A common concept tested on the GRE are direct proportions – as one thing increases another increases.The safe way to solve direct proportions – though not always the fastest, as we’ll see in a moment – is to set up a proportion and then cross-multiply to find the solution.

Let’s take a look at the following problem:

Steven gets 20 miles for every gallon. If he fills up with 5 gallons, how many miles can he drive?

(A) 4

(B) 20

(C) 40

(D) 50

(E) 100

Solution

So the more gallons Mike has, naturally the farther he can drive. Or think of it this way – as the gallons increase so to does the distance. To solve this question we can set up a simple proportion. In the numerator we are going to have the number of gallons and in denominator the number of miles Steven can travel on those gallons.

\(1/20 = 5/x\)

x in this case is the number of miles Steven can drive on 5 gallons.

Cross-multiplying we get x = 100. So Mike can drive 100 miles (E) on 5 gallons.

That’s a pretty basic example. So let’s make things a little more difficult.

One helping of a Yummy chocolate corresponds to 3/7 inches and contains 80 calories. How many helpings of chocolate has Bubba eaten if he has consumed 1120 calories of chocolate?

(A) Too many

(B) 3

(C) 6

(D) 7

(E) 14

Solution:

Obviously there are two answers here, but let’s discount (A) from the get go. So how do we arrive at the other answer?

Again, let’s set up the proportion:

\({3/7} / 80 = x/1120.\)

x will give you the number of inches, which is not the same as the number of helpings. Remember one helping is equal to 3/7 of an inch. Solving for x we get 6. (I would use the calculator function on the new GRE).

So how many helpings are there in 6 inches? Well, time for another proportion:

\({3/7}/1 = 6/x\)

The numerator represents the inches and denominator, where we’ve placed the x, represents the helpings.

Cross-multiplying we get x = 14, the number of helpings (E).

At this point I would use the calculator function on the new GRE…unless you notice that 1120 is double 560, which is 80 x 7. Therefore 80 x 14 = 1120.Or 14 helpings.



That is not to say proportions are always time-consuming. I could have set up the proportion:

1/80 = x/1120, where the numerator is the number of helpings and denominator the number of calories and gotten the answer more quickly than setting up two proportions.

Either way the correct answer is (E).

Practice Questions

1. Bob’s pickup truck averages 20 miles/gallon. If Bob fills the 12-gallon gas tank to capacity, how many miles can he travel once the ratio of unused gas to used gas is 3:1?

(A) 60 miles

(B) 140 miles

(C) 170 miles

(D) 180 miles

(E) 240 miles



2. On a square map one inch is equal to 4/3 miles. If the map covers 64 square miles, then what is the perimeter of the map in inches?

(A) 6 inches

(B) 8 inches

(C) 16 inches

(D) 24 inches

(E) 32 inches



3. For every 1.5 miles Katie runs she drinks 7 oz. How many pints of water should she bring with her if she plans on running 9 miles (8 oz = 1 pint)?

(A) 5 ¼

(B) 6

(C) 7 ½

(D) 8

(E) 9

Answers and Explanations

1. If Bob uses x gallons of gas, then we can set the ratio up like this:
(12-x)/x = 3/1
12-x = 3x
12 = 4x
3 = x

Then plug that into our ratio:
3x : 1x
3(3) : 1(3)
9 : 3

So, to have a 3:1 ratio of unused gas to used gas, wed still have 9 gallons remaining:
3 x 20 = 60 gallons, Answer (A).

2. Each side of map corresponds to 8 miles. If one inch corresponds to 4/3 of a mile, then 8 = 4/3x, x = 6, where x represents the number of inches. The question asks for the perimeter, which 6 x 4 = 24, Answer (D).

3. 1.5/7 = 9/x, x = 42. The question is asking for number of pints, so we divide 42, the number of ounces, by 8, giving us 5 1/4 pints, Answer (A).

Takeaway

When dealing with direct proportions set up a quick proportion and cross-multiply to solve.