Three sisters (R, S, T) received a total of 24 toys during Christmas. The toys were initially divided among them in a certain proportion. Subsequently, R gave some toys to S, which doubled the share of S. Then S in turn gave some of her toys to T, which doubled T's share. Next, some of T's toys were given to R, which doubled R's share. As a result of all the exchanges, the three sisters were left with an equal number of toys. How many toys did R have originally? A. 6 B. 8 C. 11 D. 12

GATE 2011 · General Aptitude · Logical Reasoning · medium

Answer: R originally had 11 toys.

1. Reverse step 3: T gave to R, doubling R: R ended with 8, so before step 3: R = 4. T ended with 8, so before step 3: T = 8 + 4 = 12. S unchanged: S = 8. State before step 3: R = 4, S = 8, T = 12.
2. Reverse step 2: S gave to T, doubling T: T was 12 after step 2, so before step 2: T = 6. S was 8 after step 2, so before step 2: S = 8 + 6 = 14. R unchanged: R = 4. State before step 2: R = 4, S = 14, T = 6.
3. Reverse step 1: R gave to S, doubling S: S was 14 after step 1, so before step 1: S = 7. R was 4 after step 1, so before step 1: R = 4 + 7 = 11. T unchanged: T = 6. Original state: R = 11, S = 7, T = 6.