RAS question
A machine applies the following operations on each number in sequence: Operation 1: Add the position number (1st number gets +1, 2nd gets +2, etc.) Operation 2: If the result is odd, multiply by 2; if even, divide by 2. Input: 4, 7, 2, 9 What is the final output?
Correct answer: (D) 10, 18, 10, 26.
The machine's final output for the input 4, 7, 2, 9 is 10, 18, 10, 26.
Explanation
First add the position number to each input: the first term gives 4+1=5, the second gives 7+2=9, the third gives 2+3=5, and the fourth gives 9+4=13. Math is Fun defines odd numbers as integers that cannot be divided exactly by 2, with last digits such as 1, 3, 5, 7 and 9; by that rule, 5, 9, 5 and 13 are all odd. The machine's second operation therefore uses the odd-number branch for every term, multiplying each by 2. That gives 5×2=10, 9×2=18, 5×2=10 and 13×2=26, so the final output is 10, 18, 10, 26.
Why the other options are wrong
- (A) A stops after adding the position number for the first and third terms, giving 5 and 5 instead of multiplying those odd intermediate results by 2.
- (B) B is only the result after Operation 1, because 5, 9, 5 and 13 still need the odd-number operation of multiplication by 2.
- (C) C incorrectly changes the first and third intermediate results to 3 before applying the second operation, although Operation 1 gives 5 for both positions.
Concept
This tests sequential machine-operation reasoning with parity, a standard RAS mental ability idea because candidates must track order, position and conditional rules without skipping a step.