> b^2 = 5929
=> b = 77

23*a*b= 13*91*77 = 91091

Correct Option: 4 Best Solution (0)

22 Jan 2018 Population

The present population of a village is 15000. If it rises to 32955 during next 3 years, then find uniform rate of growth in population.

OPtion

1) 20
2) 22.5
3) 25
4) 27.5
5) 30
6) 32.5
7) 29
8) 31
9) 33
10) None of these

Solution

Poplation after n years = P[1+R/100]^n
=> 32955 = 15000 [1+R/100]^3
=> 2.197 = [1+R/100]^3
=> [1+R/100] = 1.3
=> R = 30%

Correct Option: 5 Best Solution (5)

19 Jan 2018 Time and Work

P can do a work in 42.5 days. Q can do the same work in 25.5 days and R can do the same in 34 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+3?

OPtion

1) 25 days
2) 15 days
3) 28 days
4) 20 days
5) 24 days
6) 18 days
7) 21 days
8) 22 days
9) 23 days
10) None of these

Solution

Amount of work done by Q and R in 6 days = 6*(1/25.5 + 1/34) = 6*((2+1.5)/51) = 21/51 = 7/17
Amount of work remaining after 6 days = 10/17

Amount of work done by P in 1 day = 1/42.5
So for 1/42.5 work P takes 1 day
Hence for 12/17 work P would take (1/(1/42.5))*10/17 = 25 days

X+3 = 28
Option 3)

Correct Option: 3 Best Solution (0)

18 Jan 2018 Arrangement

How many unique ways are there to arrange the letters in the word NEIGHBOURHOOD?

OPtion

1) 1037836800
2) 345945600
3) 172972800
4) 518918400
5) 691891200
6) 701801200
7) 448941600
8) 845689000
9) 228918400
10) None of these

Solution

Total number of letters in the word NEIGHBOURHOOD = 13
Total number of repeated letters = 2+3 (H is appearing twice and O is appearing 3 times)
So total unique ways to arrange the letters of the word NEIGHBOURHOOD = 13!/(2! *3!) = 518918400
Option 4)

Correct Option: 4 Best Solution (4)