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Reverse factoring

Problem Solving — algebra and arithmetic
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by cmr209 » Tue Sep 08, 2009 8:54 pm
Ok, I'm getting frustrated here.

So it has been said that the GMAT rewards for mental flexibility, yet I'm struggling with this reverse factoring.

Example:

Solve for "k" in terms of "m"

m - 3 = k/4

k = 4(m - 3) = 4m - 12.

Using the foil method I see how that is the answer, however, How do not understand how I get to the first step of breaking apart the fraction k/4 to mean k = 4(m - 3)?

This is how I approached the problem on my first attempt:

m - 3 = k/4

m = k/4 + 3

m = k/4 + 3/1

m = k/4 + 12/4

m = k12/4

m = k3

What am I doing wrong?
Please advise.
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Source: — Quantitative Reasoning |
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Re: Reverse factoring

by bharathh » Tue Sep 08, 2009 9:13 pm
cmr209 wrote:Ok, I'm getting frustrated here.

So it has been said that the GMAT rewards for mental flexibility, yet I'm struggling with this reverse factoring.

Example:

Solve for "k" in terms of "m"

m - 3 = k/4

k = 4(m - 3) = 4m - 12.

Using the foil method I see how that is the answer, however, How do not understand how I get to the first step of breaking apart the fraction k/4 to mean k = 4(m - 3)?

This is how I approached the problem on my first attempt:

m - 3 = k/4

m = k/4 + 3

m = k/4 + 3/1

m = k/4 + 12/4
m = k12/4

m = k3


What am I doing wrong?
Please advise.

Marked in red.

You did fine until then.

Since you have a common denominator now. Add the two numerators. (k+12)/4 = m
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by cmr209 » Tue Sep 08, 2009 9:29 pm
bharathh,

I don't see how that comes to = 4m - 12?

I redid the problem at m = k/4 + 12/4

m = k + 12
           4

m = k + 3
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by bharathh » Tue Sep 08, 2009 9:56 pm
Ok I just read what you were asking for in the post.

Solve for k in terms of m

So first up that means you need k = some eqn with m in it.

You are given m - 3 = k/4

There really is only step to this.

Multiply both sides by 4... When you perform a mathematical operation to both sides of the equation, you keep the equation unchanged.

So 4*(m-3) = 4*k/4

The four multiplied to k/4 makes it k

so you are left with k = 4(m-3)

now solve it using the FOIL method.
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by bharathh » Tue Sep 08, 2009 10:08 pm
Check out this site. I would highly recommend you go through this before attempting any GMAT questions

https://serc.carleton.edu/mathyouneed/Equation.html
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by cmr209 » Tue Sep 08, 2009 10:27 pm
Nice!!

Thank you!

I now see I have to remember the basic step of when I'm trying to get rid of a division I can multiply the denominator by the other side. You've helped me realize my mistake!

Again, thank you!
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by grockit_jake » Sun Sep 13, 2009 9:03 am
m = (k + 12) / 4

4m = k + 3

You have to remember to multiply left AND right by the exact same thing. Also, when you have an addition on the top dividing a term on the bottom, you can split it up but you can't divide only 1 of the terms.
Jake Becker
Academic Director
Grockit Test Prep
https://www.grockit.com
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