Know my ABC's

[Milanproda1]

Hello,

I just signed up for MGMAT and took the initial practice exam. The question I am posting here is from my first exam:

13th Question
Question type: DS
Question name: Know my ABC's
Difficulty: 600-700
Topics Discussed:Basic Equations

If 2 + 5a - b/2 = 3c, what is the value of b?

(1) a + c = 13

(2) -12c = -20a + 4

MGMAT Answer

Solve the original equation for b:

2 + 5a - b/2 = 3c
2 + 5a - 3c = b/2
4 + 10a - 6c = b

Knowing the value of 10a - 6c will allow us to calculate the value of b. So, the rephrased question becomes: "What is 10a - 6c?"

(1) INSUFFICIENT: Knowing the sum of a and c is not enough to determine the value of 10a - 6c. For example, if a = 10 and b = 3, then 10a - 6c = 10(10) - 6(3) = 82. However, if a = 6 and b = 7, then 10a - 6c = 10(6) - 6(7) = 18.

(2) SUFFICIENT: Manipulating the equation gives us the following:

-12c = -20a + 4
20a - 12c = 4
10a - 6c = 2

The correct answer is B.

I became confused when the explanation started substituting 10 for a and b=3. I am not sure how to interpret the problem.

Also, I tried substituting for statement 1, but after reading the explanation decided that I mathematically couldnt substitute because the rephrased question "what is 10a-6c" did not have a value on the other side of the equation.

Sorry for the poor description, but thank you for all the help and suggestions.

[jnelson0612]

Hi there,
Statement 1) says that a + c = 13. The explanation is just showing that we don't really know what a and c are based on this statement. a could be 10 and c could be 3. That would make 10a - 6c equal to 82.
OR
a could be 7 and c could be 6. We can use any values of a and c as long as they add to 13. If a=7 and c=6, then 10a - 6c is 34. So statement 1) is insufficient since there are multiple values for a and c that are possible.

I hope this helps.

[Milanproda1]

Thank you very much for your help, Jaime

[jnelson0612]

My pleasure Milanproda!