M4maths Previous Puzzles

31 Dec 2019 Surface Area

A sphere of radius 49 cm is divided into 4 equal parts from center.
What would be the total surface area of one of such quarter sphere?

OPtion

1) 15092 m^2
2) 10061.33 m^2
3) 22638 m^2
4) 7546 m^2
5) 16092 m^2
6) 1.0061 m^2
7) 1.5092 m^2
8) 2.2638 m^2
9) 7.546 m^2
10) None of these

Solution

Total Surface Area of quarter sphere = (1/4) 4*Pi*r^2 + (1/2) Pi*r^2 + (1/2) Pi*r^2 = 2 Pi*r^2

Answer = 2* Pi * 49^2 = 15092 cm^2 = 1.5092 cm^2

Option 7)

Correct Option: 7 Best Solution (2)

30 Dec 2019 Average

13 typists can type 5265 pages in 810 minutes.
Find the average number of pages typed by each typist in an hour.

OPtion

1) 30.00
2) 30.25
3) 29.50
4) 31.25
5) 31.50
6) 30.75
7) 30.50
8) 32.75
9) 35.00
10) None of these

Solution

Total pages typed by 13
typists in 810 minutes/13.5 hours = 5265

Pages typed by one typist in 13.5 hours = 405 pages

Pages typed by one typist in one hour = 405/13.5 = 30

Correct Option: 1 Best Solution (6)

27 Dec 2019 Arithmetic

The sum of squares of three successive integers is 5810. Sum of these integers is?

OPtion

1) 122
2) 124
3) 126
4) 128
5) 116
6) 132
7) 118
8) 110
9) 112
10) None of these

Solution

(a-1)^2 + a^2 + (a+1)^2 = 5810
=> a^2 -2a + 1 + a^2 + a^2 + 2a + 1 = 5810
=> 3a^2 + 2 = 5810
=> a^2 = (20174-2)/3 = 1936
=> a = 44
So the 3 numbers are 43, 44 and 45 and their sum is 132

Correct Option: 6 Best Solution (2)

26 Dec 2019 Simplification

If A stands for addition, B for subtraction, C for multiplication and D for division. Then 8 A 3 C 7 B 15 D 3?

OPtion

1) 21
2) 24
3) 30
4) 32
5) 36
6) 42
7) 16
8) 28
9) 22
10) None of these

Solution

8 A 3 C 7 B 15 D 3
=> 8+3*7-15/3
=> 8+(3*7)-(15/3)
=> 8+21-5 = 24

Correct Option: 2 Best Solution (0)

25 Dec 2019 Mixture

In what ratio must milk at Rs.8.10 be mixed with milk at Rs.10.20 so that the mixture may be worth Rs.9 per kg?

OPtion

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

Solution

9 - 8.10 = 0.9
10.20 - 9 = 1.2
Required Ratio = 1.2:0.9 = 4:3

Correct Option: 5 Best Solution (0)

24 Dec 2019 Mensuration

A circle of perimeter 132 cm and a square of perimeter 132 cm given. Which figure has larger area and by how much?

OPtion

1) Square, 277
2) Square, 287
3) Square, 297
4) Square, 307
5) Square, 267
6) Circle, 297
7) Circle, 287
8) Circle, 277
9) Circle, 307
10) None of these

Solution

Perimeter of square =132 cm
4 x side = 132, side = 33
Area of square = (33)^2 = 1089 cm2
Circumference of circle =132cm
2π(radius) = 132
radius = 66*7/22 = 21 cm

Area of circle = π (radius)2
=22/7 * 21 * 21 = 1386 cm2

Area of circle – Area of square = 1386 – 1089 = 297 cm2

Correct Option: 6 Best Solution (6)

23 Dec 2019 Average

If the average of three consecutive odd numbers is 29, find the product of the largest and smallest of these numbers.

OPtion

1) 867
2) 837
3) 861
4) 841
5) 831
6) 827
7) 847
8) 857
9) 817
10) None of these

Solution

Let the first number is X, then the next two even numbers would be X+2, X+4

As per question;

(X+X+2+x+4)/3 = 29
=> 3X = 87-6
=> X = 81/3 = 27

So larges number is 27+4 =31
Answer = 27*31 = 837

Correct Option: 2 Best Solution (0)

20 Dec 2019 LCM

What is the least number which when doubled will be exactly divisible by 12, 16, 22 and 26 ?

OPtion

1) 6864
2) 6868
3) 6860
4) 13728
5) 13724
6) 13720
7) 3430
8) 3432
9) 3434
10) None of these

Solution

LCM of 12, 16, 22 and 26 = 6864

Hence the least number which will be exactly divisible by 12, 16, 22 and 26 = 6864

6864 ÷ 2 = 3432

Correct Option: 8 Best Solution (3)

19 Dec 2019 Logarithm

Find the logarithm of 144 to the base 2√3 ?
(note: 2√3 = two root three)

OPtion

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

Solution

144 = 12 x 12 = 4 x 3 x 4 x 3 = 2^4 x 3^2 = 2^4 x √3^4 = (2√3)^4

Logarithm 144 to the base 2√3 = Logarithm (2√3)^4 to the base 2√3
=> 4

Correct Option: 5 Best Solution (8)

18 Dec 2019 Probability

In a zoo, there are 15 rabbits and 10 rhinos. Three animal are selected at random. The probability that 1 rhino and 2 rabbits are selected, is:

OPtion

1) 1025/2300
2) 1040/2300
3) 1050/2200
4) 1060/2300
5) 1075/2300
6) 19/45
7) 21/46
8) 22/45
9) 23/46
10) None of these

Solution

Number ways of selecting 3 animal out of 25 = 25C3 = 2300
Number of ways that 1 rhino and 2 rabbits are selected = 10C1×15C2 = 1050

P(E) = 1050/2300 = 21/46

Correct Option: 7 Best Solution (7)