I'd definitely recommend creating a table for this. The text editor here has a nifty tool for that, so I will proceed to use it.
| Design | Rank 1 | Rank 2 | Rank 3 |
| A | | | |
| B | | | |
| C | | | |
First thing first, we see the overall conditions:1. 120 people were asked to rank.
2. Each person gave a complete ranking with no ties.
Now, to fill in the table.Of the 120, 3/10 ranked A as first. That's 120 / 10 * 3 = 36.
11 / 30 ranked B as first. That's 120 / 30 * 11 = 44.
What does that imply? As everyone is ranking everyone as either first, second, or third, each will add to 120.
So, to find how many ranked C as first, we get 120 - 36 - 44 = 40.This is our table now:
| Design | Rank 1 | Rank 2 | Rank 3 |
| A | 36 | | |
| B | 44 | | |
| C | 40 | | |
Next, we get, "among those who rank A first, 2/3rds rank B second" (that's 24 people ranking B second, until now)
"Among those who rank C first, three-quarters rank B second" (that's 30 people ranking B second, until now)
That's a total of 54 marking B second.Which means how many will people rank B third? That's, again, the difference between 120, Rank 1 and Rank 2.
120 - 54 - 44 = 22 is the answer, D.Here's how the completed table will look:
| Design | Rank 1 | Rank 2 | Rank 3 |
| A | 36 | | |
| B | 44 | 54 | 98 |
| C | 40 | | |
BunuelQuote: