Difficult Level Math Question

[glenda.lezeau]

Hi,

I came across this question and I do not know the best and quickest way to solve it. It is labeled as difficult. Any help is appreciated!

[i]Select a single answer[/i]

If 4a-2b-9c = 0, 2a+2b+2c+0, and abc is not equal to 0, then 2c is what fraction of 3a?

A. - 7/4
B. -4/7
C. 4/7
D. 7/4
E. It cannot be determined from the information given.

(Correct Answer: C)

Thanks,
Glenda

[nehaaggarwal_7]

I don't know whether there is any easier way than the following one:
Adding both equations we get:
6a-7c=0 ===> c=6/7a
Now the question is 2c is what fraction of 3a (if u didn't get this you can think like 2 is what fraction of 4.....2=X*4 ===>X=1/2)
i.e. 2c= X*3a
putting value of c
2 * 6/7a = X * 3a
12/7=X*3
X=4/7

I hope you got it...

[glenda.lezeau]

Oh ok. Thank you!!! That really helped better than the other explanation I saw! My only question is...what made you decide to add the equations together?

~Glenda

[nehaaggarwal_7]

Well As the question is about finding a relation between c and a...so we need to perform some operation on the equations so that we can get something in a and c eliminating b......

[glenda.lezeau]

Oh okay. Thank you!!

[esledge]

Hi Glenda,

I agree completely with Neha's comments. I just want to add that the common coefficient, albeit with opposite signs, on the b terms (2b in one equation and -2b in the other) is another clue that adding the equations is convenient here.

Many people routinely solve by substitution out of habit, but look for common coefficients, and you might start noticing cases when adding or subtracting whole equations from one another is faster.

[glenda.lezeau]

Hi,

I just noticed your response. Thanks for the tip! I will look for those like terms!

Glenda

[esledge]

You are welcome!