M4maths Previous Puzzles

17 Jun 2009 Milk and water

A jar of 10 litres contains 4 litres milk and another of 6 litres is filled completely with water.
6 litre mixtures are removed to second jar after pouring all the water of second jar in first. After
then the process is revised with 4 other jars of 6 litres filled with water completely. What will be
the amount of milk remained in 10 litre jar finally.

OPtion

1) 0.52675
2) 0.01024
3) 0.12500
4) 0.04096
5) 4.00000
6) 0.40000
7) 0.66667
8) 1.50000
9) 0.06400
10) 0.80000

Solution

In every mixing process 4 part of milk is present in 10 part of mixture. Hence for this
process of 5 steps remaining milk in 10 litres jar is
4×(4/10)×(4/10)×(4/10)×(4/10)×(4/10)
=0.04096

Correct Option: 4 Best Solution (1)

15 Jun 2009 letters and envelopes

Number of methods to post 4 letters in 4 envelopes such that only 1 letter goes to the
correct envelope is:-

OPtion

1) 3,
2) 4,
3) 5,
4) 6,
5) 7,
6) 8,
7) 9,
8) 10,
9) 11,
10) 12,

Solution

a b c d
A C D B
A D B C
Similarly with B, C, D

Correct Option: 6 Best Solution (1)

12 Jun 2009 Decode the word

The list given below contains some words and their ordered codes

Word Code
MAN AHB
YOU GHGE
SAID FHD
(All the codes are formed by using letters A, B, C, D, E, F, G, H, I)
Write a code for the word "SUM"?

OPtion

1) FGH
2) GHAJ
3) HAG
4) EAHG
5) BEDG
6) FKA
7) EFAB
8) EBH
9) BCKF
10)FAH

Solution

SUM =19×21×13 =5187 (According to positions of letters)
Now 5187= EAHG (According to positions of letters)

Correct Option: 4 Best Solution (0)

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)