Mathematix for the Insane I Trivia Quiz

Answer: 6.66 Kg

From 20 kgs of fresh mango, we get 6 kg of pure solid (no water) i.e. 30 % of 20 kg. Since we know dry mango contains 10% water, just divide 6 kgs by 0.9 to get the answer.

Answer: 7

2^1 divided by 11 gives a remainder of 2
2^2 divided by 11 gives a remainder of 4;
Similarly:
2^3 gives a remainder of 8,
2^4 gives a remainder of 5
2^5 givesa remainder of 10
2^6 gives a remainder of 9
2^7 gives a remainder of 7
2^8 gives a remainder of 3
2^9 gives a remainder of 6
2^10 gives a remainder of 1
2^11 gives a remainder of 2
So the cycle of remainders repeats in cycles of 10.
In the question, 7 values are left after (removing all the cycles of 10); hence the remainder will be the same as 2^7 divided by 11 i.e. 7.

Answer: 4

Since a[(a-1)! + 1] is divisible by 2a, it means [(a-1)! + 1] is divisible by 2;
which is possible for only two values of a i.e. 1 & 2 {all other values of a, (a-1)! is an even number, and hence [(a-1)! + 1] will be an odd number (which in turn means that it is not divisible by 2)}
Now only 2 is the prime number, therefore a=2 and 2^2=4.

Answer: X

he first set of numbers will be from (X-2) to (X+4).
the second set of numbers will be from (X-4) to (X+2).
So there will be 9 consecutive numbers from (x-4) to (x+4) in the final set and the average or middle number of this set is X.

Answer: 1

From 1 to 9 : 9 digits will be written;
From 10 to 99 : 90*2 (180) digits will be written;
From 100 to 999 : 900*3 (2,700) digits will be written;
From 1,000 to 9999 : 9000*4 (36,000) digits will be written;
Now, 1111 digits are still needed.
Since 10,000 onwards, each number will contribute 5 digit, we will divide 1110 (nearest multiple of 5) by 5 to get 222.
Upto 10221, we have written 39,999 digits.
The 40,000 digit will be the first digit of the next number i.e. 1 (the number being 10222).

Answer: 16

Let K be a number.
The required number is in the form of :
K*LCM(7,8) + 4 {LCM: Lowest Common Multiple)
= 56k + 4
now, 56k + 4 has to be less than 999.
Which implies k has to be less than 18
Therefore maximum value of k = 17; but when k=1 , the number is a two digit number, therefore
k= 17-1 = 16.

Answer: 2

1617 divided by 7 is 231; so the numbers are 234,233,232,231,230,229 and 228. The prime numbers are 229 and 233.

Answer: 15

Let the people who play only two games be :
x (Soccer and basketball)
y(soccer and volleyball)
z(Volleyball and basketball)
Therefore, 100 = 50 + 45 + 50 -(x+15) -(y+15) -(z+15) + 15.
Solving, we get x+y+z=15.

Answer: 64

The number of players will be (n + 1) where n is the number of matches.

Answer: 6,399,936

The sum of the digits will be equal to
(n-1)!*(sum of all the digits)*(11...11)n times (where n is the number of digits).
here n=5
therefore, sum= 4!*(2+3+5+6+8)*(11111) = 6,399,936