M4maths Previous Puzzles

18 Feb 2010 Letters and envelopes

There are 4 letters and 4 envelopes. Total no. of methods in which 2 letters can be posted correctly and 2 wrongly.

OPtion

1) 4
2) 7
3) 8
4) 9
5) 10
6) 15
7) 1
8) 6
9) 12
10) 24

Solution

Total no. of methods for selecting 2 letters out of 4 which has to be posted correctly = 4*3/2*1 = 6
No. of methods in which remaining 2 letters are posted wrongly is 1 only.
Hence total methods = 6*1 = 6

Correct Option: 8 Best Solution (5)

17 Feb 2010 Reciprocal numbers

The sum of reciprocal of two numbers is 0.45 and the sum of reciprocal of their squares is 0.1025,
then value of the numbers are

OPtion

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

Solution

Let the numbers are x and y
According to the given conditions
(1/x) + (1/y) = 0.45
And (1/x2) + (1/y2) = 0.1025
On solving these two equations , we get the two values 4 and 5

Correct Option: 2 Best Solution (7)

16 Feb 2010 King of Probability?

In a pack of playing cards, I have to draw any 6 cards. Probability of getting a set of 4 kings
and any of the 2 cards is?

OPtion

1) 2/52455
2) 6/54145
3) 1/57120
4) 5/57120
5) 1/53040
6) 5/53040
7) 3/54145
8) 5/54120
9) 9/58697
10) 3/51115

Solution

No. of methods for selecting 6 cards out of 52 are 52*51*50*49*48*47/6*5*4*3*2*1
Similarly no. of methods for selecting 2 cards out of 48 after selecting 4 kings are
48*47/2*1
Hence probability is (48*47/2*1)/( 52*51*50*49*48*47/6*5*4*3*2*1)
= 3/54145

Correct Option: 7 Best Solution (9)

15 Feb 2010 efficiency ratio?

6 boys and 8 men get a total wage of Rs 8000 in 4 days. 8 boys and 6 men get a total of Rs 6000 in 3 days.
The efficiency ratio of boy and a man respectively?

OPtion

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

Solution

By solve the equation:

6X+8Y = 2000
8X+6Y = 2000
X=Y
X:Y = 1:1

Correct Option: 3 Best Solution (12)

12 Feb 2010 smiler set

There are some sets of three numbers
(1) 3 4 24
(2) 4 5 40
(3) 5 6 60
(4) 6 7 84
A similar set of three numbers is

OPtion

(1) 7 8 112
(2) 7 8 113
(3) 7 8 111
(4) 7 8 100
(5) 7 8 99
(6) 7 8 95
(7) 7 8 110
(8) 7 8 102
(9) 7 8 104
(10) 7 8 90

Solution

Here the formula used is
a b 2ab

Correct Option: 1 Best Solution (8)

11 Feb 2010 Dish package Charge?

If 336 rupee is the charge of a dish package in the month of june then its charge for month of july is?

OPtion

(1) 342
(2) 337
(3) 348.30
(4) 347.20
(5) 330
(6) 338.50
(7) 343
(8) 342.60
(9) 350
(10) 345.20

Solution

June is a month of 30 days and july is that of 31 days
Hence charge is 336*31/30 = 347.20

Correct Option: 4 Best Solution (4)

10 Feb 2010 How much water in the Bucket?

The upper and lower part radius of a bucket is 30 cm. and 20 cm. Its height is 60 cm.
How much water can be filled in the bucket ?
It is given that: 1 litre = 1000 cm.^3

OPtion

(1) 100 litre
(2) 130 litre
(3) 120 litre
(4) 90 litre
(5) 105 litre
(6) 125 litre
(7) 150 litre
(8) 95 litre
(9) 200 litre
(10) 175 litre

Solution

On increasing the slant sides of the bucket, a cone can be obtained, whose height is obtained by the formula h/(h-60) = 30/20
On solving h = 180
Think that: two cones can be formed by increasing the slant height, their radii and heights are 30 cm.,
20 cm. and 180 cm., 120 cm.
Volume of the cone is πr^2/3
Therefore volume of the bucket is π(30)^2*180/3 – π(20)^2*120/3
= 38000π cm.^3
= 38π litre

Correct Option: 3 Best Solution (5)

09 Feb 2010 Coded Language

In a coded language IGR = RTI
and KVF = PEU
then HMO =

OPtion

(1) SNL
(2) RLK
(3) UOM
(4) TML
(5) YJG
(6) LHQ
(7) GNV
(8) DUJ
(9) JOK
(10) SLF

Solution

Every letter in this code is changed in a new letter having same position from last

Correct Option: 1 Best Solution (7)

08 Feb 2010 Profit?

A seller gets a profit of 20 % if he sells an object in 95 rupee. What will be his loss on selling it in 75
rupee.

OPtion

(1) 7.58 %
(2) 6.18 %
(3) 3.78 %
(4) 4.56 %
(5) 5.26 %
(6) 21.23 %
(7) 15.46 %
(8) 18.22 %
(9) 12.34 %
(10) 11.67 %

Solution

Original price of the object = 95/1.2
On selling the object in 75 rupee amount received = 75/(95/1.2)
= 94.74 %
Hence % loss = (100 – 94.74) % = 5.26 %

Correct Option: 5 Best Solution (3)

05 Feb 2010 Square and Cube

The difference of cube and square of a real number is equal to the difference of its square and itself.
Total number of such real numbers are

OPtion

(1) 2
(2) 0
(3) 1
(4) 3
(5) 4

Solution

Let the number is x, then according to given condition

x^3 - x^2 = x^2 - x

x^3 - 2x^2 + x = 0
x ( x^2 – 2x – 1) = 0
x (x – 1)2 = 0
either x =1 or x = 0, Hence 2 solutions are possible.

Correct Option: 1 Best Solution (4)