M4maths Previous Puzzles

09 May 2013 Root

If x^2+qx+1=0 & x^3+px^2+qx+1=0 have a common factor (x+a), a is not equal to 0, value of (p-1)^2-q(p-1)

OPtion

1) -1
2) -2
3) -3
4) -p
5) -q
6) -4
7) -5
8) -6
9) -7
10) None

Solution

According to the given condition
(x+a)is factor then put x=-a in both equation
Ist eq a^2-qa+1=0
IInd eq -a^3+pa^2-qa+1=0
Subtract we get a=(p-1)
put in Ist eq
(p-1)^2-q(p-1)+1=0
then (p-1)^2-q(p-1)=-1
ans -1
option 1

Correct Option: 1 Best Solution (5)

08 May 2013 Solve

In mixture of 45 litres, the ratio of milk and water is 4:1. How much water must be added to make the ratio 3:2?

OPtion

1) 36 litre
2) 24 litre
3) 18 litre
4) 16 litre
5) 15 litre
6) 12 litre
7) 9 litre
8) 6 litre
9) 3 litre
10)None of these

Solution

find quantity of milk and water in a mixture (using ratio 4:1 and quantity 45 litre)
that is 36 litre and 9 litre respectively
let the quantity of water to be added be x litre, then the according to given condition
36/(9+x)=3/2
solve
ans is 15 litre
option 5

Correct Option: 5 Best Solution (0)

07 May 2013 Triangle

Area of an equilateral triangle is 25*sqrt3 cm^2. Perimeter is

OPtion

1) 10 cm
2) 20 cm
3) 30 cm
4) 40 cm
5) 10*sqrt3 cm
6) 20*sqrt3 cm
7) 30*sqrt3 cm
8) 40*sqrt3 cm
9) 50 cm
10) None of these

Solution

(sqrt3/4)*a^2=25*sqrt3 (let a be the side of an equilateral triangle)
a^2=100
a=10
perimeter 30cm
option 3

Correct Option: 3 Best Solution (17)

06 May 2013 series

What is the next no of the following sequence
3/2, 5/6, 7/12, 9/20, ..........

OPtion

1) 12/29
2) 8/13
3) 5/23
4) 11/30
5) 7/11
6) 9/17
7) 10/11
8) 13/30
9) 15/43
10) None of these

Solution

1+2/1*2 = 3/2
2+3/2*3 = 5/6
3+4/3*4 = 7/12
4+5/4*5 = 9/20
next is
5+6/5*6 = 11/30
option 4

Correct Option: 4 Best Solution (0)

03 May 2013 Solve

If (x-2)(x-4)(x-6)(x-10)=(x-1)(x-5)(x-7)(x-9) then x is

OPtion

1) 6/5
2) 7/2
3) 11/2
4) 6
5) 21/2
6) 7
7) 9
8) 11
9) 13
10) None of these

Solution

(x-2)(x-4)(x-6)(x-10)=(x-1)(x-5)(x-7)(x-9)
(x^2-6x+8)(x^2-16x+60)=(x^2-6x+5)(x^2-16x+63)
(x^2-6x+8)/(x^2-6x+5)=(x^2-16x+63)/(x^2-16x+60)
By using componendo and divinendo we get
x=11/2
ans option 3

Correct Option: 3 Best Solution (8)

02 May 2013 Quadratic Equation

If a,b are the roots of x^2+px+q=0 then x^2+(a+b-ab)x-ab(a+b)=0 has roots

OPtion

1) -p,-q
2) p,-q
3) a,b
4) -a,-b
5) a,-b
6) p,q
7) -p,q
8) -a,b
9) ap,bq
10)None of these

Solution

a+b=-p
ab=q
put in second equation
x=p,q root
ans option 6

Correct Option: 6 Best Solution (0)

01 May 2013 AP

The sum of all numbers from 1 to 1000, which are neither divisible by 2 nor by 5 is

OPtion

1) 149500
2) 175000
3) 190000
4) 200000
5) 225000
6) 250000
7) 250500
8) 275000
9) 300000
10)None of these

Solution

(1+3+5+7....999)-(5+10+15....995)
solve
ans is 200000
option 4

Correct Option: 4 Best Solution (0)

30 Apr 2013 Ratio

The average score of boys in an examination of a school boy is 71 and that of girls is 73. The average score of the school in that examination is 71.8. Ratio of the number of boys to the number of girls appeared in examination is...

OPtion

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

Solution

let number of boys be x and number of girls be y
according to the given condition
(71x+73y)/(x+y)=71.8
71x+73y=71.8x+71.8y
x/y=3/2
option 2

Correct Option: 2 Best Solution (0)

29 Apr 2013 sequence

What is the next number of the following sequence
12, 60, 140, 252,.....

OPtion

1) 352
2) 376
3) 382
4) 396
5) 400
6) 422
7) 456
8) 476
9) 496
10)None of these

Solution

(1+3)^2-4=12
(3+5)^2-4=60
(5+7)^2-4=140
(7+9)^2-4=252
(9+11)^2-4=396

Correct Option: 4 Best Solution (0)

27 Apr 2013 Probability

A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is double that of a red ball, Number of blue ball is..

OPtion

1) 22
2) 18
3) 15
4) 13
5) 12
6) 10
7) 8
8) 7
9) 6
10) None of these

Solution

let number of blue ball = x
Given
Probability(Blue ball)= 2*Probability(Red ball)
(x/(5+x))=2(5/(x+5))
solve x=10
option 6

Correct Option: 6 Best Solution (9)