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

The answer should be $D$, and per foot has nothing to do with the answer. — Euler....IS_ALIVE, Aug 28 '14 at 00:36
Yes, it is interfering with my eyesight, the answer is $4$, which I thought had label C. — André Nicolas, Aug 28 '14 at 00:38
So the guy who still doesnt believe me here insists the answer is "A" and i cant figure out how else to explain it. He says im wrong. He says we are all wrong.. can someone please explain it im out of ideas. — MrPizzaFace, Aug 28 '14 at 00:41
I even drew him a diagram and he still doesnt get it.. maybe im not explaining correctly so if someone cares to give it go... — MrPizzaFace, Aug 28 '14 at 00:43

score 2 · Accepted Answer · answered Aug 28 '14 at 00:43

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.

score 1 · Answer 2 · answered Aug 28 '14 at 00:43

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.

*$m=\rho V$

simple math question from civil service exam

2 Answers2