M4maths Previous Puzzles

18 Mar 2010 Bride And Groom

There are 5 eligible Gujarati grooms of which 2 know Bengali and 5 eligible Bengali grooms of which 3 know Gujarati. There are 5 eligible Gujarati and 5 eligible Bengali brides. An eligible bride is agreeable to marry a boy of his community or a boy who knows her language. Grooms have no choice. In how many different ways 10 couples can be formed.

OPtion

1) 16550
2) 14400
3) 12000
4) 144000
5) 256920
6) 435680
7) 37200
8) 16340
9) 120
10)12800

Solution

In 5 eligible Gujarati grooms, 2 know Bengali, remaining 3 should make their pair with Gujarati girls.
No. of methods to make such couple = 5.4.3 = 60
Similarly in 5 eligible Bengali grooms, 3 know Gujarati, remaining 2 should make their pair with Bengali girls.
No. of methods to make such couple = 5.4 = 20
No. of methods to make remaining 5 couple = 5.4.3.2.1 = 120
Hence total no. of methods = 60*20*120 = 144000

Correct Option: 4 Best Solution (0)

17 Mar 2010 Fruits with different tags

There are 5 mangoes and 6 bananas. In how many different ways can a selection of fruits be made if all fruits of same kind are numbered with different tags.

OPtion

1) 2048
2) 2047
3) 1024
4) 41
5) 30
6) 11
7) 510
8) 1
9) 1023
10)512

Solution

All the fruits are numbered with different tags, thus it can be considered that all fruits are different objects,
For each fruit, we have two choices- Either select the fruit or not
Hence total number of choices are 2*2*2…….11 times – 1 = 2047

Correct Option: 2 Best Solution (3)

16 Mar 2010 Balls in equilateral triangle?

Balls are arranged in rows to form an equilateral triangle. The first row consists of one ball,
the second of two balls, the third of 3 balls and so on. If 456 more balls are added then all
the balls can be arranged in the shape of a square and each of its sides then contains 8 balls
less than the balls in each side of the triangle. Determine the initial number of balls.

OPtion

1) 913
2) 1144
3) 1065
4) 988
5) 1225
6) 840
7) 769
8) 700
9) 633
10) 568

Solution

Let number of balls in a side of the triangle are n
Thus total number of balls are
x = 1 + 2 + 3 +........+(n-2) +(n-1) + n (1)

or x = n + (n-1) + (n-2) +.......+ 3 + 2 + 1 (2)

adding (1) and (2)

2x =(n+1) +(n+1) + (n+1)+.......+(n+1) +(n+1)+(n+1)

or 2x = n.(n+1)

or x =n(n+1)/2

According to given condition n(n+1)/2 + 456 = (n-8)2

On solving or checking the options we get n = 49

Thus x = 49*50/2 = 1225

Correct Option: 5 Best Solution (6)

15 Mar 2010 Rectangular Plot

A rectangular plot of size 18*8 m^2 has to be digged upto 8 m. depth. Cost of work increases continuously
from top to bottom. It starts from 10 rupee per cubic meter at top to 60 rupee per cubic meter at bottom.
Cost of complete work is ?

OPtion

1) 30720 rupee
2) 11520 rupee
3) 69120 rupee
4) 8640 rupee
5) 3840 rupee
6) 1440 rupee
7) 640 rupee
8) 40320 rupee
9) 34560 rupee
10) 5760 rupee

Solution

Total volume of digged earth = 18*8*8 = 1152 m3
Average cost of work = (10 + 60)/2 = 35 rupee per cubic meter
Total cost of work = 1152 * 35 = 40320 rupee

Correct Option: 8 Best Solution (13)

12 Mar 2010 Paper thickness

The thickness of a paper is 0.7 mm. Number of papers in a rim of thickness 26.6 cm. are

OPtion

1) 38
2) 2060
3) 22060
4) 206
5) 380
6) 3800
7) 308
8) 1862
9) 450
10) 500

Solution

26.6 cm. = 266 mm.

Hence number of pages = 266 / 0.7 = 380

Correct Option: 5 Best Solution (10)

11 Mar 2010 Shortest Track?

If all the 9 edges along length and breadth of a chess board are the tracks, then how many ways
are possible for a man to reach the diagonally opposite point starting from a corner in shortest track.

OPtion

(1) 12870
(2) 12012
(3) 10296
(4) 13728
(5) 32760
(6) 64
(7) 120
(8) 1024
(9) 256
(10) 143432

Solution

Total number of part tracks required for reaching the destination from a corner are 16 in which 8 are along length and 8 are along breadth
Number of methods for choosing the track are
(16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1)/(8*7*6*5*4*3*2*1)2
= 12870

Correct Option: 1 Best Solution (3)

10 Mar 2010 9 stics.

There are nine sticks of equal size. Maximum number of triangles formed by using these sticks in one attempt are

OPtion

1) 8
2) 6
3) 7
4) 5
5) 9
6) 10
7) 1
8) 2
9) 3
10) 4

Solution

There are 4 small and 1 big triangle.

Correct Option: 4 Best Solution (5)

09 Mar 2010 Number of deductions?

Number of successive deductions of 20 %, required to get an object of 100 rupee in 40 rupee 96 paise.

OPtion

1) 8
2) 5
3) 6
4) 7
5) 4
6) 9
7) 1
8) 2
9) 3
10) 10

Solution

Every 20 % deduction reduces the cost to 0.8 multiple of its initial cost.
Thus 100 * 0.8 * 0.8 * 0.8 * 0.8 = 40.96
1st 2nd 3rd 4th
4 deductions are required.

Correct Option: 5 Best Solution (14)

08 Mar 2010 Unit place?

The integer in units place of 9^999 is

OPtion

1) 9
2) 8
3) 7
4) 6
5) 5
6) 4
7) 3
8) 2
9) 1
10) 0

Solution

999 is an odd number

		9*9 = 81 => a pair of 9 has 1 in units place 

		Thus 9999 = 81*81*81*81*81*81*81……………..*9

		The integer at units place is 9

Correct Option: 1 Best Solution (13)

05 Mar 2010 Cube Volume

A ball of maximum radius is cut from a cube of rubber of sides 10 cm. What will be
the remaining volume of rubber?
(Volume of sphere is given by the formula V = 4.19r^3 )

OPtion

1) 573.75
2) 523.75
3) 476.25
4) 423.25
5) 378.25
6) 453.75
7) 435.75
8) 421.25
9) 456.25
10) 534.75

Solution

Volume of rubber ball = 4.19r3 = 4.19 * 53 = 523.75
Remaining volume of rubber = 1000 – 523.75 = 476.25

Correct Option: 3 Best Solution (8)