M4maths Previous Puzzles

29 Mar 2012 time and money

There are 4 friends, who invest 1, 1, 2 and 5 lacs respectively in a business and give 8, 6, 4 and 3 hours per day respectively for the company. If output depends 60% on the investment and 40 % on work hours according to formula
Profit = effective investment ratio (minimum integral ratio) + effective work hour ratio (minimum integral ratio), then their profit ratio will be

OPtion

1) 8:6:4:13
2) 8:5:9:12
3) 6:8:8:9
4) 9:7:6:8
5) 4:3:4:5
6) 4:8:5:7
7) 8:5:6:7
8) 8:8:8:15
9) 21:6:8:8
10) none of these

Solution

effective investment ratio = 0.6:0.6:1.2:3.0 = 6:6:12:30 = 1:1:2:5
effective time ratio = 3.2:2.4:1.6:1.2 = 32:24:16:12 = 8:6:4:3
so according to the given condition profit ratio = 9:7:6:8

Correct Option: 4 Best Solution (0)

28 Mar 2012 real and positive

x is a real number greater than 1 and y is a positive real number such that
x^3 = y^2+y+1
then y = ?

OPtion

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

Solution

x^3 = y^2+y+1
implies that x^3 - 3/4 = y^2 + y + 1/4
implies that (x^3 - 3/4)^1/2 = y + 1/2
or y = [(4x^3-3)^1/2 - 1] / 2

Correct Option: 1 Best Solution (11)

27 Mar 2012 total numbers

By using all the integers at a time of the number 9910099800, how many 10 digit numbers can be formed.

OPtion

1) 6300
2) 5032
3) 3780
4) 1580
5) 1420
6) 900
7) 780
8) 196
9) 94
10) none of these

Solution

6*9*8*7*6*5*4*3*2*1/4*3*2*1*4*3*2*1
here denominator is for the revision of 0 and 9 4-4 times
and 6 in the numerator is for the possibilities in the first place.

Correct Option: 3 Best Solution (6)

26 Mar 2012 1 addition 2 subtraction 3 multiplication 4 division

next number of the sequence
4, 2, 1/2, -5/8, -47/32 ...... will be

OPtion

1) -97/64
2) -99/64
3) -123/128
4) -149/128
5) -269/128
6) -327/128
7) -327/256
8) -149/256
9) -123/384
10) none of these

Solution

(4/4)*3-2+1 = 2
(2/4)*3-2+1 = 1/2
{(1/2)/4}*3-2+1 = -5/8
{(-5/8)/4}*3-2+1 = -47/32
{(-47/32)/4}*3-2+1 = -269/128

Correct Option: 5 Best Solution (8)

23 Mar 2012 integer

10.1 % of 9.6 % of x = an integer
then minimum possible positive integer value of x will be

OPtion

1) 28500
2) 31250
3) 25000
4) 250000
5) 12500
6) 17250
7) 23500
8) 125000
9) 98250
10) none of these

Solution

according to the given condition
10.1/100 * 9.6/100 * x = I (Integer)
on solving we get x = 250*125I/303
so minimum positive value of x = 250*125 = 31250

Correct Option: 2 Best Solution (11)

22 Mar 2012 power x square x

if x^(x^2) = 100000
then x will lie between

OPtion

1) 1 and 2
2) 2 and 3
3) 3 and 4
4) 4 and 5
5) 5 and 6
6) 8 and 9
7) 10 and 11
8) 16 and 17
9) 20 and 21
10) 100 and 101

Solution

check 3^9 and 4^16

Correct Option: 3 Best Solution (15)

21 Mar 2012 1 to 10000000

How many integer x between 1 to 10000000 will satisfy the equation given below
sqrt(x)+sqrt(sqrt(x))+sqrt(sqrt(sqrt(x)))+sqrt(sqrt(sqrt(sqrt(x))))=A
here A is an integral positive number

OPtion

1) 1
2) 2
3) 3
4) 128
5) 512
6) 4096
7) 12456
8) 65536
9) more that 100000
10) not possible to calculate

Solution

since last term contains 4 sqrt so 16 powers are necessary to get an integral value
so answers will be 1^16, 2^16, 3^16 ....
but 3^16 is greater than 10000000 hence it will be a non valid answer
so 2 values of x are possible

Correct Option: 2 Best Solution (0)

20 Mar 2012 solve

if 1^2+2^2+3^2+4^2+........... +1000^2 = A
and 1^2+2^2+3^2+4^2+...........+500^2 = B
then 1^2+3^2+5^2+..............+999^2 = ?

OPtion

1) A-B
2) A-2B
3) A+B
4) A+2B
5) A-3B
6) A+3B
7) 2A+3B
8) 2A-3B
9) A-4B
10) none of these

Solution

A = 1^2+2^2+3^2+4^2+.........+1000^2
A = [1^2+3^2+5^2+........+999^2] + [2^2+4^2+........+1000^2]
A = ? + 2^2 [ 1^2+2^2+3^2+4^2+...........+500^2]
A = ? + 4 B
so ? = A - 4B

Correct Option: 9 Best Solution (0)

19 Mar 2012 divide

what will be the reminder on dividing 37^52 by 17

OPtion

1) 5
2) 7
3) 11
4) 13
5) 15
6) 3
7) 9
8) 1
9) any even number

Solution

37 and 17 are co prime and factor of 17 is only 17
so 37^[17{1-(1/17)}] will give reminder as 1 on dividing by 17
now 37^52 = (37^16)^3 * (37)^4
now 37/17 provide 3 as reminder
and 3^4/17 provide reminder as 13
so answer will be 13

Correct Option: 4 Best Solution (4)

16 Mar 2012 word maths

if TEA - EAT = 3
then NAME - ENAM = ?

OPtion

1) -8
2) -9
3) 7
4) 8
5) 9
6) 5
7) 12
8) -11
9) 20
10) none of these

Solution

change these words by the position of words in the dictionary formed by the letters of the same word.
position of EAT = 3
TEA = 6, NAME = 20, ENAM = 11

Correct Option: 5 Best Solution (6)