Proportions

A proportion is represented by two ratios which are equated to each other. In GMAT Quant questions, we would be presented with one variable and three values for proportions. Reduce the ratio in either side to the lowest possible value before cross-multiplying.

For example , a proportion can be presented as a/b = c/d or a:b = c:d

So as per our strategy reduce a/b to the smallest possible fraction

ex: 24/10 should be translated to 12/5

GMAT Proportion: A football field is 9600 square yards.  If 1200 pounds of fertilizer are spread evenly across the entire field, how many pounds of fertilizer were spread over an area of the field totaling 3600 square yards?

A. 450
B. 600
C. 750
D. 2400
E. 3200

The key word here is “spread evenly”. This implies that the relationship of fertilizer per square foot is uniform, and you can set equal the relationship of the wholes to the relationship of the parts.

A/F = 9600/1200 = 3600/x

Clearly, we can eliminate the zeros on the left side:

9600/1200 = 3600/x

96/12 = 3600/x

Then we can divide 96/12:

8 = 3600/x

Here, we can still reduce left-to-right, by canceling 4 in both:

2 = 900/x

Oh wait! There’s more! Both 2 and 900 are divisible by 2!

1 = 450/x
x = 450

It DOES NOT matter whether you start top-bottom or left-right, so long as you are reducing by the same factor. Also, start with small numbers. No need to go for the biggest common factor. You’ll eventually work your way down as the numbers progressively get easier. For this question we could have started by canceling 9600 and 3600 in the numerators, which are both divisible by 400 to get:

24/1200 = 9/x.