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

Question

https://gmatclub.com/forum/download/file.php?id=18839 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 volume.png

Bunuel · Accepted Answer

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.

Answer: A.

BangOn · Answer

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

pavan2185 · Answer

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.

Bunuel · Answer

Real GMAT questions, including 700+ questions, do not require tedious math, so even with some big numbers there would be some shortcut possible

rxn · Answer

What's the rationale behind multiplying all 3?

Bunuel · Answer

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 .

Bunuel · Answer

Similar question to practice: https://gmatclub.com/forum/if-a-rectang ... 56549.html

luckyme17187 · Answer

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

3,4 ; 3,5 ; 5,4

3*4*5=60

torreadortorment · Answer

L^2 * B^2 * H^2 = 3600.

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

mqdn · Answer

https://i.imgur.com/wGoWphA.png 
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.

Milad600 · Answer

My approach is finding the GCF(12,15,20) by using prime factorization= 2^2x3x5=60

Abhishek009 · Answer

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)

ScottTargetTestPrep · Answer

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.

https://i.imgur.com/aMYM7jI.png

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.)

mjawanzee · Answer

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.

Salamander911 · Answer

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

dave13 · Answer

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 ?

Bunuel · Answer

Please try to read the whole thread carefully: https://gmatclub.com/forum/in-the-recta ... l#p1307258

BrentGMATPrepNow · Answer

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

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

Answer: A
Cheers,
Brent

TheNightKing · Answer

dave13 You probably figured it out, I know. I was thinking the same but then you know it is GMAC and they won't mention sides. Instead, it will mention areas and make a simple 600 level question look like a 650 question

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards