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555-605 Level|   Math Related|         
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GMAT Club Olympics 2024 (Day 7): A retailer needs to purchase cuboidal 16 Jul 2024, 09:14
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Bunuel
­A retailer needs to purchase cuboidal boxes of two different sizes. The boxes are both 6 inches long and 9 inches high but differ in width. The boxes are priced by volume at $2 per cubic inch. The volume of a cuboid is length x width x height.

The base area of a cuboid is length x width. In the table below, select the value that is closest to the cost of one box of base area 24.5 square inches as well as the cost of one box of base area 32.75 square inches. Make only one selection in each column.


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­Box with Base Area 24.5 Square Inches


  1. Width: Width = 24.5/6 = 4.083 inchess
  2. Volume: Volume = 6 × 4.083 × 9 ≈ 220.491 cubic inches
  3. Cost: Cost = 220.491 × 2 ≈ 441 dollars
Box with Base Area 32.75 Square Inches


  1. Width: Width = 32.75/6 ≈ 5.458 inches
  2. Volume: Volume = 6 × 5.458 × 9 ≈ 294.786 cubic inches
  3. Cost: Cost = 294.786 × 2 ≈ 590 dollars
Closest Values


  • 24.5 square inches box: 441 dollars
  • 32.75 square inches box: 590 dollars
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­ 
­The answer should be CE

We know the value of L*B from the given area - we have to multiply the height to get volume and the for cost multiply again with $2.
 
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­Cost = volume * $ 2 
= L*B*H * $2

Given H = 9 in.

For case 1
L*B = 24.5 sq in.
Hence cost = 24.5 * 9 * 2 = $440 approx.

For case 2
L*B = 32.75 sq in.
Hence cost = 32.75 * 9 * 2 = $590 approx.
 ­
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Base is given as l *w
We know that length of both the boxes is 6, equate l as 6 in both equations, we will get width of box 1 as 4.083( 24.5/6)
Volume is given as lbw
Lengh is 6, height is 9, width of box 1 is 4.083
Multiply length *height*width and we will see that 220.4 so cost will be volume * price of box 1 will be 220.4 *2 which comes out approximately as 441

Same exercise we can do for 32.75 and answer will be 589.5 approx 590

Posted from my mobile device
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Cost of one box of base area 24.5:

Area: L X W= 24.5; H=9
Volumee= 9*24.5 ~220
Cost= 220*2= 440

Cost of one box of base area 32.75:
Area: L X W= 32.75; H=9
Volumee= 9*32.75 ~294
Cost= 2*294= 590
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Price of 24.5 base = 24.4 x 9 x 2 = 441­
Closest value is $440.

Price of 32.75 base = 32.75 x 9 x 2 = 589.5
Closest value is $590

Base area 24.5 square inches => option C
Base area 32.75 square inches => option E
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Base area 24.5, Height 9 , cost 2 per cubic inch :

Total Cost = 220.5*2 = 441

Base area 32.75, Height 9 , cost 2 per cubic inch :
Total Cost = 294.8*2 =589.5
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A retailer needs to purchase cuboidal boxes of two different sizes. The boxes are both 6 inches long and 9 inches high but differ in width. The boxes are priced by volume at $2 per cubic inch. The volume of a cuboid is length x width x height.

The base area of a cuboid is length x width. In the table below, select the value that is closest to the cost of one box of base area 24.5 square inches as well as the cost of one box of base area 32.75 square inches. Make only one selection in each column.­

We are already given the area, so we don't need to calculate the "Width". We can directly multiply the areas with height, which will provide us the volume and the cost of each cubic inch is $2, so if we multiply 18 to each area, will get the answers. 

Hence the answer will be (440, 590)
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GMAT Club Olympics 2024 (Day 7): A retailer needs to purchase cuboidal 16 Jul 2024, 10:39
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 ­After the opening day of the week, 
We're back to business.
I feel the luck is going to shift to our Green team as we get closer to the end of the Champions.
Let's get started with our explanation for this topic:

­Glance - the Question&Answer Choices:
Question: We have here a word problem. kind of geometry. (but we have all the details we need). don't worry.
Answer Choices: They have enough space between them to be able to guess if we need.

