Question

How many ice cubes can be accommodated in a container?
(I) The length and breadth of the container are 20 cm and 15 cm respectively.
(II) The edge of the ice cube is 2 cm.

• A. Statement I alone is sufficient to answer the question.
• B. Statement II alone is sufficient to answer the question.
• C. Both statement I and II together are necessary to answer the question.
• D. Both statements I and II together are not sufficient to answer the question.

Hint:

Check whether the container's height is given anywhere; without it, volume can't be found.

Answer 1

The Correct Option is D

Method: list every quantity required to solve the problem, then check which statements actually supply them.

1. To find how many identical small cubes fit inside a rectangular container, we need: container volume = length x breadth x height, and cube volume = $(\text{edge})^3$. Then number of cubes = container volume / cube volume, assuming perfect packing.
2. Required inputs: length, breadth, height of the container, and the edge of the cube. That is four numbers in total.
3. Statement I supplies only two of these: length = 20 cm and breadth = 15 cm. Height is missing.
4. Statement II supplies only the cube edge = 2 cm.
5. Adding statement I and statement II together supplies three of the four required numbers (length, breadth, edge), but height is still nowhere in either statement.
6. Since one required input (height) is permanently absent from both statements, the container's volume, and therefore the number of cubes, can never be calculated from the data given.

Both statements together remain insufficient, so the answer is option 4.

\[\boxed{\text{Option 4}}\]