Answer: D.Discussed at: 47. FractionsThe ratio of two positive numbers is 3 to 4. If k is added to each number the new ratio will be 4 to 5, and the sum of the numbers will be 117. What is the value of k?A. 1B. 13C. 14D. 18E. 21Answer: B.The ratio of two positive numbers is 3 to 4 --> , for some positive integer .If k is added to each number the new ratio will be 4 to 5 --> --> --> .The sum of the numbers will be 117 (I believe it means that the sum of the numbers after we add k to each) --> --> --> as from above --> --> .Discussed at: 48. Word Problem / PercentBefore being simplified, the instructions for computing income tax in country R were to add 2 percent of one’s annual income to the average (Arithmetic mean) of 100 units of country R’s currency and 1 percent of one’s annual income. Which of the following represents the simplified formula for computing the income tax, in country R’s currency, for a person in that country whose annual income is I. Tax is the sum of the following:2 percent of one's annual income - ;The average (arithmetic mean) of 100 units of country R's currency and 1 percent of one's

annual income - ..Answer: C.Discussed at: 49. Rate ProblemCircular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute, and gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 6 more revolutions than gear P? Note that we are given revolutions per minute and asked about revolutions in seconds. So we should transform per minute to per second.Gear P makes 10 revolutions per minute --> gear P makes 10/60 revolutions per second;Gear Q makes 40 revolutions per minute --> gear Q makes 40/60 revolutions per second.Let be the time in seconds needed for Q to make exactly 6 more revolutions than gear P --> --> .Discussed at: 50.If k is an integer, and 35^2-1/k is an integer, then k could be each of the following, EXCEPT From the answer choices only is not a factor of numerator, hence in case , won't be an integer, hence k can not be 16.Discussed at: