M4maths Previous Puzzles

26 Sep 2018 Probability

If two letters are taken at random from the word DREAM, what is the probability that none of the letters would be vowels?

OPtion

1) 2/5
2) 3/5
3) 1/2
4) 1/6
5) 1/3
6) 1/12
7) 3/10
8) 2/3
9) 5/12
10) None of these

Solution

P(first letter is not vowel) = 3/5

P(second letter is not vowel) = 2/4 = 1/2

So, probability that none of letters would be vowels is = (3/5)×(1/2)=3/10

Correct Option: 7 Best Solution (6)

25 Sep 2018 Series

10321920, 645120, 46080, 3840, ...
Find the sixth term of following series

OPtion

1) 372
2) 350
3) 300
4) 384
5) 396
6) 40
7) 64
8) 48
9) 42
10) None of these

Solution

Terms are continuously divided by 16, 14, 12, 10, 8 and so on
Series is 10321920, 645120, 46080, 3840, 384, 48...

Option 8)

Correct Option: 8 Best Solution (0)

24 Sep 2018 Simple Interest

At what simple interest rate percent per annum will a sum of money double in 12 years.

OPtion

1) 7.50
2) 8.00
3) 8.33
4) 8.50
5) 7.25
6) 8.18
7) 8.75
8) 7.75
9) 8.66
10) None of these

Solution

SI = PRT/100

SI = P

So P = P*R*12/100
= R= 100/12 = 8.33
Option 3)

Correct Option: 3 Best Solution (0)

21 Sep 2018 Simple Interest

How long will it take for a sum of money to grow from Rs.1250 to Rs.12,000, if it is invested at 9% p.a simple interest?

OPtion

1) 9.0 years
2) 9.55 years
3) 90 years
4) 95 years
5) 96.00 years
6) 95.55 years
7) 96.00 years
8) 97.00 years
9) 98.00 years
10) None of these

Solution

SI = PRT/100
SI = 12000 -1250 = 10750
P = 1250
R = 9
T= ?


T = 10750 * 100 / (1250*9) = ~95.55 years

Correct Option: 6 Best Solution (5)

20 Sep 2018 Stocks

Riya invests a part of Rs. 42,000 in 9% stock at Rs. 120 and the remainder in 15% stock at Rs. 110. If her total dividend per annum is Rs. 4500, how much does she invest in 15% stock at Rs. 110?

OPtion

1) Rs. 24000
2) Rs. 27640
3) Rs. 29480
4) Rs. 22000
5) Rs. 22500
6) Rs. 21500
7) Rs. 20000
8) Rs. 20500
9) Rs. 23000
10) None of these

Solution

Let investment in 15% stock be Rs. x.
Then, investment in 9% stock = Rs. (42000 - x).
Therefore (15/110)*x + (9/120)(42000 - x) = 4500
=> 3x/22 + 3/40(42000-x) = 4500
=> 54x/880 + 3150 = 4500
solving
=> x = 22000

Option 4)

Correct Option: 4 Best Solution (2)

19 Sep 2018 Probability

An alphanumeric character is randomly selected from following sentence:
"Ultimately, education in its

real sense is the pursuit of truth.

It is an endless journey through

knowledge and enlightenment."

What is the probability that picked character is one of the following letters C or P or V or E or S?
Note: Alphanumeric character means alphabet or number. Space and other characters should be ignored.

OPtion

1) 20/105
2) 22/103
3) 11/52
4) 23/104
5) 2/13
6) 21/104
7) 3/13
8) 24/103
9) 12/51
10) None of these

Solution

Sentence = "Ultimately, education in its real sense is the pursuit of truth. It is an endless journey through knowledge and enlightenment."


Total number of alphanumeric character in the sentence = 104
Total Number of C = 1, P = 1 or V= 0 or E=14 or S = 8
Total = 24

Probability = (24)/104 = 3/13
Option 7)

Correct Option: 7 Best Solution (2)

18 Sep 2018 Work & Time

If 13 men and 14 women can do a piece of work in 11 days and 16 men and 17 women can do it in 9 days,

how many days will 27 men and 18 women take to do it?

OPtion

1) 6.25
2) 6.33
3) 6.50
4) 6.75
5) 7.00
6) 7.25
7) 6.60
8) 7.50
9) 7.66
10) None of these

Solution

Let a man's daily work is x units and that of a woman is y units.
So total amount of work, W = 11(13x + 14y) = 9(16x + 17y)

Solving we get, 143x - 144x = 153y - 154y
=> x = y

Now, 13 x + 14 y can do work in 11 days.
So, 27 y can do work in 11 days. ( as x = y)


Now, 27x + 18y = 27y + 18y = 45y

Hence, if 27y can do work in 11 days, 45y can do work in ((27y)*11)/45y = 6.6 days.

Option 7)

Correct Option: 7 Best Solution (0)

17 Sep 2018 Discount

The marked price of a shirt is Rs.1857. A shopkeeper offers three successive discount of 5%, 15% and 25%. How much will you have to pay, finally?

OPtion

1) 1124.05
2) 1224.05
3) 1024.05
4) 1024.65
5) 1124.65
6) 1224.65
7) 1024.85
8) 1124.85
9) 1114.65
10) None of these

Solution

Price after 1st Discount = 1857*95/100 = 1764.15

Price after 2nd Discount = 1764.15*85/100 = 1499.5275

Price after 3rd discount = 1499.5275*75/100 =1124.65

Hence Option 5)

Correct Option: 5 Best Solution (0)

14 Sep 2018 Bankers Discount

The banker's discount on a bill due 6 months hence at 9% is Rs. 6300. What is the true discount?

OPtion

1) 6401.66
2) 6024.96
3) 6078.71
4) 6828.71
5) 6227.52
6) 6028.71
7) 6078.88
8) 6007.23
9) 6011.26
10) None of these

Solution

T.D.=B.D. x 100 /(100 + (R x T))
=> 6300*100/(100+(9*6/12))
=> ~6028.71

Option 6)

Correct Option: 6 Best Solution (0)

13 Sep 2018 Arrangement

In how many different ways can the letters of the word CHIMPANZEE be arranged so that all the vowels never come together?

OPtion

1) 907200
2) 1814400
3) 1753920
4) 1653920
5) 1853920
6) 1253920
7) 1553920
8) 1743920
9) 1763920
10) None of these

Solution

Let's first find out the number of arrangements without any restrictions. The word 'CHIMPANZEE' has 10 letters where E occurs 2 times.
Therefore, number of ways in which the letters of the word 'CHIMPANZEE' can be arranged without any restrictions = 10!/2! = 1814400

Now let's find out the number of arrangements where all the vowels come together. The word 'CHIMPANZEE' has 10 letters where 4 are vowels (I, A, E, E).
Vowels must come together. Therefore, group these vowels and consider it as a single letter.
i.e., CHMPNZ, (IAEE)
Thus we have total 7 different letters.
Number of ways to arrange these 7 letters = 7! = 5040


In the 4 vowels, E occurs 2 times.
Number of ways to arrange these 4 vowels among themselves = 4!/2!=12

Therefore, number of ways in which the letters of the word 'CHIMPANZEE' can be arranged where all the vowels come together =5040×12=60480



Number of ways in which the letters of the word 'CHIMPANZEE' can be arranged where all the vowels never come together= 1814400 − 60480
= 1753920
Option 3)

Correct Option: 3 Best Solution (3)