By looking at a rectangular box, a carpenter estimates that the length

Question

By looking at a rectangular box, a carpenter estimates that the length of the box is between 2 to 2.1 meters, inclusive, the breadth is between 1 to 1.1 meters, inclusive and the height is between 2 to 2.1 centimeters, inclusive. If the actual length, breadth and height of the box do indeed fall within the respective ranges estimated by the carpenter, which of the following is the closest to the maximum possible magnitude of the percentage error that the carpenter can make in calculating the volume of the rectangular box?

A. 1%
B. 3%
C. 10%
D. 18%
E. 22%

A. 1%
B. 3%
C. 10%
D. 18%
E. 22%

Archit3110 · Answer

max area ; 2.1*1.1*2.1 = 4.85
min area; 2*1*2; 4
so % of max area ; 4.85-4/4.85 = 18%
IMO D

CareerGeek · Answer

Maximum Volume possible = 210*110*2.1 cm^3 = 48510 cm^3
Minimum Volume possible = 200*100*2 cm^3 = 40000 cm^3

% error possible =  \frac{(48510 - 40000)}{48510} *100
= 18% approx

IMO Option D

Pls Hit kudos if you like the solution

RupamPaul13 · Answer

Maximum volume of the cube can be=2.1*1.1*2.1=4.851
Minimum volume of the cube can be=2*1*2=4

So maximum percentage error that the carpenter can do is (4.85-4)/4 which is approximately 22%. IMO Option E

varun2014 · Answer

Confused, since i'm not sure about what would be the denomination and why? Would it be 4 or 4.854. Some one please clarify

Posted from my mobile device

vitorcmonteiro · Answer

I have questioned myself the same thing. The explanation I came up with is that theoretically there is no problem to use 4 or 4.854 to calculate the % difference. However, the problem introduced an important constraint (Also probably a trap): "maximum possible magnitude of the percentage error".

Well, to maximize the magnitude of error we should compare to the SMALLEST volume (4). Hence, we choose 4 instead of 4.854 as denominator (Again, both are theoretically acceptable if we do not count the constraint the problem gave us). This give us 22% as the answer (E) instead of 18%.

By looking at a rectangular box, a carpenter estimates that the length

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

By looking at a rectangular box, a carpenter estimates that the length

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards