Question

The inside of a rectangular carton is 48 centimeters long, 32 centimeters wide, and 15 centimeters high. The carton is filled to capacity with k identical cylindrical cans of fruit that stand upright in rows and columns, as indicated in the figure above. If the cans are 15 centimeters high, what is the value of k?
(1) Each of the cans has a radius of 4 centimeters.
(2) Six of the cans fit exactly along the length of the carton.

• 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 D Each statement alone is sufficient.

• From statement 1, if the radius of each can is $4$ cms, the diameter of each can is $8$ cms. Along the $48$ cm length of the carton, $6$ cans can be placed; along the $32$ cm width of the carton, $4$ cans can be placed. Hence, $k=6\times 4=24$, is sufficient.
• From statement 2, if $6$ cans fit along the $48$ cm length of the carton, this implies that the diameter of each can is $8$ cms . Along the $32$ cm width, $4$ cans can be placed, and again $k=6\times 4=24$, is sufficient. Thus, each statement alone is sufficient.