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?

QUESTION

CSAT

Easy

Maths

Prelims 2023

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:

The number of possible values of $p$ is 5.
The number of possible values of $q$ is 6

Which of the above statements is/are correct?

Select an option to attempt

Explanation

tt0 is a 3-digit number ending with zero, such that $pp + qq + rr = tt0$ As $pp$ , $qq$ , and $rr$ are 2-digit numbers, the value of $tt0$ can be either $110$ or $220$ .

If $tt0 = 110$ $pp + qq + rr = 110$ or $(10p + p) + (10q + q) + (10r + r) = 110$ or $11p + 11q + 11r = 110$ or $p+q+r=10$ ....... (1)

If $tt0 = 220$ $pp + qq + rr = 220$ or $(10p + p) + (10q + q) + (10r + r) = 220$ or $11p + 11q + 11r = 220$ or $p + q + r = 20$

Statement 1: As $p < q <r$ , the possible value of $p$ in equation (1) can be 1 and 2. As $p < q <r$ , the possible value of $p$ in equation (2) can be 1, 2, 3, 4 and 5. Hence, the number of possible values of $p$ is 5. Thus, Statement 1 is correct.

Statement 2: As $p < q<r$ , the possible value of $q$ in equation (1) can be 2, 3 and 4. As $p < q <r$ , the possible value of $q$ in equation (2) can be 6, 7 and 8. Hence, the number of possible values of $q$ is 6. Thus, Statement 2 is correct.