## 1.

The Correct Answer is (C) — If the length of a list of numbers is even, the median is the mean of the middle two numbers – in this case, 3 and 6.

## 2.

The Correct Answer is (C) — There are 12 boys in a group of 12 + 18 = 30. 12/30 reduces to 2/5.

## 24.

The Correct Answer is (C) — If we take y – 4 = 4x + 3y and solve for y, we find that y = -2 – 2x. Taking 4x + 3y = -(9 – x), rearranging and simplifying gives us x + y = -3. Plugging in for y gives x – 2 – 2x = -3, and simplifying gives x = 1. Plugging this in to y = -2 – 2x, we find that y = -4.

## 25.

The Correct Answer is (C) — Bees are in the larval stage for 1 out of the 2 weeks of their development (we don’t count the two weeks of adulthood as “developing”), so selecting 200 at random should give ½ × 200 = 100 bees in the larval stage.

## 26.

The Correct Answer is (C) — We can write $\inline&space;\frac{c&space;+&space;d&space;+&space;e}{3}&space;=&space;a$, or c + d + e = 3a. The average of b, c, d, and e is $\inline&space;\frac{b&space;+&space;c&space;+&space;d&space;+&space;e}{4}$, which we can rewrite as $\inline&space;\frac{b&space;+&space;3a}{4}$.

## 27.

The Correct Answer is (D) — If we draw a line perpendicular to the side of either of the pieces of wood, we can form a triangle (where the hypotenuse is one side of the parallelogram and the short side is 4 cm, the width of the piece of wood). By using opposite angles, we can deduce that this is a 30-60-90 triangle, meaning that the hypotenuse is twice the length of the short side. We can repeat this with the other piece of wood to confirm that all four sides of the parallelogram are 8 cm long. We now have two sides (a and b) and an internal angle (θ) of the parallelogram. Given this information, the formula for the area of a parallelogram is A = ab sin θ. Plugging in, we get A = 8 × 8 × 0.5, or 32.

## 28.

The Correct Answer is (65) — To simplify this expression, we can take the natural logarithm of both sides so that the exponents become coefficients. Using the identity log(ab) = b log(a), we can write 32x + 2 as log(3)(2x + 2) and 27x – 2 as 3log(3)(x – 2), since 27 = 33. Plugging these values back in, we have log(3)(2x + 2) = 3log(3)(x – 2). Dividing out log(3) leaves us with 2x + 2 = 3(x – 2); solving for x gives us x = 8. 82 + 1 = 65.

## 29.

The Correct Answer is (5) — The price of the tickets can be written as 5x + 30y = 185, where x is the number of children and y is the number of adults. The number of family members can then be written as x + y = 12. So x = 12 – y, and plugging this in to the first equation gives 5(12 – y) + 30y = 185. Solving for y gives y = 5. (To check our answer, we can write 5(7) + 30(5) = 185, which is correct).

## 30.

The Correct Answer is (3.4) — If the sonar wave moves at 340 meters per second, and is detected by the submarine 20 seconds after it was emitted, the wave traveled 340 m/s × 20 s = 6800 m round-trip. However, this includes both the distance to and the distance from the lighthouse, so we divide by 2 to get 3400 m, or 3.4 km.

## 31.

The Correct Answer is (11.8) — The sonar signal takes $\inline&space;\frac{2040&space;\text{&space;m}}{340&space;\text{&space;m}/\text{s}}&space;=&space;6&space;\text{&space;s}$ to reach the island. In 6 s, the Wayfarer has traveled 6 m/s × 6 s = 36 m, putting it 2004 m away from the island. If we take the island as our origin, we can represent the position of the Wayfarer as y = -6x + 2004, where x is the time in seconds since the signal reflected off the island (-6 is the speed of the submarine with respect to the island and 2004 is its distance from the island). We can similarly represent the position of the returning sonar wave as y = 340x. Setting these equations equal to each other will give us the time at which the signal reaches the submarine: -6x + 2004 = 340x. Solving for x and rounding to the nearest tenth gives us 5.8. We then add this to the 6 seconds elapsed from the time the signal was emitted to the time it reflected off the island.