RAS question
A machine operates on a number as follows: If the number is a multiple of 3, divide by 3 and add 1. If the number is NOT a multiple of 3, multiply by 3 and subtract 1. Input: 9 What is the output after 2 steps?
Correct answer: (A) 11.
For input 9, the machine gives 11 after two steps: first 9 becomes 4, then 4 becomes 11.
Explanation
Start by applying the rule to the current number, not to the original input again. In step 1, 9 is a multiple of 3, so the machine uses the first rule: divide by 3 and add 1. That gives 9 / 3 + 1 = 3 + 1 = 4. In step 2, the current number is now 4. Since 4 is not a multiple of 3, the machine switches to the second rule: multiply by 3 and subtract 1. That gives 4 x 3 - 1 = 12 - 1 = 11. NCERT's Class VII mathematics exemplar frames such questions around choosing the correct arithmetic operation, which is exactly the skill tested here.
Why the other options are wrong
- (B) 9 would be the original input, but after the first step the number changes to 4 and must be processed again.
- (C) 13 comes from multiplying 4 by 3 and adding 1, but the rule for a non-multiple of 3 says subtract 1.
- (D) 4 is only the result after step 1; the question asks for the output after two steps.
Concept
This tests rule-based number operations, a common reasoning pattern in RAS mental ability because the candidate must track the current value through sequential conditions. The recurring trap is to apply the right operation to the wrong step or stop after the first transformation.