M4maths Previous Puzzles

05 Dec 2018 Perfect Square

How many factors of 4327580125 are perfect squares?

OPtion

1) 6
2) 18
3) 9
4) 12
5) 15
6) 24
7) 8
8) 32
9) 36
10) None of these

Solution

4327580125 = 37^2 * 19^1 * 11^3 * 5^3

Any factor of this number should be of the form 37^a * 19^b * 11^c * 5^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



Total number of perfect squares = 2*1*2*2 = 8

Option 7)

Correct Option: 7 Best Solution (0)

04 Dec 2018 Profit and Loss

1510 pomegranate are bought for Rs. 32465 and sold at the rate of Rs. 333 per dozen. The percentage of profit or loss is:

OPtion

1) 58.4 % Profit
2) 29.07 % Loss
3) 66.67 % Profit
4) 35.555 % Profit
5) 26.667 % Profit
6) 27.7777 % Profit
7) 28.00 % Profit
8) 66.67 % Profit
9) 31.5 % Profit
10) None of these

Solution

Cost of 1 pomegranate= 32465/1510 = 21.5
Selling price of 1 pomegranate = 333/12 = Rs. 27.75

As SP > CP so its profit
So Profit % = (27.75 - 21.5 )*100/21.5 = 29.06976744 = ~29.07 %

Option 10)

Correct Option: 10 Best Solution (3)

03 Dec 2018 Simplifcation

There are two buildings P and Q. If 75 persons are sent from P to Q, then the number of persons in each building is the same. If 105 persons are sent from Q to P, then the number of persons in P is double the number of persons in Q. How many persons are there in building P?

OPtion

1) 510
2) 620
3) 475
4) 725
5) 615
6) 465
7) 640
8) 675
9) 550
10) None of these

Solution

Let number of persons in building P be P and
number of persons in building Q be Q

P-75 = Q+75
=> P = Q + 150 ---- (i)

P+105= 2(Q-105)
=> P + 315 = 2Q ---- (ii)

Putting value of P from (i) in (ii)
Q + 150 + 315 = 2Q
Q = 465
P = 615

Correct Option: 5 Best Solution (0)

30 Nov 2018 Bankers Discount

The banker's discount on a bill due 15 months hence at 6% is Rs. 2170. What is the true discount?

OPtion

1) 2001.66
2) 2004.96
3) 2054.54
4) 2018.60
5) 2027.52
6) 2029.41
7) 2078.88
8) 2007.23
9) 2011.26
10) None of these

Solution

T.D.=B.D. x 100 /(100 + (R x T))
=> 2170*100/(100+(6*15/12))
=> ~2018.60

Option 4)

Correct Option: 4 Best Solution (0)

29 Nov 2018 Stocks

The market value of a 8.5% stock, in which an income of Rs. 341 is derived by investing Rs. 3900, brokerage being 3/4 %, is:

OPtion

1) 97.21
2) 97.40
3) 98.00
4) 96.15
5) 96.16
6) 97.96
7) 96.85
8) 96.46
9) 98.60
10) None of these

Solution

For an income of Rs. 341, investment = Rs. 3900

For an income of Rs. 8.5, investment = Rs. (3900/341) * 8.5 = 97.21
For a Rs. 100 stock, investment = Rs. 97.21

Market value of Rs. 100 stock = Rs. 97.21 - 0.75 = Rs. 96.46

Option 8)

Correct Option: 8 Best Solution (0)

28 Nov 2018 Probability

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

OPtion

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

Solution

P(first letter is not vowel) = 4/6 = 2/3


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


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

Correct Option: 3 Best Solution (4)

27 Nov 2018 Find Value of

Find the value of 2x^2 + 4zy + 3z^2
where x = Mean , y = Median and z = Mode of following numbers:
77 104 91 97
131 48 114
119 91 117 122

OPtion

1) 83701
2) 87261
3) 81261
4) 89261
5) 83261
6) 83101
7) 81101
8) 88101
9) 86261
10) None of these

Solution

Mean x = Sum of nos. / Count of numbers = 1111/11 = 101
Median y = Middle term when number are arranged in ascending order = 104
Mode z = Number which is present maximum number of times = 91
2x^2 + 4zy + 3z^2 = 2* (101)^2 + 4*91*104 + 3*(91)^2 = 83101

Option 6)

Correct Option: 6 Best Solution (1)

26 Nov 2018 Age

The present ages of A,B and C are in proportions 3:5:6. Six years ago, the sum of their ages was 66. What is the product of their present ages?

OPtion

1) 7500
2) 12960
3) 3840
4) 20580
5) 30720
6) 24000
7) 43740
8) 42000
9) 19440
10) None of these

Solution

Answer: 19440


Six years ago sum of Ages of A, B and C = 66
Six years later i.e. sum of current ages of A, B and C = 66 + 3*6 = 84

Present Age of A = 84*3/(3+5+6) = 18 years

Present Age of B = 84*5/(3+5+6) = 30 years
Present Age of C = 84*6/(3+5+6) = 36 years

Product of their ages = 19440

Option 9)

Correct Option: 9 Best Solution (7)

23 Nov 2018 Probability

If a letter is randomly taken from the word Mathematics, what is the probability that it would be a M?

OPtion

1) 2/11
2) 3/11
3) 1/11
4) 1/5
5) 1/3
6) 1/12
7) 4/11
8) 2/10
9) 2/9
10) None of these

Solution

Total Number of chacraccters in Mathematics = 11
Number of times M appears in Mathematics = 2

Probability = 2/11

Correct Option: 1 Best Solution (0)

22 Nov 2018 ODD Number

How many factors of 7721290962 are odd numbers?

OPtion

1) 288
2) 360
3) 120
4) 144
5) 150
6) 160
7) 180
8) 240
9) 125
10) None of these

Solution

7721290962 = 31^3 * 17^1 * 11^2 * 7^1 * 3^2 * 2^1

Any factor of this number should be of the form 31^a * 17^b * 11^c * 7^d * 3^e * 2^f

For the factors of this number to be an odd number f should be 0

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

Total number of odd factors = 4*2*3*2*3*1= 144


Option 4)

Correct Option: 4 Best Solution (2)