Question

What is the number of cans that can be packed in a certain carton?
(1) The interior volume of this carton is $2,304$ cubic inches.
(2) The exterior of each can is $6$ inches high and has a diameter of $4$ inches.

• A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.
• E. Statements (1) and (2) together are not sufficient.

Answer 1

The correct option is E Statements (1) and (2) together are not sufficient.

• From statement 1, there is no information about the size of each can. From statement 2, there is no information about the size of the carton.
• Considering both the statements, we get 2 cases. Case a: the dimensions of the box is $1\times 1\times 2304$ (inches), in which case $0$ cans can fit inside the carton. Case b: the dimensions of the box is $10\times 10\times 23.04$ (inches), in which case more than $0$ cans can fit inside the carton.
• Since we cannot answer the target question with certainty, the combined statements are not sufficient.