Let pp, qq and rr be 2-digit numbers where     p < q < r. If  pp + qq + rr = tt0, where tt0 is a 3-digit number ending with zero, consider the following statements:                     

1. The number of possible values of p is 5.

2. The number of possible values of q is 6.

Which of the above statements is/are correct? 

(UPSC CSAT – 2023)

1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2

Solution: Ans.(3)

pp + qq + rr = tt0

pp, qq & rr are 2-digit numbers, so tt0 would be 110 or 220, because sum of three numbers (2-digit) can not be greater than 300.

And therefore (p + q + r) = 10 or 20

Possible values of (p + q + r) are

1+2+7 = 10

1+3+6 = 10

1+4+5 = 10

2+3+5 = 10

3+8+9 = 20

4+7+9 = 20

5+6+9 = 20

5+7+8 = 20

Possible values of p are 1, 2, 3, 4, 5

Possible values of q are 2, 3, 4, 6, 7, 8

Possible values of r are 5, 6, 7, 8, 9