SAT Math Multiple Choice Practice Question 544: Answer and Explanation
1. If x and y are integers such that 4x – 8 > 0 and 4y + 8 < 0, then which of the following must be true?
A. xy is even.
B. xy is odd.
C. xy is negative.
D. xy is positive.
E. xy is equal to zero.
Correct Answer: C
C Let's start by figuring out what the values of x and y could be. You know that 4x – 8 > 0. If you add 8 to each side of the equation, you get 4x > 8, which means that x > 2. So x could be 3, 4, or any integer larger than 2. Likewise, you know that 4y + 8 < 0. If you subtract 8 from each side of this equation, you get 4y < –8, which means that y < –2. So y could be –3, –4, or any integer less than –2. Neither x nor y can be zero, so the product xy cannot be zero. This means you can eliminate E. And because you don't know whether x and y are odd or even you can also eliminate A and B. You do know, though, that x will always be positive and y will always be negative, so whatever numbers x and y are, you know their product will always be negative.