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# In the rectangular solid above, the three sides shown have

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In the rectangular solid above, the three sides shown have [#permalink]

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05 Dec 2012, 09:11
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In the rectangular solid above, the three sides shown have areas 12, 15, and 20, respectively. What is the volume of the solid?

(A) 60
(B) 120
(C) 450
(D) 1,800
(E) 3,600
[Reveal] Spoiler: OA

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Re: In the rectangular solid above, the three sides shown have [#permalink]

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05 Dec 2012, 09:14
10
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Expert's post
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Attachment:
volume.png
In the rectangular solid above, the three sides shown have areas 12, 15, and 20, respectively. What is the volume of the solid?

(A) 60
(B) 120
(C) 450
(D) 1,800
(E) 3,600

Say the dimensions of the rectangular solid are x by y by z, then the volume is xyz.

We are given that:

xy=12;
xz=15;
yz=20.

Multiply all three: (xyz)^2=12*15*20=3,600 --> xyz=volume=60.

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Re: In the rectangular solid above, the three sides shown have [#permalink]

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02 Jun 2013, 07:41
1
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What if the actual test the same questions with very big number? will the same technique hold good? that may take some massive time with bigger numbers.

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Re: In the rectangular solid above, the three sides shown have [#permalink]

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02 Jun 2013, 09:44
1
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Expert's post
pavan2185 wrote:
What if the actual test the same questions with very big number? will the same technique hold good? that may take some massive time with bigger numbers.

Real GMAT questions, including 700+ questions, do not require tedious math, so even with some big numbers there would be some shortcut possible
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Re: In the rectangular solid above, the three sides shown have [#permalink]

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02 Jun 2013, 14:09
4
KUDOS
Attachment:
volume.png
In the rectangular solid above, the three sides shown have areas 12, 15, and 20, respectively. What is the volume of the solid?

(A) 60
(B) 120
(C) 450
(D) 1,800
(E) 3,600

Another approach.
Given L*B = 20 = 5*4 ; L*H = 15 = 5*3 ; B*H=12 = 4*3
So our L = 5 ; B = 4 ; and H = 3

LBH = 60
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Re: In the rectangular solid above, the three sides shown have [#permalink]

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18 Dec 2013, 17:25
Bunuel wrote:
Attachment:
volume.png
In the rectangular solid above, the three sides shown have areas 12, 15, and 20, respectively. What is the volume of the solid?

(A) 60
(B) 120
(C) 450
(D) 1,800
(E) 3,600

Say the dimensions of the rectangular solid are x by y by z, then the volume is xyz.

We are given that:

xy=12;
xz=15;
yz=20.

Multiply all three: (xyz)^2=12*15*20=3,600 --> xyz=volume=60.

What's the rationale behind multiplying all 3?

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Math Expert
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Posts: 42249

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Re: In the rectangular solid above, the three sides shown have [#permalink]

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19 Dec 2013, 01:11
Expert's post
1
This post was
BOOKMARKED
rxn wrote:
Bunuel wrote:
Attachment:
volume.png
In the rectangular solid above, the three sides shown have areas 12, 15, and 20, respectively. What is the volume of the solid?

(A) 60
(B) 120
(C) 450
(D) 1,800
(E) 3,600

Say the dimensions of the rectangular solid are x by y by z, then the volume is xyz.

We are given that:

xy=12;
xz=15;
yz=20.

Multiply all three: (xyz)^2=12*15*20=3,600 --> xyz=volume=60.

What's the rationale behind multiplying all 3?

We need to find the volume, which is xyz. When we multiply we get (xyz)^2, so to get the volume all we need to do is to take the square root from it .
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Re: In the rectangular solid above, the three sides shown have [#permalink]

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21 Jul 2014, 14:58
Bunuel wrote:
Attachment:
volume.png
In the rectangular solid above, the three sides shown have areas 12, 15, and 20, respectively. What is the volume of the solid?

(A) 60
(B) 120
(C) 450
(D) 1,800
(E) 3,600

Say the dimensions of the rectangular solid are x by y by z, then the volume is xyz.

We are given that:

xy=12;
xz=15;
yz=20.

