Everyday Math Demystified, 2nd edition Stan Gibilisco Explanations for Quiz Answers in Chapter 2 1. Statement C does not always hold true. For some even values such as 6, 10, and 14, we get an odd whole number when we cut it in half. However, in other cases we get an even whole number after that operation. For example, if we cut 8 in half we get 4; if we cut 12 in half we get 6; if we cut 16 in half we get 8. The other three statements (given by choices A, B, and D) hold true all the time. The correct choice is C. 2. The number 39 is not prime, because 39 = 13 x 3, a product of primes. When we look at Table 2-1, we can see that the other three numbers given in this question (2, 7, and 37) are all prime. The answer is D. 3. Whenever we cut an odd number in half, we get a fractional quantity that's not a whole number. By definition, we can cut any even whole number in half and end up with another whole number. Also by definition, the odd whole numbers comprise all of those, but only those, that aren't even. The correct choice is B. 4. This question is a bit tricky. At first, you might want to choose D as your answer. Then you should recall that one prime number, 2, is even! If you cut 2 in half you get 1, a whole number. If you cut any other prime in half you get a nonwhole fraction. The correct choice is A. 5. In order to conclusively (mathematicians would say rigorously) prove that two sets of numbers are the same size, we must find a one-to-one correspondence between them. For example, the set of all even numbers and the set of all whole numbers are the same size because (1) for any particular even number, we can generate one unique whole number by cutting that even number in half, and (2) for any particular whole number, we can generate one unique even number by doubling that whole number. The correct choice is C. 6. We can use a calculator to check all four choices here, noting that the forward slash (/) represents division. When we divide 123 by 41 we get 3, so we know that the fraction 123/41 represents a whole number. In each of the other three cases, we fail to get a whole number when we do the division. The correct choice is B. 7. By definition, we call a counting number prime if we can factor it into a product of itself and 1, but not in any other way. The correct choice is A. 8. In order to work out this problem, we must "grind our way" through quite a lot of tedious division operations! Following the process described in the text for determining the prime factors of a large counting number, we find that 3723 = 73 x 17 x 3 so choice A won't work; 3717 = 59 x 7 x 3 x 3 so choice B won't work; 3703 = 23 x 23 x 7 so choice C won't work. By elimination, we conclude that the answer is D. You can (and should) verify the fact that, when you divide 3697 by any prime number smaller than or equal to 61 (the first whole number larger than the square root of 3697), you never get a whole number. Once you've gone through that process, you can have confidence that D is indeed the right choice. 9. If we cut each of the three pies into thirds, we'll get 3 x 3 = 9 identical pieces of pie, but we have 18 people! Choice A won't work. If we cut each pie into fourths, we'll get 3 x 4 = 12 indentical pieces; choice B won't work. If we cut each pie into fifths, we'll get 3 x 5 = 15 identical portions, so choice C doesn't go far enough. However, if we cut each pie into sixths, we'll get 3 x 6 = 18 identical slices of pie. Choice D is the answer. 10. Each of the 18 portions represents 1/6 of a pie. If two of our guests decide that they don't want their dessert and give their portions back to us, we'll find ourselves with 2/6 of a pie to eat later as "leftovers." If we put those two 1/6-of-a-pie slices together into their original pie pan, we'll have 1/6 + 1/6 = 2/6 = 1/3 of a pie to enjoy tomorrow (or maybe later tonight if we get hungry). The answer is C.