## 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, $2x&space;=&space;5y&space;\rightarrow&space;2x&space;\times&space;4&space;=&space;5y&space;\times&space;4\rightarrow&space;8x&space;=&space;20y$ And in the second, $2x&space;=&space;5y&space;\rightarrow&space;2x&space;\times&space;4&space;=&space;5y&space;\times&space;4\rightarrow&space;8x&space;=&space;20y$ Since 20y = 20y, then 8x =15z, so the ratio of x to z is 8:15. The correct answer choice is A.

## 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.