SSAT Math Question 337: Answer and Explanation
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Question: 337
6. The heights of a basil plant and mint plant have a ratio of 5:4. If the basil plant grew 2 inches and 2 inches was cut off the top of the mint plant, the ratio of their heights would be 2:1. How much taller is the basil plant than the mint plant?
- A. 2 inches
- B. 4 inches
- C. 6 inches
- D. 8 inches
Correct Answer: A
Explanation:
The answer is A
Because a ratio can be expressed in reduced form, let x be the factor by which the initial ratio must be increased to arrive at the actual heights. That is, the basil plant was 5x inches, and the mint plant is 4x inches. The basil plant grew to 5x + 2 inches, while the mint plant was cut to 4x - 2 inches. As these heights can be reduced to a ratio of 2:1, set up a proportion: 
. Now cross multiply: 5x + 2 = 2(4x - 2). Distribute the 2: 5x + 2 = 8x - 4. Subtract 5x from both sides and add 4 to both sides: 6 = 3x. Divide both sides by 3: x = 2. Therefore, the basil plant was initially 5 × 2 = 10 inches, and the mint plant was initially 4 × 2 = 8 inches. The difference is 2.
You can attack this problem using guess-and-check. While a ratio can be expressed in a red