# Numbers Aptitude Test Paper 7

31) Find the largest 4 digit number that is exactly divisible by 66.

1. 9987
2. 9912
3. 9916
4. 9966

Explanation:
Largest 4-digit number = 9999 So, the number is: 9999 - 33 = 9966.

32) Find the value of the expression:

1+1/ (1+1/ (1+1/ (1+1 /x)))

1. (7x+3)/(5x+2)
2. (3x+3)/(7x+2)
3. (5x+3)/(3x+2)
4. (11x+3)/(9x+2)

Explanation:
Solve (1+1/x) = (x+1)/x, then
1+1/ ((x+1)/x) = (2x+1)/ (x+1), then
1+1/ ((2x+1)/(x+1)) = (3x+2)/ (2x+1), then
1+1/ ((3x+2)/ (2x+1)) = (5x+3)/ (3x+2)
Hence, we get (5x+3)/ (3x+2)

33) Find the number which is completely divisible by 45.

1. 306990
2. 331145
3. 256987
4. 181660

Explanation:
A number, which is divisible by 3, 5, and 9, is also divisible by 45.

A number is divisible by 3 if the sum of its entire digits is divisible by 3.
A number is divisible by 9 if the sum of its entire digits is divisible by 9.
The number which ends with 0 or 5 is divisible by 5.

The number 306990 fulfils all the requirements, so the answer is 306990.   