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GRE Math: Direct Proportions

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:
9 x 20 = 180 gallons, Answer (D).

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).



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

By the way, students who use Magoosh GRE improve their scores by an average of 8 points on the new scale (150 points on the old scale.) Click here to learn more.

29 Responses to GRE Math: Direct Proportions

  1. Queque January 3, 2015 at 6:51 am #

    Sorry to keep nagging on the same issue but in question 1, since there are still 9 gallons remaining, should the answer not be 20*9=180 instead of 3*20=60?

    • Chris Lele
      Chris Lele January 7, 2015 at 12:18 pm #

      Hi Queque,

      Your interpretation is correct. That is a typo. I amended it in the comments section but forgot to in the explanation. Sorry for any confusion. The answer is 180.

      • Aditi July 13, 2016 at 8:59 am #

        Hi Chris-

        I’m confused. In your earlier comments you stated that the answer is 60 and now you’re saying that the answer is 180. I interpreted the question to be asking how many miles would he have driven to get the tank to the ratio of 3:1. Any insights would be helpful! Thanks!

        • Magoosh Test Prep Expert
          Magoosh Test Prep Expert July 13, 2016 at 10:01 am #

          60 was incorrectly identified as the right answer in the text of the post. But 180 actually is the correct answer.

          As for the way the ratio works, you’re close on how the ratio of 3:1 should be used in the problem… but you’re not quite using that ratio correctly. The wording in the problem is a little tricky, so let’s look at some important keywords again:

          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

          I’ve put the important words in italics. What the problem is asking for is the number of miles Bob can drive without refueling, AFTER the gas tank has already reached a ration of 3 parts unused gas to 1 part used gas. This would be 180 miles, because at an unused to used gas ratio of 3:1, Bob would have 9 gallons of unused gas that he could still burn through. And 9 X 20 = 180.

          Since the question focuses only on what might happen after the gas tank reaches n unused fuel/used fuel ration of 3:1, exactly how many miles Bob had to drive before the ratio got to 3.1 is not as important, and is not the needed answer. That being said, if you did calculate how many miles Bob would have driven to get the tank to 3:1, 60 miles would be the correct answer.

  2. Nitish July 7, 2013 at 8:41 am #

    For that 2nd ques :

    in the solution u have said one side is 8 miles … so is it due to the following fact :

    The map covers 64 sq miles therefore 64^2=8*8*8*8

    therefore one side =8 miles (as square has 4 sides) ??

    i’m not quite sure about it please tell me

    • Chris Lele
      Chris Lele July 8, 2013 at 2:28 pm #

      Hi Nitish,

      So it looks like the part that you got confused on is the 64 square miles. This is not the same as 64^2. 64 square miles is the result of 8 miles x 8 miles (or in this case the sides of the square map).

      Hopefully that helps clear things up :)!

      • Nitish July 9, 2013 at 7:38 am #

        OK i was actually confused with that conversion

        Thanks a lot 😀 !!

        • Chris Lele
          Chris Lele July 9, 2013 at 1:13 pm #

          You are welcome :)!

  3. siddharth mehra June 5, 2013 at 10:27 pm #

    can u tell me how in 2 nd question we concluded that 8 miles corresponds to 1side??

  4. Arpita August 22, 2012 at 6:57 pm #

    Hi Chris,

    I wanted to ask if unit conversions such as oz to pints is usually given on the test. Are there some commonly occurring ones that we should just know?

    Also, is Kaplan Quant too easy in comparison to what shows up on the test?

    And thanks for this great website!

    • Chris Lele
      Chris August 24, 2012 at 12:11 pm #

      Hi Arpita,

      Thanks for the kudos!

      As for the measurements, the test will provide the conversions. Nonetheless, I think it is always a good idea to remember some of the more basic conversions (just in case ETS changes its mind, though a highly doubt it will).

      1 Pint = 16 oz.
      1 Yard = 3 ft.

      In general, as these aren’t international units, I can’t imagine ETS not providing the conversions :).

  5. Aditya July 16, 2012 at 8:45 am #

    Hey Chris,

    I must admit that you are doing a fabulous job, and I will recommend all my friends to refer your blog. My GRE is just one day away and I am kinda nervous and excited. Hope it all goes well.

    Thanks once again. 🙂

    • Chris Lele
      Chris July 17, 2012 at 8:56 pm #

      Thanks for the kind words, Aditya :).

      Best of luck on the test, and let us know how it goes!

  6. Craig July 14, 2012 at 2:33 pm #

    Chris, when we do percent problems with sales items,etc. When the proportion is made if the perent decrease is say 70 percent. For the percent part of the proportion do er put .70, 70 itself, .30 or 30. I have seen it done many different ways. Hw can I tell which goes to which? Thanks so much.

