Proportions are extremely common on the GRE. If you don’t have a strong grasp of them, and you are busy trying to figure out combinations/permutations or probability, stop. Focus your attention on mastering proportions before moving on to more tertiary concepts.

So let’s start basic. Proportions can be broken up into two groups: direct proportions and indirect proportions. In this post I am going to focus on direct proportions. They are more intuitive than indirect proportions and are also the more common on the GRE.

## Direct Proportion

Below is an example of a direct proportion:

[pmath]x/5 = 8/20[/pmath]

To solve for x we cross multiply, giving us: [pmath]20x = 40[/pmath]; [pmath]x = 2[/pmath].

This is a direct proportion because as the ‘5’ becomes larger (namely it quadruples to become 20) the x also gets larger (it quadruples to become 8). That is both sides are getting larger.

I can almost guarantee that you will not see such a straightforward equation on the GRE Quant section. Instead, you will be given either a word problem or a graph and you will have to translate the information into an equation like the one above.

Let’s take a look at two problems:

In 2004, 2,400 condos sold, 15% of the total housing units sold that year. If 25% of the homes sold in 2004 were four-bedroom houses, then how many four-bedroom homes sold in 2004?

(A) 3,600

(B) 4,000

(C) 4,200

(D) 4,800

(E) 6,000

**Explanation**

Here we want to set up an equation. [pmath]15/2400 = 25/x[/pmath]; [pmath]15x = 60,000[/pmath]; [pmath]x = 4,000[/pmath]. (B).

Some things to note: you can take off the last two zeroes in 2,400 to get 24, a step which will make the math easier. Remember to bring the two zeroes back, which makes sense: x =40, is clearly too low and not amongst the answer choices.

Speaking of answer choices, notice that 25% is less than double of 15%. Therefore, the number of four-bedroom houses sold has to be less than twice the number of condos sold. (D) and (E) cannot be answer. (A) 3600 is only 50% greater than 2,400, so it is probably too low as well. Elimination, esp. if you are short on time, or getting tangled up in the calculation can be very effective.

Now let’s put a spin to this question. Nothing too tricky; indeed you should be able to solve this using the method above.

In 2004, 2,400 condos sold, 15% of the total housing units sold that year. How many units sold in 2004 were not condos?

(A) 16,000

(B) 13,600

(C) 12,400

(D) 11, 200

(E) 8,600

**Explanation:**

To approach this question, a good idea is to find the number of units in the total market. Then to find the number that are not condos subtract the condos from the total.

My reason for this approach is it is easier to do the math when we are working with 100 vs. 85 (which would be the percent of home that are not condos).

The solution is as follows:

[pmath]15/24 = 100/x[/pmath]; [pmath]x = 160[/pmath]. Remember to add the two zeroes: 16,000. Now we have to subtract the total condos (2,400) to find the number of units that are not condos: 16,000 – 2,400 = 13,600.

## Takeaway:

Setting up a proportion is essential to solving a range of GRE math questions. Make sure you can confidently and quickly solve this question type before more on to more challenging – but less common – concepts.

P.S. Ready to improve your GRE score? Get started today.

This is what i’m afraid of in gre. For a non-US person, its hard to figure out how the question construes its meaning to the data given. Here the condo’s sentence was baffling to many of these students.

Actually I’m talking about many of the questions I came across in various books that needs to have what you call a US social context like “a double burger” and so on. How would you come to resolve this issue?

Hi there,

I can definitely see your concern, but I will say that for most problems on the GRE you should be able to answer the question without a US social context. Typically, problems will contain terms that are familiar, or at least be presented in a way that you will be able to draw from the context. Although this may seem intimidating, the best action you can take is to continue doing more practice problems, as well as reading articles (as described in this blog post) to practice active reading and vocab for the Verbal section. By taking these steps, you can get more exposure to potential unfamiliar terms, as well as get great practice for the exam.

Chris,

Could you explain me the proportion part of both the questions, i am confused.

Hi Siddharth,

So what I’m doing is taking 15% of a number and figuring out what a 100% of that number is. Let’s call that number x, for now. When I increase it by finding what 100% of that number is, I come up with y.

15/x = 100/y

The good news is we don’t need to have an x because the problem has already given us the x: 2,400.

So we get 15/2400 = 100/y.

Hope that makes sense!

Hi Chris,

I still din’t get the first equation that you set up!

How did you interpret the question as :

15/2400=25/x

??

Can you pls explain?

I actually get confused with such sums! 🙁

Hi Anki,

Sure! So…think of it this way: the two fractions equal each other, in the same way that 1/2 = 2/4, or 1/5 = 3/15. For the latter, let’s say we wanted to solve ‘x’, as in 1/5 = 3/x. Notice, the ‘x’ has to be three times larger than the ‘5’, just as the 3 is three times larger than the 1. Typically, we just use cross multiplication to solve this.

The ’15’ stands for the condos, which total 2,400. We want to see how many 4-bedroom houses there are if 25% of the total are 4-bedroom houses. That’s why we put the ‘x’ below the 25%.

Hope that helps!

I get it now,does this statement “2,400 condos sold, 15% of the total housing units sold that year”, mean that 2400 sold condos were 15% of the total housing units sold?

Yes, that is the correct interpretation :).

HI, I don’t understand problem 1. Please explain it. How can you set a proportion such that 15 percent is to 25 percent as 2400 is to x? shouldn’t the equation be:

2400+(25/100)(15/100)T/ T = 15/100?

please tell me where I am wrong.

Thanks.

Hi Chris

Thanks for the problems and explanation.

For the 2nd problem it is also possible to subtract the % at first ie 100-15=85% and make the equation like

15/2400=85/x

x= 13600

Anyway, can we expect more difficult problem than these? In fact both problems were easy for me & could solved it in one try.

Regards

Farooqui

Hi Farooqui,

In terms of difficulty, there will definitely be tougher ones than these. On the whole, though, these are pretty typical GRE problems on the lower end of the spectrum. The key is working through them accurately and quickly, so as to leave time for the harder problems. Looks like you are on track :).