M4maths Previous Puzzles

14 Dec 2018 Mean, Median and Mode

Find the value of x*y*2*z/5
where x = Mean , y = Median and z = Mode of following numbers:
57 59
56 81 69
55 64
63 81

OPtion

1) 331395
2) 331495
3) 331595
4) 331695
5) 331795
6) 132378
7) 132478
8) 132578
9) 132678
10) None of these

Solution

Mean x = Sum of nos. / Count of numbers = 585/9 = 65 = x
Median y = Middle term when number are arranged in ascending order = 63 = y
Mode z = Number which is present maximum number of times = 81 = z
=> x*y*2*z/5 = 65*63*2*81/5 = 132678


Option 9)

Correct Option: 9 Best Solution (0)

13 Dec 2018 Mixture

A merchant has 640 kg of sugar, part of which he sells at 2% loss and the rest at 6% profit. He gains 3% on the whole. What is the difference between the quantities of sugar sold at 2% loss and that sold at 6% profit?

OPtion

1) 180 kgs
2) 120 kgs
3) 105 kgs
4) 115 kgs
5) 125 kgs
6) 160 kgs
7) 135 kgs
8) 110 kgs
9) 240 kgs
10)None of these

Solution

(Quantity of Cheaper)/(Quantity of Dearer) = (Price of Dearer - Mean Price)/(Mean Price - Price of Cheaper)

(Quantity of Cheaper)/(Quantity of Dearer) = (106 - 103)/(103-98) = 3/5

Total Quantity = 640 KG

The quantity sold at 2% loss is = (3/8) * 640 = 240 Kgs
The quantity sold at 6% profit is = (5/8) * 640 = 400 Kgs
Difference between Quantity = 400-240 = 160 Kgs


Option 6)

Correct Option: 6 Best Solution (0)

12 Dec 2018 Series

What is the seventh term of following series:
34, 55, 89, 144, 233

OPtion

1) 291
2) 293
3) 377
4) 333
5) 510
6) 590
7) 610
8) 367
9) 387
10) None of these

Solution

Series is formed by Fibonacci numbers starting at 34 and 55 so next number is 144+233 = 377

So seventh term = 233+377 = 610

Option 7)

Correct Option: 7 Best Solution (3)

11 Dec 2018 Probability

A prime number number less than 50 is randomly picked, what is probability that one of its digit will be 1?

OPtion

1) 1/4
2) 5/16
3) 5/14
4) 3/7
5) 2/5
6) 1/3
7) 7/15
8) 7/13
9) 6/13
10) None of these

Solution

Total number of prime numbers less than 50 = 15 => 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
Number of positive outcomes i.e. number where at least one of its digit is 1 = 6

Probability = 6/15 = 2/5

Correct Option: 5 Best Solution (0)

10 Dec 2018 Interest

There is 60% increase in an amount in 5 years at simple interest. What will be the compound interest of Rs. 10,000 after 3 years at the same rate (compounded annually)?

OPtion

1) 4149.28
2) 4049.28
3) 4949.28
4) 4249.28
5) 4349.28
6) 4449.28
7) 4549.28
8) 4649.28
9) 4749.28
10) None of these

Solution

Let P be Rs 100 then SI after 5 years is Rs. 60

R = (SI/P*T) *100 = (60/100*5)*100 = 12%


CI = A{[ 1+ R/100]^T - 1 }
=> 10000 { [ 1 + 12/100]^3 - 1}
=> 10000 { [112/100]^3 - 1} = 4049.28
Option 2)

Correct Option: 2 Best Solution (10)

07 Dec 2018 Area

Given hypotenuse of a right angled triangle ABC is 17cm and its base is 15cm, what is the area of triangle ABC in cm^2?

OPtion

1) 60
2) 30
3) 120
4) 40
5) 25
6) 90
7) 50
8) 80
9) 10
10) None of these

Solution

B= 15, H=17 and L =?

L^2 + B^2 = H^2
=> L^2 = H^2 - B^2 = 17^2 - 15^2 = 64
=> L = 8

Area of triangle = 8*15/2 = 60cm^2

Correct Option: 1 Best Solution (3)

06 Dec 2018 Probability

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

OPtion

1) 2/7
2) 1/7
3) 4/7
4) 1/5
5) 1/8
6) 3/8
7) 13/70
8) 3/7
9) 2/9
10) None of these

Solution

Total Number of chacraccters in OCTOPUS = 7
Number of VOWELS 2 Os and 1 U= 3

Probability = 3/7

Correct Option: 8 Best Solution (3)

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 (4)

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)