Rephrase - Reading and Understanding the question:
Given:
Long = 6         Height = 9     Width 1 = x       Width 2 = y 
1 cubic = 2 $
[?]: What is the cost of 2 boxes: one with a base of 24.5 and the second with 32.75

Solve:
First let's find the volume of each box
1) 6 * x = 24.5
x = [24.5][/6] this is the box width. 
Volume = 6 * 9 * [24.5][/6] =>  9 * 24.5
we know that each cubic = 2$.  Thus, let's multiply by 2.
9 * 24.5 * 2 = 441    => 440. 

2) 6 * y = 32.75
y = [32.75][/6] this is the box width. 
Volume = 6 * 9 * [32.75][/6] =>  9 * 32.75
we know that each cubic = 2$.  Thus, let's multiply by 2.
9 * 32.75 * 2 = 589    => 590. 

So our answer here is : 440 and 590.


THE END
I hope you liked the explanation, I have tried my best here.
Let me know if you have any questions about this question or my explanation.
­  
 
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­The boxes are both 6 inches long and 9 inches high but differ in width.(w1 and w2)
The boxes are priced by volume at $2 per cubic inch.
The volume of a cuboid is length x width x height.

The base area of a cuboid is length x width.
  1. value that is closest to the cost of one box of base area 24.5 square inches.
  2. length x width = 24.5 square inches.
  3. Volume = length x width x height. = 24.5 * 9 = 220.5
  4. Box Price = 2*220.5 = $441
  5. Answer Option C $440
 
  1. value that is closest to the cost of one box of base area 32.75 square inches.
  2. length x width = 32.75 square inches.
  3. Volume = length x width x height. = 32.75 * 9 = 294.75
  4. Box Price = 2*294.75 = $589.5
  5. Answer Option E $590
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We know from the stimulus that:

Lenght = 6 inch
Width = 9 inch
Price = $2 per cubic inch

Volume = lenght * width * height
Base = lenght * width

For 24.5 base, we can estimate to be 25 * 9 * 2 = 270, closest to 290
For 32.75, we can estimate 33*9*2 = 594, closest to 590­
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GMAT Club Olympics 2024 (Day 7): A retailer needs to purchase cuboidal 16 Jul 2024, 11:03
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Bunuel
­A retailer needs to purchase cuboidal boxes of two different sizes. The boxes are both 6 inches long and 9 inches high but differ in width. The boxes are priced by volume at $2 per cubic inch. The volume of a cuboid is length x width x height.

The base area of a cuboid is length x width. In the table below, select the value that is closest to the cost of one box of base area 24.5 square inches as well as the cost of one box of base area 32.75 square inches. Make only one selection in each column.


­
 


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­The cost of one box of base area 24.5 square inches = 24.5 (base area) * 9 (height) * 2 (cost ) = $441
The cost of one box of base area 32.75 square inches = 32.75 (base area) * 9 (height) * 2 (cost ) =  $589.5

The value that is closest to the cost of one box of base area 24.5 square inches is $440
The value that is closest to the cost of one box of base area 32.75 square inches is $590
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For the small one
The volume is 6*9*24.5/6 = 220.5
Then the cost is 2*220.5 = 441 dollars

So for 24,5 base correct answer is 440
For the bigger one
The volume is 6*9*32.75/6 = 294.75
Then the cost is 2*294.75 = 589.5 dollars which is approximately 590
So for 32,75 base correct answer is 590
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GMAT Club Olympics 2024 (Day 7): A retailer needs to purchase cuboidal 16 Jul 2024, 11:44
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A retailer needs to purchase cuboidal boxes of two different sizes. The boxes are both 6 inches long and 9 inches high but differ in width. The boxes are priced by volume at $2 per cubic inch. The volume of a cuboid is length x width x height.

