SAT Math Multiple Choice Practice Question 213: Answer and Explanation

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Question: 213

15. The arithmetic mean of four positive integers, a, b, c, and d, is 15. When the largest number is subtracted from the product of the smallest three numbers, the result is 34. If a < b < c < d, which of the following pairs of equations could correctly express the information given?

A. a + b + c + d = 15
bcd - a = 34
B. a + b + c + d = 15
abc - d = 34
C. a + b + c + d = 30
abc - d = 34
D. a + b + c + d = 60
bcd - a = 34
E. a + b + c + d = 60
abc - d = 34

Correct Answer: E

Explanation:

E. The arithmetic mean, also known as the average, is when you add up a bunch of numbers and divide by the number of numbers. So, the arithmetic mean of a, b, c, and d would be . None of the answer choices have fractions like this, so multiply both sides by 4 to get a + b + c + d = 60. The correct answer must be Choice (D) or (E). Next, you want to subtract the largest number from the product of the smallest three numbers. The problem tells you that a < b < c < d, so a is the smallest number and d is the biggest. Therefore, the product of the smallest three numbers is abc, and when you subtract the largest, you get abc - d = 34, Choice (E).

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