M4maths Previous Puzzles

11 Jun 2009 Find the equation.

If x=1^2-2^2+3^2-4^2+5^2-6^2+.........+99^2-100^2
y=1^2+2^2+3^2+4^2+5^2+.........+49^2+50^2

Then 1^2+3^2+5^2+7^2+9^2+.........+99^2 is equal to?
^ is for square

OPtion

1) x+y
2) x-y
3) x-4y
4) x+2y
5) x+3y
6) 2x-y
7) 2x-3y
8) x+4y
9) 4x-y
10) 4x+y

Solution

1^2-2^2+3^2-4^2+5^2-6^2+……………+99^2-100^2
x= (1^2+3^2+5^2+7^2+…….99^2)-(2^2+4^2+6^2+8^2+……100^2)
x= (1^2+3^2+5^2+7^2+…….99^2)-4(1^2+2^2+3^2+4^2+…………......+49^2+50^2)

Correct Option: 8 Best Solution (0)

10 Jun 2009 2 digit divisors

The sum of all 2 digit divisors of the number obtained by the difference of a 3 digit number
of successive digits in decreasing order and a 3 digit number having same digits in reciprocal
order. Only 1, 2, 3, 4, 5, 6, 7, 8, 9 can be used as digits

OPtion

1) 250
2) 249
3) 448
4) 29
5) 19
6) 16
7) 31
8) 198
9) 150
10) 456

Solution

321-123=198

2 digit divisors of 198 are 11, 18, 22, 33, 66, 99.

Correct Option: 2 Best Solution (1)

09 Jun 2009 Next number will be

What will be the next number of this series:-
1, 4, 11, 24, 47, 88, 163 ...

OPtion

1) 263,
2) 279,
3) 301,
4) 208,
5) 199,
6) 258,
7) 304,
8) 274,
9) 317,
10) 327,

Solution

Differences of elements are the sum of two series
02, 04, 08, 16, 32, 64
01, 03, 05, 07, 09, 11

03, 07, 13, 23, 41, 75 Sum of these two series

Correct Option: 7 Best Solution (1)

08 Jun 2009 sum of the number

Sum of all 120 numbers formed by using 1, 2, 3, 3, 3, and 4 is?

OPtion

1) 35555516
2) 34555606
3) 45555516
4) 35555520
5) 45555520
6) 45555506
7) 34562816
8) 48355520
9) 48355516
10) 35455520

Solution

Unit place =20(1+2+3+3+3+4)
Tens place=20(1+2+3+3+3+4) +32 ;( 32 is carry from units place)
Hundreds place=20(1+2+3+3+3+4) +35(carry from previous)
Similarly others

Correct Option: 4 Best Solution (1)

05 Jun 2009 Birds and tree...

Some birds sit on a tree. Square root of total birds moves away from there. Twice of the
remaining birds are equal to the square of sum of birds flown away & square root of birds
flown away. How many birds was on tree.

OPtion

1) 64
2) 16
3) 81
4) 56
5) 49
6) 99
7) 100
8) 121
9) 144
10) 256

Solution

2(x-√x) = (√x+√√x)²

Correct Option: 3 Best Solution (0)

04 Jun 2009 rubbber and pencil

Total cost of 2 rubbers and 3 pencils is greater than 20 rupee whereas total cost of
3 rubbers and 2 pencils is less than 24 rupee. If cost of pencil is less then 7 rupee then
for what prize of rubber and pencil total cost of 4 rubbers and 5 pencils is minimum

OPtion

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

Solution

2x+3y > 20
3x+2y < 24
y < 7
We have to find a condition such that 4x+5y is minimum

Correct Option: 8 Best Solution (0)

03 Jun 2009 water bag prize...

A bookseller says to a customer "The prize of water bag is greater than 400 rupees and I
shall give you a scheme of 50%+50%+50%+50% off after giving you a discount of 100 rupees."
If after then the cost of water bag is square root of its original value, then prize of
water bag is…… (Leaving paisa if any).

OPtion

1) 400
2) 441
3) 424
4) 484
5) 510
6) 432
7) 525
8) 529
9) 584
10) 520

Solution

First method:
(x-100)(1/2)(1/2)(1/2)(1/2) = √x (eq.1)

On solving we get the solution
apply shridharacharya rule (-b +_√(b^2-4ac))/2a

Second method:
eq.1 can be written as (x-100)/16=√x

Find that value of x for which L.H.S. & R.H.S. are nearest

For 432 (true solution)

L.H.S. =20.75

R.H.S. =20.785

Difference =0.035

For other options difference is greater than this difference

Correct Option: 6 Best Solution (0)

02 Jun 2009 Next will be...

What will be the next number of this series:-
162; 2123; 3204; 4305; 5426; 6567; 7728; .......

OPtion

1) 8829
2) 8739
3) 8919
4) 8839
5) 8909
6) 8729
7) 8929
8) 8849
9) 8719
10) 8009

Solution

First and last digits are successive and middle is given by [y.x+(y+x) +(y-x)]

Correct Option: 5 Best Solution (0)

01 Jun 2009 Chess Game Puzzle...

In a chess game a man plays 16 moves, one move to every piece in the following manner:-
• King can move 1 step in any direction
• Queen can move in any direction
• Rook can move straight in any direction
• Bishop can move in slant squares
• Knight can move 2 forward then 1 turned step
• Every pawn can move 1 or 2 step forward
What is the probability that after that move all the piece are arranged in third
and fourth row if initially they are arranged in first and second row as the rule of game.

OPtion

1) 0
2) 1/2
3) 1/3
4) 1/4
5) 4/5
6) 5/6
7) 2/3
8) 3/4
9) 2/5
10) 3/5

Solution

Since King can move only one place in any direction hence it is impossible to take it in
third or fourth row.

Correct Option: 1 Best Solution (0)

01 Apr 2008 Simplification

There are two buildings P and Q. If 143 persons are sent from P to Q, then the number of persons in each building is the same. If 186 persons are sent from Q to P, then the number of persons in P is double the number of persons in Q. How many persons are there in building P?

OPtion

1) 1010
2) 822
3) 866
4) 1130
5) 1103
6) 875
7) 1113
8) 844
9) 1210
10) None of these

Solution

Let number of persons in building P be P and
number of persons in building Q be Q

P-143 = Q+143
=> P = Q + 286 ---- (i)

P+186= 2(Q-186)
=> P + 558 = 2Q ---- (ii)

Putting value of P from (i) in (ii)
Q + 286 + 558 = 2Q
Q = 844
P = 1130

Correct Option: 4 Best Solution (0)