Ratios and Proportions on the GMAT

A ratio expresses the relationship between two or more things. A proportion is a relationship that is formed by setting two ratios equal. Learn how to solve proportion problems using equivalent ratios on the GMAT….like a rockstar on this Learnboard!

Once you’ve reviewed the board, try this Data Sufficiency problem on your own:

For each month, the number of accounts, a, that a certain salesman has contracted that month is directly proportional to his efficiency score, e, which is directly proportional to his commission rate, c. What is a if c = 3.0?

(1) Whenever c = 4.0, e = 0.3

(2) Whenever c = 6.0, a = 80

Explanation:

It will be helpful to first note that because a is directly proportional to e, which is in turn directly proportional to c, a is then directly proportional to c. To say that a is directly proportional to c is just to say that there is a constant k such that ck = a, or, perhaps more simply, that there is a fixed ratio between a and c. A statement, or set of statements, will be sufficient if and only if it determines that ratio.

Statement (1): From this, the proportional relationship between e and c can be determined. However, a is directly proportional to e, and nothing is said about that relationship; therefore, the value of a when c = 3.0 cannot be found; NOT sufficient.

Statement (2): This gives you the ratio you want. You don’t need to actually calculate the value of a if c = 3.0. You just need to know that it’s possible. Don’t believe me? Because a is directly proportional to c: a/c = 80/6.0. Since the question asks for the value of a when c = 3.0, divide the numerator and denominator each be 2. a = 40. Or, if you’re determined to cross multiply: substitute the given value for c: a/3.0 = 80/6.0. By cross multiplication, 6a = 240. Therefore, a = 40; SUFFICIENT. The credited response is B.

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