M4maths Previous Puzzles

01 Apr 2010 Its complicated calculation?

Double of one twenty eighth part of square of cube of fourth root of 16 % of 10 lacs is

OPtion

1) 16, 00, 000
2) 12, 00, 000
3) 12, 80, 000
4) 8, 50, 000
5) 5, 80, 000
6) 10, 00, 000
7) 20, 70, 000
8) 4, 00, 000
9) 9, 50, 000
10) 1, 40, 000

Solution

2*(1/128)*[{(10, 00, 000*16/100) 1/4} 3] 2 = 10, 00, 000

Correct Option: 6 Best Solution (9)

31 Mar 2010 Possible value of Y?

If 6^x + 7^y = ....4, where x and y are integers from 0 to 9.
Then sum of all possible values of y is?

OPtion

1) 13
2) 11
3) 10
4) 9
5) 6
6) 8
7) 4
8) 15
9) 14
10) 16

Solution

The only possible cases are
6^0 + 7^3 = ....4
6^0 + 7^7 = ....4
Sum of possible values of y = 3 + 7 = 10

Correct Option: 3 Best Solution (9)

30 Mar 2010 Man and his 3 children?

A man divides his property between 3 children in such a way that Suresh gets 60 % of the total property.
Mahesh gets eighth part of the remaining property. If Sudheer gets 1 lacs 68 thousand rupee, then the total property is

OPtion

1) 2, 40, 000
2) 2, 88, 000
3) 1, 92, 000
4) 24, 000
5) 1, 68, 000
6) 1, 20, 000
7) 4, 80, 000
8) 4, 00, 000
9) 80, 000
10) 1, 32, 000

Solution

Total property = 100 %

Part of Suresh = 60 %

Part of Mahesh = 40 % / 8 = 5 %

Part of Sudheer = 35 %

35 % = 1, 68, 000

Thus total property = 1, 68, 000 * 100 / 35 = 4, 80, 000

Correct Option: 7 Best Solution (12)

29 Mar 2010 Code with 9 symbols?

How many codes of 9 symbols can be formed by using the integers 1, 2, 3, 4, 5, 6 and letters a, b, c, if
the 3 letters are necessarily taken together.

OPtion

1) 720
2) 5040
3) 30240
4) 362880
5) 120
6) 610
7) 7
8) 42
9) 4320
10) 3024

Solution

Suppose the set of 3 letters is a symbol, Then total symbols = 7

Methods for arranging these 7 symbols = 7*6*5*4*3*2*1 = 5040

Methods for arranging 3 letters = 3*2*1 = 6

Hence total number of codes formed = 5040*6 = 30240

Correct Option: 3 Best Solution (6)

26 Mar 2010 Cube volume

On increasing the side of a cube by 50 %, its volume increases by ?

OPtion

1) 125.75 %
2) 337.5 %
3) 150 %
4) 50 %
5) 100 %
6) 125.5 %
7) 237.5 %
8) 75.5 %
9) 90.25 %
10) 200 %

Solution

Let the side of the cube is 1 meter

Then volume of that cube = 1*1*1 = 1 cubic meter

50 % of 1 meter = 0.5 meter

Hence new volume of the cube = 1.5*1.5*1.5 = 3.375 = 337.5 %

Increment in the volume = (337.5 – 100) % = 237.5 %

Correct Option: 7 Best Solution (5)

25 Mar 2010 x/y?

If x^y = 2^12 (1)

and y^(x-2) = 2^12 (2) then x/y =

OPtion

1) 6
2) 2.5
3) 1/6
4) 1.5
5) 2/3
6) 1/2
7) 2
8) 16/3
9) 3/16
10) 32

Solution

xy = 212 (1)

Equation (1) gives the following possibilities
x y xy

2 12 2^12

4 6 4^6 (1)

8 4 8^4 (2)

16 3 16^3 (3)

64 2 64^2 (4)

4096 1 4096^1 (5)

Only (2) case satisfies the second equation.

