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GMAT Club Olympics 2024 (Day 7): A retailer needs to purchase cuboidal

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Gemmie

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17 Jul 2024, 00:31

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L: 6
H: 9
W: a and b

Base area = 24.5
=> Volume = 24.5 * 9
=> Price = 24.5 * 9 * 2 = 441
==> 440

Base area = 32.75
=> Volume = 32.75 * 9
=> Price = 32.75 * 9 * 2 = 589.5
==> 590

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17 Jul 2024, 00:38

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This is one of the easy questions

Cuboid cost of base area 24.5= 24.5xheightxcost per cubic inch
= 24.5x9x2
=440

Cuboid cost of base area 32.75= 32.75xheight x cost per cubic inch
=32.75x9x2
=590

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The volume of the box of base area 24.5 :
$24.5*9=220.5$
The cost of the box of base area 24.5:
$220.5*2$=441$$

The volume of the box of base area 32.75:
$32.75*9=294.75$
The cost of the box of base area 32.75:
$294.75*2$=589.5$$

Therefore, the cost of the box of base area 24.5 is 440$ and the cost of the box of base area 32.75 is 590$.

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17 Jul 2024, 00:56

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Both length is 6 inches

Base area 24.5 square inches
24.5*9*2=$441

Base area 32.75 square inches
32.75*9*2=589.5

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17 Jul 2024, 01:16

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Question stem gives us following details,
There are two types of boxes. Both are 6 inches long and 9 inches high but differ in width.
Volume of Box A =$ 6 * 9 * w_a$
Volume of Box B =$ 6 * 9 * w_b$

We need to find 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.
Base area is given by,
Base Area of Box A = $6 * w_a$ = $24.5$
Base Area of Box B = $6 * w_b$ = $32.75$

Looking at the options, difference between them is quite large. So, we should be able approximate to find correct answer.

$w_a = \frac{24.5 }{ 6}$ = $4$
$w_b = \frac{32.75 }{ 6}$ = $5.5$

Both values are approx.

Now,
Volume of Box A = $ 6 * 9 * w_a$ = $ 6 * 9 * 4$ = $216$
Volume of Box B = $ 6 * 9 * w_b$ = $ 6 * 9 * 5.5$ = $300$

And the boxes are priced by volume at $2 per cubic inch.

So,
Price of Box A = $2 * 216$ = $432$
Price of Box B = $2 * 300$ = $600$

Closest answers are 440 and 590.

Final answer -
440 for base area 24.5 square inches and 590 for base area 32.75 square inches

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17 Jul 2024, 01:20

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A=L×W.
For 24.5 square inches: 24.5=6×W => W= 4.083
For 32.75 square inches: 32.75=6×W = > W= 5.45
Next, we calculate the volume of each box:

Volume of the box with base area 24.5 square inches:
Volume=L×W×H=6×4.083×9=220.5 cubic inches

Volume of the box with base area 32.75 square inches:
Volume=L×W×H=6×5.45×9=294.75 cubic inches
Now, we calculate the cost of each box at $2 per cubic inch:

Cost of the box with base area 24.5 square inches:
Cost=220.5×2=$441

Cost of the box with base area 32.75 square inches:
Cost=294.75×2=$589.50

Thus, the correct answers would be
=>
Base area 24.5 square inches: $440
Base area 32.75 square inches: $590

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17 Jul 2024, 01:34

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Cost of box with Base area 24.5 square inches : 440 $
Cost of box with Base area 32.75 square inches : 590 $

Given:

Length of cuboid box = 6 inches
Height of cuboid box = 9 inches
Cost per unit volume = 2$ per cubic inch

Length and height are common for both the boxes, whereas width is different

Total cost = (volume) * (cost per unit volume)
= ( length * width * height ) * ( 2 )

Cuboid box 1 with base 24.5 square inches = base * height * cost = 24.5 * 9 * 2 = 49 * 9 = ~50 * 9 = ~ 450 (slightly less than 450)

Cuboid box 2 with base 32.75 square inches = base * height * cost = 32.75 * 9 * 2 = 65.5 * 9 = ~650 - 65 = ~590

Matching choices for with base 24.5 square inches is Choice 3 440 $, and Matching choices for with base 32.75 square inches is Choice 5 590 $

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17 Jul 2024, 02:18

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Bunuel

Volume of a cube= length x width x height, where length=6, height=9
Base area= length x width,
Volume= Base area x height

Two cubes say C1 and C2.
For C1, Base area= 24.5
6*w1=24.5
Volume= 24.5*9 ~ 24*9= 240-24=>216 cubic inch
For 1 cubic inch cost is $2, for 216- cost will be >$432 closest to $440.

For C2, Base area= 32.75
Volume= 32.75*9 ~ 32*(10-1)= 320-32= >288
Cost of this cube= >288*2= >$576 therefore $590.

Hence, the answer.

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17 Jul 2024, 02:27

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1. 24.5*9*2 = 441....nearest 440
2. 32.75*9*2=589.50...nearest 590

Answer 440 & 590

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17 Jul 2024, 03:48

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Bunuel

This question was provided by Experts' Global
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Box1- l=6,h=9 w1

So base area= l*w
24.5= 6*w1
so w1=4.083

So cost of box= 6*9*4.083*2=440.964=440

Box2- l=6,h=9 w2

So base area= l*w
32.75= 6*w2
so w2=5.46

So cost of box= 6*9*5.46*2=440.964=589.7=590

So ans is
Base area 24.5 square inches -440
Base area 32.75 square inches-590

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17 Jul 2024, 04:39

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Total Cost= Base*Height*Cost

Base area 24.5 square inches: $440
Base area 32.75 square inches: $590
1- 3 2-5

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Let the width of the first cuboid box and the second cuboid box be x and y respectively.

