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: Work out every valid pairing from W, X, Y, Z.
The taste group has three possible picks: A and B, A and C, or B and C. For each, work out which pairs from W, X, Y, Z still survive once the ban rules remove some letters.

Step 2: Pair A and B.
Here B is present, so W is banned (B-W rule). That leaves X, Y, Z to pick two from, but Y and Z cannot go together either, so only X-Y and X-Z survive.

Step 3: Pair A and C.
Here C is present, so Y is banned (C-Y rule). That leaves W, X, Z to pick two from, giving W-X, W-Z and X-Z, all allowed.

Step 4: Pair B and C.
Now both W (from B) and Y (from C) are banned, leaving only X and Z, so X-Z is the single option here.

Step 5: Check each statement against this full list.
Statement I, Y and W together, never shows up in any valid pair above, so it is impossible. Statement II, B and C together, is possible using X and Z, so it is not impossible. Statement III, using W, X and Z together, needs three ingredients from the second group, but the rules only allow two from that group in total, so it can never happen.

Final Answer:
Statements I and III are impossible. \[ \boxed{\text{III and I only}} \]