GRE Ratio And Proportion

Hello, I had applied for the GRE exam and I am not strong in the Ratio and Proportion. Please provide me some problems with solution on the topic.

[Shaleen]

Hello, here I am providing you the problems and solutions of the Ratio and Proportion for the GRE exam as under:

Calculate x if 4:15 = 16:x

Solution

The equation is written in a more obvious form:

Cross multiply to get 4x = 16(15) therefore, x = 60

Example 2
The ratio of two numbers is 4:1, and their sum is 40. Find the two numbers.

Solution

This is expressed mathematically as:

x/y = 4/1 = 4
x + y = 40.

The first equation can be written in the form x = 4y. This is substituted into the second equation to yield 4y + y = 40. 5y = 40, therefore, y = 8.

Since x = 4y, we find that x = 4(8) = 32. The two numbers are 8 and 32.

Also, in a ratio, the sum of the ratio (in this case 5) will be multiplied by some number in order to get it to the real total. In this problem, 5 is multiplied by 8 to get 40. You can now use the multiplier for each part of the ratio to find out their actual value. In this case, x, or 4, is multiplied by 8 to get 32. And y is multiplied by 8 to get 8. In this way, if you know the ratio and one "real" value, you can find the multiplier and figure out the rest of the values in the equation.



Example 3
If an airplane travels 1,200 miles in 2.5 hours, how far will it travel in 10 hours?

Solution

This represents a direct proportion: both the distance traveled and time increase. Consequently, if we let x = distance the airplane will travel, we have:

12,000 = 2.5x
x = 4,800 miles


Example 4
What is the ratio of 2/3 to 5/4?

Solution

The ratio is (2/3)/(5/4), which is equal to 2/3 × 4/5 = 8/15.

Example 5

If 100 dollars can buy 0.07 grams of a rare radioactive material, how many grams can you buy with 106 dollars?

(A) 7
(B) 70
(C) 700
(D) 7000
(E) 70000
Solution

Set up the question as a proportion

100/.07 = (106)/x
cross multiply and solve for x. We get:

100x = .07(106)
x = .07(104) = 700
The correct answer is C.

Below is an example of a direct proportion:

x/5 = 8/20


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


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. 15/2400 = 25/x; 15x = 60,000; x = 4,000. (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:

15/24 = 100/x; x = 160. 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.