Solution:
80 = 2 x 5 x 8 Since 653xy is divisible by 2 and 5 both, so y = 0. Now, 653x is divisible by 8,
so 13x should be divisible by 8. This happens when x = 6. x + y = (6 + 0) = 6.

8. If 60% of 3 / 5 of a number is 36, then the number is:

Solution:
By hit and trial, we find that 47619 x 7 = 333333.

10. In a division sum, the remainder is 0. As student mistook the divisor by 12 instead of 21 and obtained 35 as quotient. What is the correct quotient ?

Solution:
By hit and trial, we put x = 5 and y = 1 so that (3x + 7y) = (3 x 5 + 7 x 1) = 22, which is divisible by 11.
Therefore, (4x + 6y) = ( 4 x 5 + 6 x 1) = 26, which is not divisible by 11; (x + y + 4 ) = (5 + 1 + 4) = 10,
which is not divisible by 11; (9x + 4y) = (9 x 5 + 4 x 1) = 49, which is not divisible by 11; (4x - 9y) = (4 x 5 - 9 x 1) = 11, which is divisible by 11.

13. The largest 5 digit number exactly divisible by 91 is:

Solution:
The largest 5 digit number is 99999
On dividing 99999 by 91, we get
=> Quotient =1098
=> Remainder = 81
So, 99999 – 81 = 99918
Thus the largest 5-digit number exactly divisible by 91 = 99918

14. The smallest 6 digit number exactly divisible by 111 is:

Solution:
437 > 22
All prime numbers less than 22 are : 2, 3, 5, 7, 11, 13, 17, 19.
161 is divisible by 7, and 221 is divisible by 13.
373 is not divisible by any of the above prime numbers.
373 is prime number.

Solution:
Required sum = (2 + 4 + 6 + ... + 30)
This is an A.P. in which a = 2, d = (4 - 2) = 2 and l = 30. Let the number of terms be n.
Then, tn = 30 a + (n - 1)d = 30 2 + (n - 1) x 2 = 30 n - 1 = 14 n = 15 Therefore,
Sn = n/2 (a + 1 ) = 15 / 2 x (2 + 30 ) = 240