The base area of a cuboid is length x width. In the table below, select the value that is closest to the cost of one box of base area 24.5 square inches as well as the cost of one box of base area 32.75 square inches. Make only one selection in each column.

Volume of Box A=length x width x height
Vol(A)=24.5 square inches x 9 inch ≈ 25x9=225 inch cube
cost of box A ≈ 225x2=450

Volume of Box B=length x width x height
Vol(A)=32.75 square inches x 9 inch ≈ 33x9=297 inch cube
cost of box A ≈ 297x2=594

$293
$367
$440  Box A
$515
$590 Box B
$663­
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The trick here is that we are already given the bottom area, and we only need to multiply it by height (9 inches) to get the volume.

Box 1:
\(V = area * 9 = 25 * 9 = 225\) (cubic inches) - rounding the surface to 25
\(Price = V * $2 = $450\)

Box 2:
\(V = area * 9 = 33*9 = 297\) (cubic inches) - rounding the surface to 33
\(Price = V * $2 = $594\)

Therefore, the answer for Box 1 is closest to (C) 440, whereas for Box 2 it's closest to (E) 590.­
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GMAT Club Olympics 2024 (Day 7): A retailer needs to purchase cuboidal 16 Jul 2024, 13:28
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­Let's take the box with base area (l X b) 24.5 sq. inches.
Volume = l X b X h
           =  24.5 X 9
           = 220.5 cu. in.
Price = 2 X 220.5 = $441 which is approx $440.

Now, let's take the box with base area (l X b) 32.75 sq. inches
Volume = l X b X h
           = 32.75 X 9
           = 294.75 cu. in
Price = 2 X 294.75 = $589.5 which is approx $590.

Hence, the answers.
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GMAT Club Olympics 2024 (Day 7): A retailer needs to purchase cuboidal 16 Jul 2024, 13:38
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We can solve this problem in the following way.

We are given the length and height of two different cuboidal boxes and are told that the width is different for each box and uknown at this point. We are also given the base area of the boxes which are equal to their length*width.

We can summarise all the information we are given as follows:

Base Area of a cuboid: length*width
Volume of a cuboid: length*height*width
Boxes priced at $2 per cubic inch

Box A dimensions

Length: 6 inches
Height: 9 inches
Width: x
Base Area: 24.5 square inches 

Box B dimensions

Length: 6 inches
Height: 9 inches
Width: y
Base Area: 32.75 square inches 

Although we do not know the width of the two boxes there is no need to calculate them. The formula for the base area is length*width and the formula for the volume is  length*height*width. So all we need to do is multiply the base area by the height and we have the volume. 

*Note: briefly have a look at the answers to see how accurate you have to be. In this case, not very accurate.

Volume of Box A
24.5*9 (We can do 25*10 and then subtract 25 which would give us 225)

Volume of Box B
32.75*9 (Here we can do 33*9 to get approximately 300) 

Now we multiply both values by 2 since we need to calculate the cost and the boxes are priced by volume at $2 per cubic inch.

So the total values we get are approximately $450 for box A and $600 for Box B. 

There is an answer choice of $440 and of $590 and these are the answer choices for the box with base area 24.5 square inches and box with base area 32.75 square inches respectively. 

Bunuel
­A retailer needs to purchase cuboidal boxes of two different sizes. The boxes are both 6 inches long and 9 inches high but differ in width. The boxes are priced by volume at $2 per cubic inch. The volume of a cuboid is length x width x height.

The base area of a cuboid is length x width. In the table below, select the value that is closest to the cost of one box of base area 24.5 square inches as well as the cost of one box of base area 32.75 square inches. Make only one selection in each column.


­
 


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­
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1-440
2-590

box of base area 24.5 square inches = 24.5*9(ht)*2(cost) ~ 450
box of base area 32.75 square inches = 32.75*9(ht)*2(cost) ~ 590
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Cost for Base area 24.5 square inches = 24.5*9*2 = 440$ approx
Cost for Base area 32.75 square inches = 32.75*9*2 = 590$ approx

440$ and 590 $
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