simple math question from civil service exam

Question

The weight per foot of a length of square bar 4" x 4" in cross section as compared with one 2" x 2" in cross section, is ______ as much.

A. Twice B. 2 1/2 times C. 3 times D. 4 times

This question exactly as writtin appears in NY states civil service exam. The answer key says the correct answer is C.

Someone over at the test writing center is smoking some good stuff.

This is one of several incorrect answers and oddish question.

Can someone please give the correct answer as I am arguing with another gentleman about it

Answer 1

The $4''\times 4''$ square bar has four times the cross-sectional area as the $2''\times 2''$ bar. (Draw the cross-sections to see this.) If the bars are of the same length and (uniform) mass density, then the weight of the $4''\times 4''$ bar is four times the weight of the $2''\times 2''$ bar.

If your friend still doesn't see the point after showing him a drawing, then ask him to put four of the $2''\times 2''$ bars together to form one similar in size and shape to the $4''\times 4''$ bar.

Answer 2

Mass is proportional to volume *. If we ignore density and take each bar to be $l$ inches long, the first bar has volume $4"\cdot\,4"\cdot\,l=16l$ & the volume of the second bar is $2"\cdot\,2"\cdot\,l=4l$. Clearly $16l=4\cdot4l$ so the volume (& thus, mass) is $4$ times greater.

*$m=\rho V$