Question 159 Problem Solving 2018 GMAT Official Guide

Question 159 Problem Solving 2018 GMAT Official Guide

Video explanation: The interior of a rectangular carton is designed by a certain…

Comments

Alexsays

another way of looking at it, but it might be cumbersome, is assuming the b/w/h = 3, 2 and 2. Thus, total volume = 12 cubic feet. Plugging that into the answer choices, you’ll soon come to realise the only answer choice that produces a clean root is B.

You are absolutely right. Plugging in $x=12$ will indeed flush out the correct answer, which is B, the only one that turns out to be equal to $2$. The only drawback with this approach is that it is possible to have two answer choices that give the same results. I have seen this often in the case of official GMAT questions, not in this particular example. For example, if I were writing this question, I would have added the expression $\dfrac{1}{3} \sqrt[3]{18x}$ as one of the answer choices, which also gives an answer of $2$ when we replace $x$ with $12$. This is because I know from experience that most students who plug in numbers would have chosen the values of $3$, $2$, and $2$ for the length, width, and height of the rectangular solid.

Alex says

another way of looking at it, but it might be cumbersome, is assuming the b/w/h = 3, 2 and 2. Thus, total volume = 12 cubic feet. Plugging that into the answer choices, you’ll soon come to realise the only answer choice that produces a clean root is B.

GMAT Quantum says

Hi Alex,

You are absolutely right. Plugging in $x=12$ will indeed flush out the correct answer, which is B, the only one that turns out to be equal to $2$. The only drawback with this approach is that it is possible to have two answer choices that give the same results. I have seen this often in the case of official GMAT questions, not in this particular example. For example, if I were writing this question, I would have added the expression $\dfrac{1}{3} \sqrt[3]{18x}$ as one of the answer choices, which also gives an answer of $2$ when we replace $x$ with $12$. This is because I know from experience that most students who plug in numbers would have chosen the values of $3$, $2$, and $2$ for the length, width, and height of the rectangular solid.

Thanks for the comment.

Dabral