## 1.

The Correct Answer is (C) — If we plug in 1 for x, we get (1 – 1)(1 + 4). This simplifies to (0)(5) = 0.

## 2.

The Correct Answer is (A) — When multiplying two exponential terms with the same base (for example, 25 and 27), the exponents are added (not multiplied). So (B) is incorrect, since 23 × 24 = 27. When an exponential term is itself raised to a power (for example, (26)6), the exponents must be multiplied. So (C) is also incorrect because (26)6 = 236. Finally, 26 + 26 is equal to 2(26) or 21 × 26, which is the same as 27, so (D) is incorrect.

## 3.

The Correct Answer is (C) — If a wren has 5 chicks, she must catch 5 × 8 = 40 insects for them. With the 20 she must catch for herself, she must catch a total of 60 insects. If it takes 1 hour to catch 6 insects, it will take 10 to catch 60.

## 4.

The Correct Answer is (D) — We can rewrite a # 8 = 0 as a2 – 2(8) = 0, or a2 – 16 = 0 (which is the same as expression II). So a2 = 16 and a = 4 (expression III). Since a is squared, a can also equal -4 (expression IV). Expression I would only be true if a = 0.

## 5.

The Correct Answer is (C)B is the set {2, 7, -2, 0, 8} with each number halved, giving us {1, 3.5, -1, 0, 4}. The range is the difference between the smallest and largest elements in the list, in this case -1 and 4. The difference between -1 and 4 is 5.

## 6.

The Correct Answer is (B) — For two hours, the lawyer charges $600. For the next hour, he charges$400, for a total of $1000 for three hours. Since the next hour is free, the lawyer charges$1000 for four hours. $1000/4 =$250.

## 7.

The Correct Answer is (A) — We can rewrite this relationship as 0.5m + 0.5n = 0.75m. Subtracting 0.5m from both sides gives 0.5n = 0.25m. Dividing both sides by 0.25 gives 2n = m, so n is 50% of m.

## 11.

The Correct Answer is (A) — There were 35 sedimentary rocks found below 1000 feet, out of 60 sedimentary rocks total. 35/60 ≈ 58%.

## 12.

The Correct Answer is (D) — Suppose there are only 3 gorillas of each species. If the ages of the 3 lowland gorillas are, for example, 1, 12, and 14, then the median age is 12 (as stated in the question) but the average age is 9, which means (A) and (C) may not be true – and since the question asks which statements must be true, we can eliminate them. Similarly, if the ages of the Cross River gorillas are 1, 2, and 33, the average age is 12 (as stated in the question), but the median age is 2, so we can eliminate (B).

## 13.

The Correct Answer is (D) — Set the equations equal to each other: 2a = 2a + 8. Plugging in 1 for a gives 2 = 10; plugging in 2 gives 4 = 12; plugging in 4 gives 16 = 16.

## 14.

The Correct Answer is (A) — The range of a group is the difference between its largest and smallest numbers – in this case, 13 and 60. To increase the range by 5, we must either add 5 to 60 or subtract 5 from 13. Thus, our options are 65 and 8; only 65 is given as an option.

## 15.

The Correct Answer is (A) — Each point on the graph represents one student, and there are 8 points at and above 3 hours.

## 16.

The Correct Answer is (B) — There are 13 students, so the median is the 7th highest heart rate – in this case, 80.

## 17.

The Correct Answer is (B) — The average heart rate is about 77. The median is 80 (as we found in the previous question). The mode is the value that appears most often, in this case, 80, which appears four times. Given this information, (B) is true: the average heart rate (77) is less than the mode (80). (The range is only 100 – 60 = 40, so (D) is not true).