M4maths Previous Puzzles

30 Aug 2012 integers

By using integers 8, 6, 4, 3, 2 and 0 (an integer only once), how many numbers of 6 digits can be made?

OPtion

1) 360
2) 720
3) 180
4) 400
5) 600
6) 900
7) 90
8) 120
9) 200
10) none of these

Solution

choice for first place integer = 5
for next place = 5 and so on
total numbers = 5*5*4*3*2*1 = 600

Correct Option: 5 Best Solution (0)

29 Aug 2012 area

The area of a rectangle is equal to the area of a circle of radius [1/sqrt(pi)]m. If length of the rectangle is twice the width. Then sum of length and width will be

OPtion

1) 3/2
2) 2/5
3) sqrt(2)
4) sqrt(2) + sqrt(3)
5) sqrt(3)
6) sqrt(3)/2
7) 3/sqrt(2)
8) 3
9) 2
10) none of these

Solution

according to the given condition
l*w = pi(r)^2 r is radius and is given as 1/sqrt(pi)
so l*w = 1
so l*l/2 = 1
or l = sqrt(2)
so w = 1/sqrt(2)
so sum = [sqrt(2)] + 1/[sqrt(2)]
= 3/sqrt(2)

Correct Option: 7 Best Solution (0)

28 Aug 2012 work

A and B complete a work in 10 days, B and C complete the same in 15 days, C and A in 20 days. How many days are required to do the same work if A, B, C work together.

OPtion

1) 90/13
2) 80/13
3) 45/13
4) 30/13
5) 60/13
6) 120/13
7) 20/13
8) 150/13
9) 200/13
10) none of these

Solution

one day work of all the 3 pairs are 1/10, 1/15, 1/20 respectively
so one day work of A, B, C will be 1/2[(1/10)+(1/15)+(1/20)] = 13/120
so days required = 120/13

Correct Option: 6 Best Solution (0)

27 Aug 2012 sequence

k,4,n,40,121,364 is a sequence.Then k+n will be

OPtion

1) 20
2) 19
3) 18
4) 15
5) 14
6) 12
7) 11
8) 10
9) 9
10) none of these

Solution

k,4,n,40,121,364
364-121 = 243 = 3^5
121-40 = 81 = 3^4
so
40-n will be 27 = 3^3
so n = 13
and 13-4 = 9 = 3^2
so 4-k will be 3 = 3^1
so k = 1
so k+n = 14

Correct Option: 5 Best Solution (0)

24 Aug 2012 lines

There are 10 points in a plane out of which 4 are collinear. How many lines can be drawn.

OPtion

1) 40
2) 42
3) 45
4) 55
5) 60
6) 64
7) 68
8) 30
9) 24
10) none of these

Solution

Total no of lines (10 points) = 10*9/2 = 45
Total no of lines (4 points) = 4*3/2 = 6
so answer = 45-6+1 = 40

Correct Option: 1 Best Solution (0)

23 Aug 2012 percentage

4%of64 + x%of96 = 12%of140
then x will be

OPtion

1) 46/7
2) 45/8
3) 67/5
4) 76/5
5) 85/4
6) 89/6
7) 92/3
8) 99/5
9) 100/7
10) none of these

Solution

4*64/100 + x*96/100 = 12*140/100
on solving x = 89/6

Correct Option: 6 Best Solution (18)

22 Aug 2012 work time problem

Arun and Tarun can do a work in 10 days. After 4 days Tarun went to his village. How many days are required to complete the remaining work by Arun alone. Arun can do the work alone in 30 days.

OPtion

1) 6
2) 8
3) 10
4) 12
5) 15
6) 18
7) 20
8) 21
9) 24
10) none of these

Solution

After 4 days Tarun went to his village.
then remaining work = 6/10 part
one day work of Arun = 1/30 part
so days required = 6/10/1/30 = 180/10 = 18 days

Correct Option: 6 Best Solution (0)

21 Aug 2012 lcm

lcm of x^3+1, x^2-1, x^3-1 will be

OPtion

1) (x^2+x+1)(x^2-x+1)
2) (x^4-1)
3) (x^6-1)(x^2+1)
4) (x^6+1)(x^2-1)
5) (x^6-1)
6) (x^6+1)
7) (x^3+x^2+x+1)
8) (x-1)(x^2+1)(x+1)(x^2-1)
9) (x^4+1)
10) none of these

Solution

x^3+1 = (x+1)(x^2-x+1)
x^2-1 = (x+1)(x-1)
x^3-1 = (x-1)(x^2+x+1)
so lcm = (x+1)(x-1)(x^2+x+1)(x^2-x+1) = (x^3-1)(x^3+1) = (x^6-1)

Correct Option: 5 Best Solution (0)

20 Aug 2012 find the next number

7, 15, 25, 39, 61, ?

OPtion

1) 77
2) 79
3) 81
4) 83
5) 87
6) 91
7) 93
8) 99
9) 107
10) none of these

Solution

4, 8 , 12, 16, 20, 24
1, 3, 5, 7, 9, 11
2, 4, 8, 16, 32, 64

Correct Option: 8 Best Solution (23)

17 Aug 2012 series of 2

solve
[2+1][2^2+1][2^4+1][2^8+1][2^16+1]...........[2^256+1]

OPtion

1) 19865432443242
2) 2^256+2^128+1
3) 2^512-1
4) 2^512+2^128+1
5) 2^512-2^256+2^128-1
6) 2^512+1
7) 2^511
8) 2^511-1
9) 2^511+1
10) none of these

Solution

[2+1][2^2+1][2^4+1][2^8+1][2^16+1]...........[2^256+1]
on multiplying [2-1] in the numerator and denominator, we get
[2-1][2+1][2^2+1][2^4+1][2^8+1][2^16+1]...........[2^256+1]/[2-1]
now we know that (a+b)(a-b) = a^2-b^2 so next line will be
[2^2-1][2^2+1][2^4+1][2^8+1][2^16+1]...........[2^256+1]/1
=[2^4-1][2^4+1][2^8+1][2^16+1]...........[2^256+1]
=[2^8-1][2^8+1][2^16+1]...........[2^256+1]
=[2^16-1][2^16+1]...........[2^256+1]
=[2^32-1][2^32+1]...........[2^256+1]
solve this, final result will be 2^512-1

Correct Option: 3 Best Solution (5)