Practice question #1: D Explanation: If the starting salaries were 0 (or anything close to 0), then the $10,000 difference between raises in year 2 would dwarf the 10% difference in year 1, and A would end up with a higher salary. But if the starting salaries were high (a million dollars, say), then the 10% difference in year 1 would dwarf the $10,000 difference in year 2, and B would end up with a higher salary. Practice question #2: B Explanation: We need to solve the ratio X miles / 6 inches = 700,000 calories / 250 calories. Write this as (5280X feet) / (.5 feet) = 700,000 calories / 250 calories, or 5280X / .5 = 700,000 / 250. Solving, we get X = (700,000 / 250) (.5 / 5280) = .265, which is about 1/4. Practice question #3: D The population increased by 11.4 million minus 9 million, or 2.4 million. This represents a proportional increase of 2.4 million / 9 million, or 0.2667, or 26.67%. However, the denominator (9 million) has only one significant digit, so the 2.4 / 9 has only one significant digit, and we must round 26.67% to 30%. Recall that one is not supposed to round intermediate steps. If you rounded 2.4 million down to 2 million before dividing by 9, you would get 0.2222, and then rounding again (using one significant digit), you would get 20%, which is not as good an approximation to the true answer as 30%. Practice question #4: D Explanation: $400 / $20 = 20 = 2000%. Practice question #5: B Explanation: Assume a population of 10,000 men. Of these men, 5% (= 500) have prostate cancer and the rest (= 9500) don't. Of the 500 who have prostate cancer, 95% (= 475) will test positive the rest (25) will test negative. Of the 9500 who don't have prostate cancer, 90% (= 8550) will test negative, and the rest (950) will test positive. Thus, out of the 475+950 = 1425 men who test positive, only 475 actually have prostate cancer. 475/1425 = .33 = 33%. Practice question #6: C Explanation: When you put your money in the Cassidy bank for a year, it gets multiplied by 1.12; when you put your money in the Dillinger bank for a year, it gets multiplied by (1.03)^4. So, if you put your money in each bank for a year, at the end of two years it will have been multiplied by 1.12 x (1.03)^4, under both scenarios. Practice question #7: D Explanation: By the Savings Plan Formula (with A = $1000, APR = 12%, n = 12, and Y = 1/4, you must deposit $1000 x (0.01)/(1.01^3-1) = $330 per month. Practice question #8: B Explanation: If we plug into the Loan Payment Formula (P = unspecified, APR = 0.12 for Frankie and 0.06 for Johnny, n = 12, and Y = 15 for Franie and 30 for Johnny), we see that Frankie's monthly payment equals P times (0.12/12)/[1-(1+0.12/12)^(-12*15)], or P times 0.012, while Johnny's monthly payment equals P times (0.06/12)/[1-(1+0.06/12)^(-12*30)], or P times 0.006.