An open box in the shape of a cube measuring 50 centimeters on each si

Question

An open box in the shape of a cube measuring 50 centimeters on each side is constructed from plywood. If the plywood weighs 1.5 grams per square centimeter, which of the following is closest to the total weight, in kilograms, of the plywood used for the box? (1 kilogram = 1,000 grams)

A. 2
B. 4
C. 8
D. 13
E. 19

NEW question from GMAT® Quantitative Review 2019

(PS08051)

A. 2
B. 4
C. 8
D. 13
E. 19

NEW question from GMAT® Quantitative Review 2019 
(PS08051)

EgmatQuantExpert · Accepted Answer

Solution

Given:  
 • An open box in the shape of a cube measuring 50 cm on each side is constructed from plywood
• Plywood weighs 1.5 grams per square cm
• 1 kilogram = 1,000 grams

To find:  
 • The closest value, of the total weight, in kilograms, of the plywood used for the box

Approach and Working:   
As it is an open box, we are assuming that there will be only 5 surfaces made of plywood.
 • Area of each surface = 50 * 50 sq. cm.
• So, area of 5 surfaces = 5 * 50 * 50 sq. cm.
• Therefore, total weight = 5 * 50 * 50 * 1.5 grams = 18750 grams = 18.75 kg 
 
Hence, the correct answer is option E.

Answer: E

Arro44 · Answer

I agree with the explanations above.

However, I am surprised that the GMAC did not take the opportunity to include something like 22.5 in the answer choices to set a trap for the people who forgot that the box only consists of 5 parts of wood due to being open at the top.

sudarshan22 · Answer

Surface area of each side = 50 * 50
Surface area of all sides = 5 * 50 * 50 (since it is an open box, sixth side will be missing)

weight of the box in gms = 5 * 50 * 50 * 1.5 = 18750 = 19000(approx)
weight of the box in Kgms = 19000 / 1000 = 19

Hence,   E  .

ScottTargetTestPrep · Answer

If the open box is in the shape of a cube measuring 50 centimeters on each side, then it has five faces, each measuring 50^2 = 2500 square centimeters, and thus its surface area is 5 x 2500 = 12,500 square centimeters. Since each square centimeter of plywood weighs 1.5 grams, the plywood needed to constructed the open box is 12,500 x 1.5 = 18,750 grams or 18.75 kilograms.

Answer: E

ArupRS · Answer

I agree. Inclusion of the option 22.5 would have trapped me too.

Regards,
Arup

Kinshook · Answer

Given: 
1. An open box in the shape of a cube measuring 50 centimeters on each side is constructed from plywood. 
2. The plywood weighs 1.5 grams per square centimeter

Asked: Which of the following is closest to the total weight, in kilograms, of the plywood used for the box? (1 kilogram = 1,000 grams)

Total surface area of the box = 5*50*50 = 12500 cm^2

Total weight = 1.5 * 12500 /1000 kg = 18.75 kg = 19 kg approx

IMO E

dcummins · Answer

Open box means one face is missing. Don't neglect this.

We can use surface area to determine square cm area of the open-cube.
5*S^2 = 5(50)^2 = 12500cm^2 
12,500cm^2* 3/2g per square cm = 18,750g
divide by 1000 since there are 1000grams per kilo
18.75 or ~19kg

LoneSurvivor · Answer

This is open box which why we need 5a^2

Basshead · Answer

50 * 50 = 2500 cm^2

2500 * 1.5 = 3,750 grams = 3.75 kilograms

Since the cube is open, there will be 5 sides instead of 6.

3.75 * 5 = 18.75

Answer is E.

MHIKER · Answer

The surface area of a cube  = 6S^2 , as the cube is open so need to calculate the surface area of  5  sides =  = 5S^2

Now,  \frac{5*50*50*1.5}{1000}

= \frac{75}{4}   =18.75 
 
  =19

The answer is E

ueh55406 · Answer

It's an  OPEN cube , which means the top side doesn't have any plywood. so, we're left with five faces.

total area of the five faces:  5*(side)^2 =  5*(50)^2 =  12500 cm^2

1.5 gm/sq cm is the weight of plywood. so, 12500* 1.5= 18750 gm. (for the whole box)

now, it's safe to convert it to Kg's by dividing this by 1000 =  18750/1000  = 18.75= 19Kg's (approx)

PS: try not to convert anything in the middle of the calculation, if possible. as was the case in this question. we converted the gm's to kg's at the very end.

QQ: it's tagged at 700, shouldn't it be at 600-700.?

junii · Answer

I have converted everything at the beginning and my answer was close to 2, so in such questions is it better to convert everything at the end/?

Abhishek009 · Answer

\frac{50*50*5*1.5}{1000}  ~  19 , Answer must be (E)

MBAB123 · Answer

junii  It doesn't really matter when you convert, the answer would still be the same. And the best time/moment to convert depends entirely on the question. For this one in particular, I felt it was better to just divide the whole setup by 1000, i.e, convert at the end.

ThatDudeKnows · Answer

Most of the answers in the thread are correct. I just wanted to take a moment to point out that there's an opportunity here to skip at least a little of the math if we use the answer choices. Get in the habit of glancing at the answer choices as you work so you know when you can stop doing math.

50x50=2500 square cm per side
5x2500=12500 total area
We are about to multiply that by 1.5. Do we really need to do the math, or is there only one answer choice that's close?

Answer choice E.

ThatDudeKnowsBallparking

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An open box in the shape of a cube measuring 50 centimeters on each si

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