M4maths Previous Puzzles

04 Jul 2013 Prolem

A person has a certain number of coins. If he distributes a certain sum to each of nine persons, he has five coins left. If he distributes the same sum of six persons he has twenty coins left. What amount did he give to each persons?

OPtion

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

Solution

Let x be the number of coins given to each person.
After giving x number of coins to each of the 9 persons, he has 5 coin left with him.
This means initially he has 9x+5 coins. (i)
When he distributes x coins each to 6 person he has left with 20 coins with him.
According to this he should have 6x+20 coin initially (ii)
From (i) and (ii), we get
9x+5=6x+20
3x=15
x=5
He gave 5 coins to each person
option 4

Correct Option: 4 Best Solution (0)

03 Jul 2013 Probability

What are the odds in favour of throwing atleast 7 in a single throw of two dice.

OPtion

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

Solution

Total number of possible outcomes = 36 (solve)
Let E be the event "Sum of the numbers on the two dice is atleast 7
therefore
E = (1,6)(2,5)(3,4)(4,3)(5,2)(6,1)(2,6)(3,5)(4,4)(5,3)(6,2)(3,6)(4,5)(5,4)(6,3)(4,6)(5,5)(6,4)(5,6)(6,5)(6,6)
n(E)=21, n (not E) = 36-21=15
P(E)=21/36 and P(not E) = 15/36
Odd is favour of the event E = P(E):p(not E)
(21/36):(15/36) = 7:5
7/5
option 3

Correct Option: 3 Best Solution (1)

02 Jul 2013 Solve

If +,-,*,$ represent multiplication, division, addition and subtraction then 2*3+5-3$2

OPtion

1) 1/2
2) 1
3) 3/2
4) 3
5) 5/2
6) 5
7) 7
8) 9
9) 19/2
10)None of these

Solution

solve
we get 5
option 6

Correct Option: 6 Best Solution (22)

01 Jul 2013 Sequence

What is the next number of the following sequence
5,11,19,29,41,.........

OPtion

1) 55
2) 71
3) 76
4) 87
5) 89
6) 90
7) 104
8) 111
9) 144
10) None of these

Solution

1+2^2=5
2+3^2=11
3+4^2=19
4+5^2=29
5+6^2=41
6+7^2=55
option 1

Correct Option: 1 Best Solution (19)

29 Jun 2013 ratio

If (6x^2-xy):(2xy-y^2)=6:1, find x:y

OPtion

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

Solution

Divide the Nr and Dn by y^2,
then let x/y=p
we get 6p^2-p=12p-6
6p^2-13p+6=0
solve
p=3/2 and p=2/3
option 8

Correct Option: 8 Best Solution (16)

28 Jun 2013 Circle

All the four vertices of a rhombus are on a circle of area 2826 cm^2. Find the area of rhombus (pi=3.14)

OPtion

1) 1000 cm^2
2) 1200 cm^2
3) 1400 cm^2
4) 1600 cm^2
5) 1800 cm^2
6) 2000 cm^2
7) 2200 cm^2
8) 2400 cm^2
9) 2600 cm^2
10) None of these

Solution

The rhombus here is a square. As the rhombus is cyclic, cum of opposite angles is 180 degree, which are equal. So, each angle is 90 degree and the rhombus is a square.
Area of circle = 2826 cm^2
pi*r^2=2826 (let the radius of circle be r)
r=30 cm
Each diagonal = 2r
Area of square = 1/2 (D)^2
solve
ans 1800 cm^2
option 5

Correct Option: 5 Best Solution (9)

27 Jun 2013 Problem

90%(A) and 97%(B) pure acid solutions are mixed to obtain 21.0 litre of 95% pure acid solution, find the amount of (B) to be mixed to form the mixture.

OPtion

1) 5 litre
2) 6 litre
3) 15 litre
4) 16 litre
5) 20 litre
6) 23 litre
7) 28 litre
8) 30 litre
9) 35 litre
10) None of these

Solution

Let 90% pure acid solution be A litre and 97% pure acid solution B
A+B = 21
90% of A + 97% of B = 95% of 21

=> 90A/100 + 97B/100 = 95*21/100
90A + 97B = 1995
By Solving A = 6, B=15
So 97% of pure acid is 15 Litre

Correct Option: 3 Best Solution (15)

26 Jun 2013 Probability

In a single throw of two dice, what is the probability of getting a total of less than 6.

OPtion

1) 1/12
2) 2/7
3) 11/36
4) 5/18
5) 1/6
6) 1/3
7) 1/8
8) 1/18
9) 5/19
10) None of these

Solution

A total of less than 6:
Total number of favourable outcomes = 10
P(less than 6) = 10/36 = 5/18

Correct Option: 4 Best Solution (31)

24 Jun 2013 Sequence

What is the next number of the following sequence
2,12,30,56,90,......

OPtion

1) 99
2) 100
3) 110
4) 120
5) 132
6) 144
7) 169
8) 108
9) 196
10) None of these

Solution

1*2=2
3*4=12
5*6=30
7*8=56
9*10=90
11*12=132
option 5

Correct Option: 5 Best Solution (0)

21 Jun 2013 Trigonometry

Find the value of the following trigonometry term
tan1.tan2.tan3.tan4............tan89 (Use 1,2,3,4..89 in degree term)

OPtion

1) Infinite
2) 1/sqrt3
3) 1/sqrt2
4) 1
5) 0
6) 1+sqrt2
7) 1+sqrt3
8) sqrt2+sqrt3
9) sqrt3
10) None of these

Solution

tan1.tan2.tan3.......tan89
(tan1.tan(90-1)).(tan2.tan(90-2))...............(tan44.tan(90-44).tan45
(tan1.cot1).(tan2.cot2).............(tan44.cot44).tan45
solve
1.1.1..........tan45
1
option 4

Correct Option: 4 Best Solution (0)