Multiply all three: (xyz)^2=12*15*20=3,600 --> xyz=volume=60.

Similar question to practice: if-a-rectangular-box-has-two-faces-with-an-area-of-30-two-174562.html
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Re: In the rectangular solid above, the three sides shown have [#permalink]

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11 Sep 2014, 05:23
1
KUDOS
Attachment:
volume.png
In the rectangular solid above, the three sides shown have areas 12, 15, and 20, respectively. What is the volume of the solid?

(A) 60
(B) 120
(C) 450
(D) 1,800
(E) 3,600

two side should share the same length
area 12, 15, 20

3,4 ; 3,5 ; 5,4

3*4*5=60

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Re: In the rectangular solid above, the three sides shown have [#permalink]

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28 Dec 2015, 23:26
L^2 * B^2 * H^2 = 3600.

Square both sides and you get LBH = 60 (Remember, volume has to be positive).

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Re: In the rectangular solid above, the three sides shown have [#permalink]

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01 Feb 2016, 03:47
1
KUDOS
Attachment:
volume.png
In the rectangular solid above, the three sides shown have areas 12, 15, and 20, respectively. What is the volume of the solid?

(A) 60
(B) 120
(C) 450
(D) 1,800
(E) 3,600

We could see that the horizontal rectangular is the largest area, so it is 20. The second largest is 15, and the vertical rectangular on the right is 12.
All of the rectangles share side. And the formula for area is l * w. For the smallest rectangular: 12 = 3 * 4, and 15 = 5 * 3, where they share side 3 with each other.
20 = 4 * 5. And the volume for a box is l * h * w = 3 * 4 * 5 = 60

This took me 20 seconds.

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Re: In the rectangular solid above, the three sides shown have [#permalink]

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23 Apr 2016, 05:44
My approach is finding the GCF(12,15,20) by using prime factorization= 2^2x3x5=60

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In the rectangular solid above, the three sides shown have [#permalink]

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23 Apr 2016, 10:28
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My approach is finding the GCF(12,15,20) by using prime factorization= 2^2x3x5=60

Another approach will be -

$$Volume \ of \ a \ Cuboid$$ = $$\sqrt{Area1 * Area2 * Area3}$$

$$Volume \ of \ a \ Cuboid$$ = $$\sqrt{12 * 15 * 20}$$

$$Volume \ of \ a \ Cuboid$$ = $$\sqrt{3600}$$

$$Volume \ of \ a \ Cuboid$$ = $$\sqrt{60}$$

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Re: In the rectangular solid above, the three sides shown have [#permalink]

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01 Jun 2016, 07:38
Attachment:
volume.png
In the rectangular solid above, the three sides shown have areas 12, 15, and 20, respectively. What is the volume of the solid?

(A) 60
(B) 120
(C) 450
(D) 1,800
(E) 3,600

We are given a rectangular solid and also are given areas of three of the sides. Let’s draw the figure out. We label the length, width, and height. We also label each side as side A, side B, and side C.

We see that the area of side A is length times height, that of side B is length times width, and that of side C is height times width.

We are given that the sides have areas of 12, 15, and 20.

Let’s say:

Side A area = 20

Thus we can set up the following equation for area:

length x height = 20

Side B area = 15

Thus we can set up the following equation for area:

length x width = 15

Side C area = 12

height x width = 12

Analyzing the two equations, length x height = 20 and length x width = 15, we see that both 15 and 20 are multiples of 5 and we also see that each equation contains the common term of “length”. Thus, we can deduce that the length could equal 5. When length is 5, we see height is 4, and when length is 5, we see that width is 3. We now have our dimensions for length, width, and height.

length = 5

width = 4

height = 3

Since volume of a rectangular solid = length x width x height, the volume is:

5 x 4 x 3 = 60.

(Note: If we were struggling to know which side, was side A, B, and C, we could have selected those sides in any order and we would have ended up with the same value for the volume. If that were not the case, we would have to have been given more specific instructions about which sides corresponded to which areas.)
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Re: In the rectangular solid above, the three sides shown have [#permalink]

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04 Jul 2017, 05:58
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