Question Explanations For

Problem Solving and Data Analysis (Ratios, Rates, and Proportions)

1.

The Correct Answer is (B) — If the rectangle becomes a square by doubling x and tripling y, this means the new width is equal to the new height. In other words, 2x = 3y. Divide by 2 on both sides to isolate x to get x = (3/2)y, choice B.

2.

The Correct Answer is (A) — We can solve this problem by utilizing using the shared variable in the two equations provided. Both equations share the variable y, so we can find the ratio of x to z if we set the y values equal to one another. From both equations, we can create 20y. In the first, And in the second, Since 20y = 20y, then 8x =15z, so the ratio of x to z is 8:15. The correct answer choice is A.

3.

The Correct Answer is (C) — The sale price of the guitar is 80 x 0.9 = 72. Remember that instead of multiplying 80 by 10% (0.10) and then subtracting that value from 80, we can accomplish this all in one step by multiplying 80 by 90% (0.90). Antony pays 8% tax on this reduced price, so in total he pays 72 x 1.08 = $77.76. The correct answer choice is C.

4.

The Correct Answer is (B) — If the Monarch butterflies travel an average of 5 miles per hour for 12 hours each day, they are traveling 60 miles per day. According to the diagram, the Monarchs need to travel 620 miles, so it will take them 620/60 = 10.33 which rounds to 11, days to reach their destination.

5.

The Correct Answer is (C) — If the store owner wants to make a 10% profit on the CDs, she needs to sell each CD for 12 x 1.10 = 13.2 dollars each. Since she sells her CDs for 20% off the display price, we can find the display price through the following: 0.8x = 13.2, therefore x =16.5. The correct answer choice is C.

6.

The Correct Answer is (D) — In order to solve this problem, we need to first calculate the number of questions she answered correctly per exam: 1st exam = 0.85 x 20 = 17, 2nd exam = 0.93 x 40 = 37.2, 3rd exam = 0.91 x 60 = 54.6, 4th exam = 0.97 x 80 = 77.6. In sum, this means she scored 17 + 37 + 54.6 + 77.6 = 186.4 of 200 total questions correctly. This means she answered 186.4/200 = 93% of the questions correctly. The correct answer choice is D.

7.

The Correct Answer is (B) — The total tonnage of defective nails is 120 x 0.04 = 4.8. Similarly, the total tonnage of defective screws is 72 x 0.06 = 4.32. In order to find the total percent defective of both nails and screws, we need to divide the sum of their total tonnage of nails and screws by the total tonnage of nails and screws that is produced: (4.8 + 4.32)/((30 + 90) + (18 +54)) = 4.75% The correct answer choice is B.

8.

The Correct Answer is (8) — In order for Mark to travel 120 miles, his car needs 120/36 = 3.33 gallons. Gas costs $2.40 per gallon, so we can find his total cost of gas by multiplying these two numbers to get $8.

9.

The Correct Answer is (6/17) — If the ratio of purple to black is 12:7 and the ratio of purple to red is 4:5, then there must be 15 red buttons in the jar: a purple:red ratio of 12:15, which matches 4:5. We know there are 12 purple among 12 purple + 7 black + 15 red = 34 total. 12/34 = 6/17. You may leave fractions unsimplified on the SAT.

10.

The Correct Answer is (4) — If Lily, Arjun, and Emily can file 3 papers every 4 seconds, this means 2/8 + x/4 + 4/16 = 3/4 Find a common denominator (4) and solve for x: x =1(you don’ t need to cross-multiply this one). Since Arjun can file 1 paper per 4 seconds, it would take him 60 x 4 = 240 seconds or 4 minutes to file 60 papers.