New SAT Math Problem Solving and Data Analysis

Covering 29% of the concepts on the test, this section is the second most common on the test, after Heart of Algebra. This is a part of the New SAT that has definitely been fleshed out since the old SAT. Keeping in line with real world scenarios, many problems will ask you to infer information based on a study with any number of participants. This is actually something that the SAT has never done before and is a welcome change, given that you’ll be learning lots about cause and effect and inferential statistics in college. Ratio, Proportion, Units, and Percentage This question type shouldn’t come as a surprise since it has probably been part of your math courses for the last five years (yep, you most likely went over this stuff, in some form, all the way back in early middle school). I’ll start with ratios. Ratios A good way to think of ratios is apples and oranges. Say I have two oranges and three apples, the ratio of oranges to apples is 2:3. Seems straightforward. What if I have four apples and 6 oranges? If you answered of the total (2 + 5 + 7 = 14). You think you got that? Well, here’s a question on ratios: Easy Question The ratio of shirts to shorts to pairs of shoes in Kevin’s closet is 5 : 2 : 3. If Kevin owns 10 shirts, how many pairs of shoes does he have to give away so that he ends up having the same number of shorts as he does pairs of shoes? A) 1 B) 2 C) 4 D) 5 Explanation Okay, this question is slightly evil, since shorts sounds like shirts and it is easy to get the two mixed up when you are reading fast. So always pay attention, even on easier questions! Since we know that Kevin has 10 shirts, and that 10 therefore corresponds to the number ‘5’ in the ratio, that the actual number of shorts, shirts, etc., he owns is double the number in the ratio. Thus, he owns four shirts and six pairs of shoes. So he’ll have to give away two pairs of shoes so that he’ll have the same number of shoes as he does shorts. Answer: (B). On some questions, you’ll have to figure out the proportion between two different units. Easy Question Niles takes an interstate road trip over the course of two days. If he covers 610 miles in nine hours the first day and 300 miles in four hours on the second day, what is high average speed per hour? A) 55 miles per hour B) 65 miles per hour C) 70 miles per hour D) 75 miles per hour Explanation To figure out the average speed of the entire trip, divide the total distance by the total number of hours. The handy equation D = rt, where D is total distance, r is rate, and t is time, will make this easier. D = 910, r = ?, t = 9 + 4 = 13 hours. 910 = 13r, r = 70, answer C). Difficult Question A cartographer owns a square map in which one inch corresponds to 7/3 of a mile. What is the area of the map in square inches if the map covers a territory of 49 square miles? SPR: ______________ Explanation We know that 7/3 of mile = one inch. We also know that the area is 49 square miles, meaning that each side = 7: √49 = 7). To find how many inches correspond to 7 miles, we set up the following equation: 7 = 7/3x, x = 3 Here is the little twist that you want to watch out for. The question is asking for square miles in inches, so we have to take 3^2 , which equals 9. Another possible question type, and one that most are familiar with and probably dread, is the percent question. To reduce something by a certain percentage, either turn that percent into a ratio over 100 or convert the percent into a decimal by moving the point back two spaces. For example, 2,000 D) 176,000 Difficult In a popular department store, a designer coat is discounted 20% off of the original price. After not selling for three months, the coat is further marked down another 20%. If the same coat sells online for 2,000. Answer C). 2. When you are not given a specific value for a percent problem, use 100 since it is easiest to increase or decrease in terms of %. 1st discount: 20% off of 100 = 80. 2nd discount: 20% off of 80 = 64. Online, the coat sells for /50 3) .375, 375/1000 or 3/8 4) 1.25, 5/4 next - Problem Solving and Data Analysis Part II