ISEE Mathematics Achievement Question 324: Answer and Explanation

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Question: 324

8. The sum of three positive integers is 9 and their product is 24. If the smallest of the integers is 2, what is the largest?

  • A. 4
  • B. 6
  • C. 8
  • D. 9

Correct Answer: A

Explanation:

A This question gives a fair amount of information in the question, that the smallest of the three integers is 2, the sum of 2 + x + y = 9, and the product of 2xy = 24. Simplify these equations first and then use PITA to solve. Subtract 2 from either side of the sum to find that x + y = 7, and divide by 2 in the second equation to find that xy = 12. Now Plug In, starting with the largest number to find the largest number as efficiently as possible. Eliminate (C) and (D) right away since 8 or 9 added to another positive integer cannot equal 7. Try (B): Plug In 6 to get 6 + y = 7, so y would have to equal 1. This cannot be true, however, since the smallest integer has to be 2. Eliminate (B). Choice (A) is the only answer left, so it must be correct. Stop work and move on! If you have time later to check, you'll see that if you Plug In 4 that 4 + y = 7 means that y = 3. These are both larger than 2, the smallest number. Do these numbers work in the second equation? Yes! 3 × 4 = 12. The correct answer is (A).

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