# Lesson: Factoring – Greatest Common Factor

## Comment on Factoring – Greatest Common Factor

### Hi Brent,

Hi Brent,

Thank you.

A certain list consists of 21 different numbers. If n is in the list and n is 4 times the average (arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list?

1/20

1/6

1/5

4/21

5/21

### Here's my full solution:

Here's my full solution: https://gmatclub.com/forum/a-certain-list-consists-of-21-different-numbe...

Aside: In the future, please post your questions under the related video lesson.
This question is about averages (means). So, it would have gone well under the Statistics lesson on Averages/Means

Cheers,
Brent

### Hi Brent,

Hi Brent,
Could you please explain how to factorise an expression into two binomials or into polynomial. In the video you have shown only how to factorise monomial.

### The above lesson on Greatest

The above lesson on Greatest Common Factor factoring is the first of 4 lessons on factoring.
You'll find what you need in the next 3 lessons.

Cheers, Brent

### Brent, can you help me

Brent, can you help me understand the thought process that would lead one to think of factoring out the ∆.OOO + O. ∆∆∆ in this question?
I follow your explanation, but I don't think I would have considered factoring as a kick-off right off the bat (even when trying to rephrase the target question).
https://gmatclub.com/forum/if-o-and-are-digits-what-is-the-value-of-ooo-o-315327.html

Here's a rough play-by-play summary of my thought process:

When I saw that I need to find the sum ∆.OOO + O.∆∆∆, I first thought about how that sum might look.
If we line up the two numbers as though we're going to add them in the way we learned in school, we get:
∆.OOO
O.∆∆∆

At this point, it seems like the sum MAY be a number in which all of the digits are the same.
If I felt uncertain of this, I could always test a case or two:
If ∆ = 3 and O = 2, we get: 3.222 + 2.333 = 5.555
If ∆ = 2 and O = 7, we get: 2.777 + 7.222 = 9.999
If ∆ = 1 and O = 6, we get: 1.666 + 6.111 = 7.777

ASIDE: Of course, this changes if ∆ and O add to a value that's greater than 9.

At this point, I failed to recognize that all of the sums are multiples of 1.1111
In fact, the sum seems to always equal to (∆+O)(1.111)
Recognizing this relationship would have saved me a bit of time. Instead, I followed a different path...

I noticed that ∆.OOO = ∆ + O(0.111)
Likewise, O.∆∆∆ = O + ∆(0.111)

So, when we add them, we get 1.111(∆) + 1.111(O), which is the same as writing 1.111(∆ + O)

The rest of the solution can be found here: https://gmatclub.com/forum/if-o-and-are-digits-what-is-the-value-of-ooo-...

Does that help?

### Ok, so for this question, I'm

Ok, so for this question, I'm not sure how I wrote like this thus concluded that the answer should be C

https://gmatclub.com/forum/if-o-and-are-digits-what-is-the-value-of-ooo-o-315327.html

This is my factor function (∆ * O)(1.111+1.111), can you see why I'm doing this? I must have confused myself...

### I'm not sure how you got: (∆

I'm not sure how you got: (∆ * O)(1.111 + 1.111)

Did you take 1.111(∆) + 1.111(O) and simplify it to get (∆ * O)(1.111 + 1.111)?
If so, that's where your error occurred.

Instead, we can take 1.111(∆) + 1.111(O) and factor out 1.111 to get: 1.111(∆ + O)

Here's my full solution: https://gmatclub.com/forum/if-o-and-are-digits-what-is-the-value-of-ooo-...