Everyday Math Demystified, 2nd edition
Stan Gibilisco
Explanations for Quiz Answers in Chapter 4
1. The fraction 15/10 equals 150/100, while the counting number 1 equals 100/100. If we want to express how much larger 150/100 is (in percentage terms) than 100/100, we should note that the starting value, which forms the basis for comparison, is 100/100. The numerator 150 exceeds the numerator 100 by 50, so the fraction 150/100 exceeds the fraction 100/100 by 50%. The correct choice is C.
2. We have the same numerical values as we did in Problem 1, but this time we must use 150/100 as the "starting point" or basis for comparison. The question is also worded differently, so we had better take care! Instead of asking us to calculate how much of a percentage change we get when we go from one value to another, this question asks us to compare, in percentage terms, one value to another. If we want to express the portion of 150/100 that 100/100 represents (in percentage terms), we must divide 100 by 150 and then multiply by 100. When we do that and round off to the nearest whole-number value, we get 67%. The correct choice is B.
3. In an inversely proportional sequence of ratios, one of the values goes up at the same rate, multiplication-wise, as the other one goes down. Only the sequence in choice B behaves in this manner here. Each time we divide the left-hand quantity by 3, we multiply the right-hand quantity by 3. The correct choice, therefore, is B.
4. You start out with $5000.00, and increase it by exactly 3% each year for 10 years, rounding off to the nearest penny every year. You should multiply the original amount by 1.03 (representing an increase of 3%), and then multiply each succeeding value by 1.03 until you have done a total of 10 multiplication operations. Let's go through the whole process:
  • After one year: $5000.00 x 1.03 = $5150.00
  • After two years: $5150.00 x 1.03 = $5304.50
  • After three years: $5304.50 x 1.03 = $5463.64
  • After four years: $5463.64 x 1.03 = $5627.55
  • After five years: $5627.55 x 1.03 = $5796.38
  • After six years: $5796.38 x 1.03 = $5970.27
  • After seven years: $5970.27 x 1.03 = $6149.38
  • After eight years: $6149.38 x 1.03 = $6333.85
  • After nine years: $6333.85 x 1.03 = $6523.87
  • After 10 years: $6523.87 x 1.03 = $6719.59

The correct choice is A.
5. The Model Y furnace produces 100,000 Btu/h, while the Model X system produces 80,000 Btu/h. When we divide 100,000 by 80,000, we get 1.25. Any ratio in which the left-hand quantity equals 1.25 times the right-hand quantity will, technically, provide a correct answer to this question. All three of the ratios given in choices A, B, and C fulfill this requirement, so they're all correct. The answer is D, "All of the above."
6. This question simply asks us to reverse the ratio from the scenario in Question 5. Any ratio in which the right-hand value equals 1.25 times the left-hand value will work here. Only choice B turns out that way, so that's the correct answer.
7. Your friend's Bluesdale Bank account balance equals exactly eight times her Happyville Bank account balance. You can see this fact when you divide the larger figure (Bluesdale) by the smaller (Happyville):

$2757.28 / $344.66 = 8
= 8/1
= 8:1

The Bluesdale-to-Happyville ratio equals 8:1. The correct choice is B. (You might think for a moment that choice C also works. In fact it would constitute a valid answer to this question, except for one little problem: It's expressed the wrong way around.)
8. We start with two endless repeating decimal numbers, both of which are rational:
  • The first number is 0.555555..., which equals 5/9
  • The second number is 0.777777..., which equals 7/9

When we multiply these two fractions by each other, we get a new fraction (or ratio) in which the numerator equals the product of the original numerators, and the denominator equals the product of the original denominators. Here's the arithmetic:

(5/9) x (7/9) = (5 x 7) / (9 x 9)
= 35/81

Because this new quantity equals the ratio of an integer (in this case 35) to a positive integer (in this case 81), we know that it's a rational number by definition. The correct choice is B.
9. We start with two endless repeating decimal numbers, both of which are rational:
  • The first number is 0.567567567..., which equals 567/999
  • The second number is 0.765765765..., which equals 765/999

If we want to divide the first fraction by the second fraction, we invert the second one and then multiply the two resulting fractions by each other. Therefore, we want to find the product

(567/999) x (999/765)

When we multiply these two fractions by each other, we get

(567/999) x (999/765) = (567 x 999) / (999 x 765)
566, 433 / 764,235

Because this new quantity equals the ratio of an integer (in this case 566,433) to a positive integer (in this case 764,235), we know that it's a rational number by definition. The correct choice is C.
10. In a directly proportional sequence of ratios, one of the values goes up (or down) at the same rate, multiplication-wise, as the other one goes up (or down). Of the four sequences shown here, only sequence C obeys this rule; the left-hand quantity always equals three times the right-hand quantity. Therefore, C is the right choice.