SAT Math Multiple Choice Question 22: Answer and Explanation

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Question: 22

2. If xy < 0, which of the following must be true?

I. x + y = 0

II. 2y - 2x < 0

III. x2 + y2 > 0

  • A. I only
  • B. III only
  • C. I and III
  • D. II and III

Correct Answer: B


B A question with unknown variables indicates a good place to plug in. You need numbers for x and y that will give you a negative product. Try x = 1 and y = -2. If you plug these into the statements in the Roman numerals, you find that (I) is false, but (II) and (III) are true. You can eliminate any answer choice that contains (I). This leaves (B) and (D). Now try different numbers to see if you can eliminate another choice. If you try x = -1 and y = 2, you find that (II) is false and (III) is still true. This leaves you with (B) as the only correct answer.

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