    • Chris Lele
      Chris July 17, 2012 at 8:59 pm #

      A percent decrease of 70 percent is equivalent to .3. To illustrate, if you have a shirt that is 70% off an original price of $100, then it will be .3 the amount, or 30 dollars.

  7. Ad July 14, 2012 at 10:57 am #

    Hi Chris
    I have a small doubt..would be glad if you could clarify. In data interpretation questions, if the answer one gets doesn’t match the choices then should one go in for the upper approximation or the lower one?(percentage problems in particular) Also, what should be done for absolute number problems in general?

    • Chris Lele
      Chris July 17, 2012 at 9:00 pm #

      Yes, definitely approximate on Data Interpretation. Indeed some questions will specifically ask you to do so.

      As for you second question, do you mean absolute value?

  8. Jesse July 11, 2012 at 10:47 pm #


    I need some help my friend. I need to take the GRE in roughly 2.5 weeks! I need the best crash course…study outline possible. I’ve been doing quite a bit of research, and Magoosh seems like the best place for my business by far.

    Please give me your best recommendations and resources and that’s the regime I’ll endure.

    I appreciate what you and your team do and am grateful for any advice you can offer.

    Thank you!


    • Chris Lele
      Chris July 17, 2012 at 9:03 pm #

      Hi Jesse,

      Over the next 2.5 weeks, use Magoosh to its full extent – lesson videos, questions, ebooks, blogs. Make sure to take a practice test from ETS:

      Also, make note of your weak areas and work on them so they become your strong areas. A regime of 3-4 a day should help improve your score in the short time you have left.

      Good luck, and don’t hesitate to ask any more questions :).

  9. Emily July 10, 2012 at 4:00 pm #

    Unrelated, unfortunately:

    Is there a video lesson outlining special properties of triangles and inscribed angles that make them similar? I have seen a few questions here and in the Manhattan books that require you to know things like “two inscribed angles that share a chord are the same size” but I have yet to find these properties written anywhere. Unfortunately, there’s also so much review of very basic information that sorting through the videos for this is really frustrating.

    Also, since a related issue occured above, I would like to recommend that you transcribe your video lessons. As as ESL teacher, I can tell you that this tedious practice can be enormously helpful to non-native speakers and learners like myself who learn most effectively through reading. That said, I have so-far been very impressed with the level of clarity of speech in the videos.

    • Chris Lele
      Chris July 11, 2012 at 10:16 pm #

      Hi Emily,

      As for as some of the lesser known geometry rules I do not think they are all covered in the videos. For instance, the chord one you mentioned above is pretty random – I can only think of one question I’ve seen in all my test prep days that tests that. Often you still derive the information by looking at the figure.

      As for the transcriptions that is some helpful advice, especially for non-native speakers. We’ll look at user feedback and be more attuned when students tell us when they have listening problems (we’ve had a few). If such a reaction amongst users becomes more frequent, we might consider this option.

      Thanks for the recommendation!

  10. David July 9, 2012 at 3:02 pm #

    I’m with the other posters. I’m confident that if question #1 survived ETS’s statistical screening, the correct answer would be (A).

    • Chris Lele
      Chris July 11, 2012 at 10:11 pm #

      Yes, I made a small typo there – basically I mixed up the used and unused gas myself :). Sorry for any confusion!

  11. Prasanth July 8, 2012 at 11:59 pm #

    The question is “how may miles can he travel once the ratio of used gas to unused gas is 3:1?”
    You calculated “x” which is 9 (used gas) and the rest 3 (unused gas)
    So like Esteban said it i too calculated for the 3 gallons.
    Can you please explain how did you interpret this problem?

    • Chris Lele
      Chris July 9, 2012 at 3:19 pm #

      Hi Prasanth,

      Sadly, I mixed up ‘used and ‘unused.’ Sorry for any confusion; you’re interpretation is correct.

  12. Esteban July 5, 2012 at 9:37 am #

    When you say “once the ratio of used gas to unused gas is 3:1” I thought that we should have calculated the miles once we had 25% left in the tank… Maybe it’s because I’m non-native in English speaker but I still don’t get the difference in the wording of the problem.

    • Sam July 7, 2012 at 11:51 am #

      I am a native english speaker and I agree with Esteban. I thought the question was asking how many miles were driven using ONLY the last 3 gallons of fuel.

      • Chris Lele
        Chris July 9, 2012 at 3:18 pm #

        Hi Sam,

        It has nothing to do with your speaking skills. It is totally my fault. I, the native speaker, got mixed up by my own problem.

        Sorry for any confusion :).

    • Chris Lele
      Chris July 9, 2012 at 3:14 pm #

      Yes, you are totally right :). I must have fooled myself on my own problem. But the remaining gas is 3 gallons. I will change the question to read: ‘unused to used’.

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