Volume of the first cuboid = 6*9*x = 54*x cubic inches;
Volume of the second cuboid = 6*9*y = 54*y cubic inches;

As both of the cuboid contribute $2 per cubic inches, thus

Cost of the first cuboid = 2*54*x = $108*x; ----(1)
Cost of the second cuboid = 2*54*y = $108*y; ----(2)

For the base area of 24.5 sq. inches,

Base area of the first cuboid = 6*x = 24.5;
Therefore, x = 4; (By ballparking 24.5 into 24)

For the base area of 32.5 sq. inches,

Base area of the second cuboid = 6*y = 32.5;
Therefore, y = 5; (By ballparking 32.5 into 30)

By substituting x = 4 in (1) and y = 5 in (2),

Cost of the first cuboid = 108 * 4 = $432; (approximately $440) - Option (C)
Cost of the second cuboid = 108 * 5 = $540; (approximately $590) - Option (E)

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17 Jul 2024, 05:13

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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.

height = 9
Base area = length x width = 24.5 and 32.75
Volume = length x width x height
Box 1 :
volume = 24.5 * 9
price = 24.5 * 9 * 2 = 441 aprox 440

Box 2:
volume = 32.75 * 9
price = 32.75 * 9 * 2 = 589.5 apox 590

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17 Jul 2024, 05:59

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Volume of Box= Length*Width*Height
Area of Box= Length*Width
Volume of Box= Area of Box* Height
Height= 9 inches

Cost of Base area 24.5 square inches
Volume = 24.5*9 = 220.5
Cost of box = Volume*$2
Cost of box= 220.5*2 = $441

Cost of Base area 32.75 square inches
Volume = 32.75*9= 274.75
Cost of box = Volume*$2
Cost of box = 274.75*2= $589.5 $590(approx.)

Imo 1-3, 2-5

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17 Jul 2024, 06:12

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Bunuel

This question was provided by Experts' Global
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Volume is Base Area * Height. Using this

V1 = 24.5*9
Cost 1 = 24.5*9*2 =440.

//Y V2 = 32.75*9
Cost 2 = 32.75*9*2 = 590.

Hence IMO 440, 590

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Area = Width * Length
Volume is = Width * Length * Height
So we can simply multiply the respective areas with height to obtain the volume
Box 1 = 24.5*9
Box 2 = 32.75*9
Now the cost can be obtained by multiplying each volume by the given cost.
Box 1 = 24.5*9*2 = 441 round off to 440
Box 2 = 32.75*9 *2 = 589.50 roundoff to 590

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17 Jul 2024, 06:19

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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.

The cost of one box of base area 24.5

$24.5*9*2 = 49*9 = 441 \approx 440 $$

The cost of one box of base area 32.75

$ 32.75*9*2 = 65.5*9 = 589.5 \approx 590 $$

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17 Jul 2024, 06:20

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Bunuel

This question was provided by Experts' Global
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To determine the cost of the boxes, we need to calculate the volume of each box using the given dimensions and then multiply the volume by the price per cubic inch.

The given dimensions for the boxes are:
- Length: 6 inches
- Height: 9 inches
- The widths are calculated based on the given base areas.

### For a base area of 24.5 square inches:

1. **Calculate the width:**

\[
\text{Width} = \frac{\text{Base area}}{\text{Length}} = \frac{24.5 \text{ square inches}}{6 \text{ inches}} = 4.0833 \text{ inches}
\]

2. **Calculate the volume:**

\[
\text{Volume} = \text{Length} \times \text{Width} \times \text{Height} = 6 \text{ inches} \times 4.0833 \text{ inches} \times 9 \text{ inches} = 220.5 \text{ cubic inches}
\]

3. **Calculate the cost:**

\[
\text{Cost} = \text{Volume} \times \text{Price per cubic inch} = 220.5 \text{ cubic inches} \times 2 \text{ dollars per cubic inch} = 441 \text{ dollars}
\]

For a base area of 32.75 square inches:

Volume=Length×Width×Height=6 inches×5.4583 inches×9 inches=295.5 cubic inches

Cost=Volume×Price per cubic inch=295.5 cubic inches×2 dollars per cubic inch=591 dollars

### Selections:
- The cost of one box with a base area of 24.5 square inches is closest to **$441**.
- The cost of one box with a base area of 32.75 square inches is closest to **$591**.

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17 Jul 2024, 06:28

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Bunuel

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Length = 6 inches
Height = 9 inches

2$ per cubic inch

Base area 24.5 square inches: $440
Base area 32.75 square inches: $590

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17 Jul 2024, 06:29

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Ans: First column : C; second column: E
Cost = $2 per cubic inch
Cube 1: Height = 9 inch; Base area = 24.5 sq inch; Cost = 24.5*9*2= $441 = ~ 440
Cube 2: Height= 9 inch; Base area = 32.75 sq inch; cost = 32.75*9*2 = $589.5 = ~ 590

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