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# In the rectangular solid above, the three sides shown have areas 12

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Manager
Joined: 02 Dec 2012
Posts: 177
In the rectangular solid above, the three sides shown have areas 12  [#permalink]

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05 Dec 2012, 09:11
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Difficulty:

35% (medium)

Question Stats:

72% (01:24) correct 28% (00:54) wrong based on 1329 sessions

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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

Attachment:

volume.png [ 7.95 KiB | Viewed 19376 times ]
Math Expert
Joined: 02 Sep 2009
Posts: 50042
In the rectangular solid above, the three sides shown have areas 12  [#permalink]

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05 Dec 2012, 09:14
12
8

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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Manager
Joined: 15 Apr 2013
Posts: 72
Location: India
Concentration: Finance, General Management
Schools: ISB '15
WE: Account Management (Other)
Re: In the rectangular solid above, the three sides shown have areas 12  [#permalink]

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02 Jun 2013, 07:41
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.
Math Expert
Joined: 02 Sep 2009
Posts: 50042
Re: In the rectangular solid above, the three sides shown have areas 12  [#permalink]

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02 Jun 2013, 09:44
1
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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Joined: 27 Feb 2012
Posts: 121
Re: In the rectangular solid above, the three sides shown have areas 12  [#permalink]

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02 Jun 2013, 14:09
4
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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Posts: 11
Re: In the rectangular solid above, the three sides shown have areas 12  [#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?
Math Expert
Joined: 02 Sep 2009
Posts: 50042
Re: In the rectangular solid above, the three sides shown have areas 12  [#permalink]

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19 Dec 2013, 01:11
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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Posts: 50042
Re: In the rectangular solid above, the three sides shown have areas 12  [#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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Posts: 115
Re: In the rectangular solid above, the three sides shown have areas 12  [#permalink]

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11 Sep 2014, 05:23
3
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 areas 12  [#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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Posts: 9
Re: In the rectangular solid above, the three sides shown have areas 12  [#permalink]

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01 Feb 2016, 03:47
1
1
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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Joined: 20 Jul 2015
Posts: 1
Re: In the rectangular solid above, the three sides shown have areas 12  [#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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Re: In the rectangular solid above, the three sides shown have areas 12  [#permalink]

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23 Apr 2016, 10:28
1
1
My approach is finding the GCF(12,15,20) by using prime factorization= 2^2x3x5=60

Milad600 Welcome to GMATCLUB !!

Another approach will be -

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

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

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

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

Hence answer will be (A)
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Re: In the rectangular solid above, the three sides shown have areas 12  [#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.

The answer is A.

(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 areas 12  [#permalink]

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17 Feb 2018, 21:01
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

Finding the LCM of all three areas will provide you the answer.

LCM of 12,15,20 = 60

I have tried it on similar questions and this method works.
Intern
Joined: 05 Dec 2017
Posts: 5
Re: In the rectangular solid above, the three sides shown have areas 12  [#permalink]

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07 Mar 2018, 11:45
Prime factorize the three areas we will gest 3*4,3*5,4*5 we know this is a rectangle therefore take all the different digits 3*4*5=60 [a]
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Re: In the rectangular solid above, the three sides shown have areas 12  [#permalink]

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22 Mar 2018, 11:08
Bunuel wrote:

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.

hello i am curious to know why the answer is 60 and not 3600 ?

isnt the volume formula = lenght*width*height ? why it doesnt work here ?
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Posts: 50042
Re: In the rectangular solid above, the three sides shown have areas 12  [#permalink]

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22 Mar 2018, 11:10
dave13 wrote:
Bunuel wrote:

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.

hello i am curious to know why the answer is 60 and not 3600 ?

isnt the volume formula = lenght*width*height ? why it doesnt work here ?

Please try to read the whole thread carefully: https://gmatclub.com/forum/in-the-recta ... l#p1307258
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Re: In the rectangular solid above, the three sides shown have areas 12  [#permalink]

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30 Apr 2018, 10:08
Top Contributor

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

Attachment:
volume.png

Let the dimensions (length, width and height) of the box be x, y and z
Volume = (length)(width)(height) = xyz

So, our GOAL is to find the value of xyz

The three sides shown have areas 12, 15, and 20, respectively
If one (rectangular) side has area 12, then we can say that xy = 12
If one (rectangular) side has area 15, then we can say that xz = 15
If one (rectangular) side has area 20, then we can say that yz = 20
[notice that we've accounted for all 3 dimensions]

Now, we'll apply the following property: If a = j, and b = k and c = l , then abc = jkl

So, we can write: (xy)(xz)(yz) = (12)(15)(20)
Simplify: x²y²z² = 3600
Rewrite left side as: (xyz)² = 3600
Take the square root of both sides to get: xyz = 60

So, the volume = 60

Cheers,
Brent
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# In the rectangular solid above, the three sides shown have areas 12

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