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

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

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 .

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

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

3,4 ; 3,5 ; 5,4

3*4*5=60

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

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

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.

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)

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.)

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.

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]

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

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

Answer: A
Cheers,
Brent

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