Question

Shared setup (chef and ingredients): A chef is preparing a recipe using four ingredients out of six liquids. Two of these ingredients must come from the taste group A, B and C, and the other two must come from the group W, X, Y and Z. Three combinations are never allowed: B with W, C with Y, and Y with Z.

Which of the following combination of liquids is impossible?

I. Using Y and W together
II. Using B and C together
III. Using W, X and Z together

• A. I only
• B. II only
• C. III and I only
• D. II and I only

Hint:

List every valid two-from-four combination first, then test each roman numeral statement against that list.

Answer 1

The Correct Option is C

Step 1: Check statement I directly.
For Y to be used, C must drop out of the taste group (C-Y rule), so the taste pair becomes A and B. A and B means B is in the mix, and B bans W (B-W rule). So Y and W can never sit together in any valid recipe. Statement I is impossible.

Step 2: Check statement II directly.
B and C together is already a valid two-ingredient taste pick. It only bans W (from B) and Y (from C), leaving X and Z free to use. So B and C with X and Z is a real, working recipe. Statement II is possible.

Step 3: Check statement III directly.
The recipe rule fixes exactly two ingredients from W, X, Y, Z, never three. Using W, X and Z together needs three from that group, which breaks the basic count rule on its own, no need to even check the ban list. Statement III is impossible.

Final Answer:
Only statements I and III cannot happen, so the impossible ones are III and I. \[ \boxed{\text{III and I only}} \]