M4maths Previous Puzzles

01 Mar 2012 chess board

If size of every box of chess board is 1*1, then what will be the probability to get a square of size 4*4, if we have to choose a square of any size in the chess board of size 8*8.

OPtion

1) 25/204
2) 25/194
3) 4/51
4) 8/97
5) 3/68
6) 9/194
7) 3/8
8) 2/5
9) 16/125
10) none of these

Solution

total squares of size 4*4 = 5*5 = 25
total squares = 1*1 + 2*2 + 3*3 + 4*4 + 5*5 + 6*6 + 7*7 + 8*8 = 204
so probability = 25/204

Correct Option: 1 Best Solution (9)

29 Feb 2012 x + 1/x

if x + 1/x = 4
then 6[x^2 + 1/x^2] + 9[x^3 + 1/x^3] will be

OPtion

1) 448
2) 502
3) 552
4) 602
5) 608
6) 660
7) 668
8) 694
9) 682
10) none of these

Solution

x^2 + 1/x^2 = [x + 1/x]^2 - 2
x^3 + 1/x^3 = [x + 1/x]^3 - 3[x + 1/x]
on applying values we can obtain the correct answer 552

Correct Option: 3 Best Solution (4)

28 Feb 2012 fruits

The rate of four fruits are given
Orange 60 rupee per Kg
Apple 100 rupee per Kg
Grapes 80 rupee per Kg
Pomegranate 140 rupee per Kg
Maximum amount of fruits (in integral Kg) in the exact investment of 1000 rupee will be
(Given that it is compulsory to purchase minimum 1 Kg fruits of all the types.)

OPtion

1) 8
2) 9
3) 10
4) 11
5) 12
6) 13
7) 14
8) 15
9) 16
10) none of these

Solution

10 kg orange, 2 Kg grapes, 1 Kg apple, 1 Kg pomegranate

Correct Option: 7 Best Solution (25)

27 Feb 2012 sequence

6, 3, 9, 4.5, 13.5, .........
next number of the sequence will be

OPtion

1) 5
2) 6
3) 7
4) 8
5) 9
6) 10
7) 4.75
8) 5.5
9) 12.5
10) none of these

Solution

the sequence follows /2, *3 rule
so next number will be 6.75

Correct Option: 10 Best Solution (11)

24 Feb 2012 monday

Maximum number of days between a monday and tuesday respectively in a year duration. Terminal monday and tuesday are not countable.It is given that the year starts from monday and is not a leap year.

OPtion

1) 363
2) 361
3) 360
4) 365
5) 357
6) 5
7) 28
8) 56
9) 7
10) none of these

Solution

the first and last day of the year will be monday so upto last tuesday total days = 365-6-2 = 357

Correct Option: 5 Best Solution (7)

23 Feb 2012 team

There are 4 teams. In how many ways 2 semifinals and 1 final can be played.( You should make all the possible cases)

OPtion

1) 3
2) 6
3) 18
4) 12
5) 21
6) 27
7) 30
8) 15
9) 8
10) none of these

Solution

ab/cd (semifinal), ac, ad, bc, bd (final)
similarly others

Correct Option: 4 Best Solution (5)

22 Feb 2012 share

A share is purchased at a rate of 23.60 and sold at a rate of 36.40. If brokerage at the time of buy and sell is 50 paisa per 100 rupee, then net profit will be. (excluding any other government charges)

OPtion

1) 12.80
2) 12.30
3) 12.40
4) 12.90
5) 12.50
6) 11.90
7) 11.50
8) 11.80
9) 12.60
10) none of these

Solution

total buy-sell = 23.60 + 36.40 = 60
brokerage = 60*50/100 = 30 paisa
profit = 36.40 - 23.60 = 12.80
so net profit = 12.80 - 0.30 = 12.50

Correct Option: 5 Best Solution (8)

21 Feb 2012 sum

Sum of all the 5 digit numbers formed by the integers 2,3,4,5,8 is
(Repetition is not allowed)

OPtion

1) 5686608
2) 5866608
3) 5688806
4) 5686808
5) 5666808
6) 5886606
7) 5808088
8) 5866068
9) Not possible to sum
10) None of these

Solution

There will be total 120 numbers.
Total sum in units place = 24(2+3+4+5+8) = 528
same will be the sum in all the places so
grand sum = 5280000+528000+52800+5280+528 = 5866608

Correct Option: 2 Best Solution (0)

20 Feb 2012 function

f(x) = 6x^2-7x+9 where x belongs to R

OPtion

1) Least value of f(x) will be 7/12
2) Least value of f(x) will be 6
3) Least value of f(x) will be -7
4) Least value of f(x) will be 9
5) This function f(x) has a least value
6) Greatest value of f(x) will be 7/12
7) This function f(x) has a greatest value
8) Zero is the least value of the function
9) The least value of the function is negative
10) None of these

Solution

Since coefficient of x^2 is positive so the function will have a least value

Correct Option: 5 Best Solution (4)

17 Feb 2012 group

In a group of 5 boys and 5 girls, how many teams of 8 persons can be selected by choosing at least 4 boys and 3 girls at a time.

OPtion

1) 35
2) 10
3) 25
4) 56
5) 64
6) 50
7) 102
8) 120
9) 180
10) none of these

Solution

methods of selecting 4 boys and 4 girls = 5*5 = 25
methods of selecting 5 boys and 3 girls = 1*(5*4/2) = 10
total methods = 25+10 = 35

Correct Option: 1 Best Solution (10)