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Sample Excerpt 3 from Guerrilla Tactics for the SAT™*: Secrets and Strategies the Test Writers Don’t Want You to Know
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A Sample Trick with Ratios
Strategy 27. For some questions, the writers will offer an answer choice that reads: "it cannot be determined from the information given." Although many students select this answer for tough questions (which they cannot solve), it is usually a trap. In rare situations, however, it IS the correct answer. Consider the following examples.
a. 3:2
Example 2: When American Idol auditions were held in New York City, the judges allowed an equal number of men and women to take the stage. At the end of a grueling day, the ratio of female to male singers who advanced to the next round was 3 to 2. At the very end of the day, the judges had a change of heart and agreed to add one additional female singer and one additional male singer to the group that advanced. If the total number of singers who advanced was 32, what was the original number of men chosen to advance?
At first glance, these problems are identical. However, if If you read the last line carefully, they are as different as night and day. Although you can multiply and divide ratios (or parts of them), you cannot simply add or subtract from them, UNLESS you know something about the quantities that they represent. In Example 1, the SAT writers do not tell us anything about the original number of singers (male or female) or how many of them advanced to the next round. We simply have a ratio. Hence, the correct answer is e, we cannot determine the final ratio without additional information. However, Example 2 is a different story, because we have been given enough information to solve the problem. In the original scenario, the 3:2 ratio of female to male singers applied to a population of 32 - 2, or 30. Hence, the original 30 selected to advance included 18 women and 12 men (a 3:2 ratio). The correct answer for the original number of men chosen to advance is c, 12.
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