Correct Option: 7 Best Solution (8)

24 Mar 2010 Round Temple

A round temple has cylindrical base and hemispherical top of radius 3 meter. If total height of the temple is 8 meter
then total volume of air in the temple is
(Given that 1 cubic meter = 1000 litre)

OPtion

1) 10000 litres
2) 22000 litres
3) 198000 litres
4) 198 litres
5) 80000 litres
6) 22 litres
7) 800 litres
8) 100 litres
9) 160000 litres
10) 80 litres

Solution

Height of cylinder = (8-3) meter = 5 meter
Volume of cylinder = п r2h = п (3)2 (5)
Volume of hemisphere = (2/3) п r3 = (2/3) п (3)3
Total volume = п (3)2 (5) + (2/3) п (3)3
= п (3)2 (5 + 2) = (22/7) * 9 * 7 = 198 cubic meter
= 198000 litres

Correct Option: 3 Best Solution (5)

23 Mar 2010 TV rent

A hotel has 4 rooms for rental and they are always occupied. The owner has 3 TV sets available on the rental Rs. 50 per day per set.
Only one set will be supplied to one occupant if he wants it. The chance that an occupant will want to hire a set is 1/3.
Find the probability that the hotel owner will get Rs. 150 per day by renting the sets.

OPtion

1) 1/81
2) 2/9
3) 8/81
4) 1/9
5) 16/81
6) 32/81
7) 8/27
8) 5/27
9) 2/5
10) 3/28

Solution

If no occupant hires a TV set, the probability of getting 0 rupee is
2/3*2/3*2/3*2/3 = 16/81

If one occupant hires a TV set, the probability of getting 50 rupee is
[4]*1/3*2/3*2/3*2/3 = 32/81

If two occupants hire a TV set, the probability of getting 100 rupee is

[(4*3)/(2*1)]*1/3*1/3*2/3*2/3 = 24/81

If three occupants hire a TV set, the probability of getting 150 rupee is
[(4*3*2)/(3*2*1)]*1/3*1/3*1/3*2/3 = 8/81

If four occupants want to hire a TV set, the probability of getting 150 rupee is [(4*3*2)/(3*2*1)]*1/3*1/3*1/3*1/3 = 1/81

Hence required probability is (8/81) + (1/81) = 9/81 = 1/9

Correct Option: 4 Best Solution (3)

22 Mar 2010 Probability of meeting?

Ram and Rahim agree to meet at a place between 4 P.M. to 6 P.M. The first one to come waits for 24 minutes and then leaves. If the time of their arrival are independent and at random then what is the probability of a meeting between Ram and Rahim.

OPtion

1) 16/25
2) 1/25
3) 9/25
4) 1/5
5) 4/5
6) 3/5
7) 1/2
8) 2/3
9) 1/3
10)1/120

Solution

Total interval = 120 minutes
There are two persons hence total areal time interval = 120*120
Meeting interval = 24 minutes
Interval in which meeting is not possible = 96 minutes
There are two persons hence the total areal time interval for cancellation of meeting = 96*96
Total areal time interval for meeting = 120*120 � 96*96
Probability = (120*120 � 96*96)/ 120*120
= 9/25

Correct Option: 3 Best Solution (0)

19 Mar 2010 Rectangular and Circular block

Rectangular marbles are taken to make a floor. The length and breadth of a marble are 4 feet and 3 feet respectively.
A circular block of radius 1 feet is thrown on the floor at random. The chance that it falls entirely on one rectangular
block is

OPtion

1) 7/12
2) 1/12
3) 3/4
4) 1/2
5) 2/3
6) 5/6
7) 1/6
8) 3.14/7
9) 1.57/6
10) 1.57/3

Solution

The centre of the circular block can be moved in a rectangular area of length and breadth 2 and 1 feet respectively.
Hence chance that it falls entirely on one rectangular block is 2*1/4*3 = 2/12
= 1/6

Correct Option: 7 Best Solution (15)