Question

Mr. Mendel grew one hundred flowering plants from black seeds and white seeds, each seed giving rise to one plant. A plant gives flowers of only one colour. From a black seed comes a plant giving red or blue flowers. From a white seed comes a plant giving red or white flowers. How many black seeds were used by Mr. Mendel?
A. The number of plants with white flowers was 10.
B. The number of plants with red flowers was 70.

• A. The question can be answered by using one of the statements alone, but cannot be answered using the other statement alone.
• B. The question can be answered by using either statement alone.
• C. The question cannot be answered even by using both statements together.
• D. The question can be answered by using both statements together, but cannot be answered using either statement alone.

Hint:

Let b be the number of black seeds and see what the constraints on red, blue and white flowers give: only inequalities for b, not a single value.

Answer 1

The Correct Option is C

Step 1: Let there be \(b\) black seeds and \(w=100-b\) white seeds. Blue flowers come only from black seeds; white flowers only from white seeds; red flowers from either.

Step 2: A alone: 10 white-flowered plants means \(w\ge 10\), so \(b\le 90\). No unique value.

Step 3: B alone: 70 red, so 30 plants are blue or white; \(b\) can vary. No unique value.

Step 4: Together: White = 10, red = 70, so blue = 20. Blue plants come from black seeds, so \(b\ge 20\); the 10 white-flowered plants come from white seeds, so \(w\ge 10\), \(b\le 90\). Any \(b\) between 20 and 90 is possible (e.g. 20 black seeds all blue and 80 white seeds with 10 white, 70 red; or 90 black seeds with 20 blue, 70 red, and 10 white seeds all white).

Final Answer:
The correct option is (3): The question cannot be answered even by using both statements together.