A tip for those looking for an easier way to do specific Math problems

So I know alot of you guys get stumped by questions like:

The “c” cars in a car service use a total of “g” gallons of gasoline per week. If each of the cars uses the same amount of gasoline, then, at this rate, which of the following represents the number of gallons used by 10 of the cars in 3 weeks?

Well first, look for what you are solving for, which is gallons per car. Because of this, we KNOW the answer must be a division with g in the numerator and c in the denominator. So you can immediately rule out any that are solely multiplication or have c in the numerator and g in the denominator. Then, this will usually get your answer choices down to either two or three, which you can just plug in numbers to see which is correct.

Well, this is just unit analysis. The correct answer obviously must contain the correct units. But yes, it does help eliminate some choices sometimes.

What is the answer though?

@amdcous actually, here is my question for you: why must the answer contain g/c when the answer is looking for the number of gallons? Why can’t it just contain g? However you are right that it contains g/c.

@ethiolita The right answer is 30g/c. One car uses g/c gallons per week, or 3g/c gallons in 3 weeks. Then 10 cars use 30g/c gallons in 3 weeks.

(You all knew I would say this but…)

Yes, a lot of people do have trouble with this kind of question. But your proposed method will often only narrow down the choices…and then you suggest making up numbers. Why not just start with made-up numbers?

This time, I picked c= 5 and g = 100. So each car uses 20 gallons per week and 60 in 3 weeks. And 10 cars will use 600 gallons.

If you put my numbers into @MITer94 's answer, you will see that they match.

And by the way, it looks like the new SAT is going to be vulnerable to this evasion here and there as well.