Answers and explanations

Quiz I

1. B is correct. The question asks for the greatest value, so you want the number farthest to the right on a number line. The two absolute values convert to 7.7 and 4.5. Of all five numbers, 7.7 is the greatest, so B is the best answer.

Quiz II

1. E is correct. Adding two negative numbers will just result in an even smaller (further to the left) negative number. So m + n < 0 and I is true. You know that a negative multiplied by a negative results in a positive number. So mn > 0 and II is true. This also means that mn is greater than any negative number, including n. Therefore mn > n and III is true. So the answer is E.

2. D is correct. You know that an odd integer multiplied by an odd integer results in an odd integer. So vw is odd and you can eliminate A. An odd integer plus an odd integer results in an even integer. So v + w is even, but v + w + 1 is odd and you eliminate B. Dividing an odd integer by an odd integer gives you either an odd integer, such as 15/5=3, or a non-integer, such as 17/5=3 2/5. So eliminate C. An even number times an odd is even, so 2v is even. Adding an even to an odd is odd, so 2v + w is odd and you should cross off E. As we saw earlier, v +w is even and multiplying by 2 keeps it even. (Even if v + w were odd, multiplying by 2 would make it even.) So D is the best answer.

III. Playing a trick with numbers