Unit 7 · Finding Procedures
Ducks and Cats — Supposition Method
Lesson 2 of 5
Let's start with one of the most elegant shortcuts in OC MR — the supposition method. Instead of setting up two equations, you make one bold assumption ('suppose all animals are ducks'), measure how wrong you are, and use that gap to find the answer in two arithmetic steps.
Supposition (or "guess and adjust") problems appear in almost every OC MR paper, usually in the easy-to-medium range. They include legs-and-animals, tables-and-chairs, coin problems, and container questions — all sharing the same two-step shortcut.
The examiner is checking whether you know to assume everything is one type, compare the resulting total against the real total, and divide the gap by the per-swap difference — rather than setting up two simultaneous equations or trial-and-error across the answer options.
Two types of items each contribute a different fixed amount to a total (e.g. ducks have 2 legs, cats have 4 legs). You are given the number of items and the total contribution. You must find how many of each type there are.
Best approach: Step 1: Suppose all items are the lower-value type. Multiply to get the expected total. Step 2: Find the gap between the expected total and the real total. Step 3: Each swap from the lower type to the higher type increases the total by the difference in their values. Divide the gap by that difference. That is your answer — no simultaneous equations needed.
Question
There are 14 ducks and cats in a farm. The total number of legs of these animals is 36. How many cats are there?
Select an answer to see the explanation.
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