M4maths Previous Puzzles

20 Jun 2013 Problem

A man sells a table for Rs.96 and gains as much % as the cost of the table. Find the cost price of the table.

OPtion

1) 120
2) 100
3) 80
4) 86
5) 70
6) 72
7) 60
8) 56
9) 48
10)None of these

Solution

Let x be the cost price of the table
so x% is the gain
x+(x*x/100)=96
solve
As x can not be negative, x=120/2 = 60
Cost price Rs.60
option 7

Correct Option: 7 Best Solution (0)

19 Jun 2013 Triangle

The hypotenuse of a right triangle is 1m less than twice the shortest side. If the third side is 1m more than shortest side, find the sides of the triangle.

OPtion

1) 4m,5m,sqrt41m
2) 3m,4m,5m
3) 6m,7m,sqrt85m
4) 15m,20m,25m
5) 5m,8m,sqrt89m
6) 8m,12m,4*sqrt13
7) 5m,6m,8m
8) 11m,15m,17m
9) 15m,20m,24m
10)None of these

Solution

Let shortest side AB=x m, then hypotenuse=(2x-1)m and third side=(x+1)m.
In the given right triangle : (2x-1)^2=(x+1)^2+x^2
solve
x=0,x=3
The sides of the triangle are 3m,4m,5m... option 2

Correct Option: 2 Best Solution (0)

18 Jun 2013 Quadratic Equation

If one root of a quadratic equation 3x^2+px+4=0 is 2/3. Find the other root of the equation.

OPtion

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

Solution

One root is 2/3
3(2/3)^2+p(2/3)+4=0
solve, p=-8
Equation is
3x^2-8x+4=0
solve
x=2/3,x=2
other root x=2
option 7

Correct Option: 7 Best Solution (0)

17 Jun 2013 Sequence ) Sequence

What is the next no of the following sequence
0,4,18,48,100,....

OPtion

1) 144
2) 180
3) 216
4) 225
5) 289
6) 318
7) 325
8) 400
9) 625
10) None of these

Solution

1^3-1^2 = 1-1 = 0
2^3-2^2 = 8-4 = 4
3^3-3^2 = 27-9 = 18
4^3-4^2 = 64-16 = 48
5^3-5^2 = 125-25 = 100

6^3-6^2 = 216-36 = 180
option 2

Correct Option: 2 Best Solution (0)

14 Jun 2013 Solve

Solve
x^(2/3)-2*x^(1/3)=15

OPtion

1) x=1,x=8
2) x=4,x=-64
3) x=3,x=-27
4) x=5,x=125
5) x=27,x=-64
6) x=125,x=64
7) x=125,x=-27
8) x=9,x=125
9) x=7,x=144
10) None of these

Solution

Put x^(1/3)=t to get t^2-2t=15
solve
t=5,t=-3
therefore x^(1/3)=5, x^(1/3)=-3
Taking cube on both sides, we get
x=125,x=-27
option 7

Correct Option: 7 Best Solution (22)

13 Jun 2013 Problem

A and B each has some money. If a gives Rs.30 to B then B will have twice the money left with A. But if B gives Rs.10 to A, then A will have thrice as much as is left with B. How much money does each have?

OPtion

1) A:Rs50, B:Rs20
2) A:Rs52, B:Rs24
3) A:Rs62, B:Rs34
4) A:Rs68, B:Rs28
5) A:Rs72, B:Rs36
6) A:Rs78, B:Rs42
7) A:Rs80, B:Rs46
8) A:Rs84, B:Rs44
9) A:Rs92, B:Rs54
10) None of these

Solution

Let A has Rs.x and B has Rs.y
After giving Rs.30 to B
A has left with Rs. x-30 and B will have Rs.y+30
By the given condition
y+30=2(x-30) (i)
After giving Rs.10 to A, B is left with Rs.y-10 and A will have x+10
x+10=3(y-10) (ii)
solve (i) and (ii) eq.
A has Rs.62 and B has Rs.34

Correct Option: 3 Best Solution (27)

12 Jun 2013 AP

Find the common difference of an A.P. whose first term is 1 and the sum of first four terms is one-third of the sum of the next four terms.

OPtion

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

Solution

By given condition a=1 and S4=1/3(S8-S4)
solve (Using Sn=n/2(2a+(n-1)d))
d=2
option 8

Correct Option: 8 Best Solution (16)

11 Jun 2013 Problem

Ramesh repays a loan of Rs.6500 by paying Rs.40 in first month and then increasing the payment by Rs.30 every month. In how many months will he be able to clear the loan?

OPtion

1) 20
2) 30
3) 40
4) 50
5) 55
6) 60
7) 65
8) 70
9) 75
10) None of these

Solution

Using AP
Sn=n/2(2a+(n-1)d)
given a=40, d=30, S=6500
6500=n/2(2*40+(n-1)30)
solve
n=20 month
option 1

Correct Option: 1 Best Solution (22)

10 Jun 2013 Sequence

What is the next number of the following sequence
13,35,57,79,911,......

OPtion

1) 913
2) 1315
3) 1113
4) 988
5) 1112
6) 1215
7) 1311
8) 1114
9) 1499
10) None of these

Solution

1 3 13
3 5 35
5 7 57
7 9 79
9 11 911
11 13 1113 option 3 1113
13 15 1315

Correct Option: 3 Best Solution (26)

07 Jun 2013 Equation

Solve for the following equation
5^(2x)-5^(x+3)+125=5^x

OPtion

1) x=1, x=2
2) x=2, x=0
3) x=3, x=1
4) x=3, x=2
5) x=3, x=4
6) x=5, x=1
7) x=3, x=0
8) x=1, x=0
9) x=4, x=5
10) None of these

Solution

Let 5^x=k
k^2-k.5^3+125=k
k^2-126k+125=0
solve
k=125 or k=1
5^x=125 or 5^x=1
5^x=5^3 or 5^x=5^0
x=3, x=0
option 7

Correct Option: 7 Best Solution (11)