**Problem Solving**

Solve t h e problem and indicate the best of the answer choices given.

** Numbers: **All numbers used are real numbers.

** Figures: **All figures accompanying problem solving questions are intended to provide information useful in solving t h e problems. Figures are drawn as accurately as possible. Exceptions will be clearly noted. Lines shown as straight are straight, and lines that appear jagged are also straight. The positions of points, angles, regions, etc., exist in t h e order shown, and angle measures are greater t h a n zero. All figures lie in a plane unless otherwise indicated.

**Data Sufficiency**

Each data sufficiency problem consists of a question and t w o statements, labeled (1) and (2), which contain certain data. Using these data and your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), decide whether the data given are sufficient for answering the question and then indicate one of t h e following answer choices:

- Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- EACH statement ALONE is sufficient.
- Statements (1) and (2) TOGETHER are not sufficient.

**Note:** In data sufficiency problems that ask for t h e value of a quantity, the data given in the statements are sufficient only w h e n it is possible to determine exactly one numerical value for t h e quantity.

**Example:**

**Explanation:** According to statement (1) PQ — PR; therefore, ΔPQR is isosceles and y = z. Since x + y + z = 180, it follows that x + 2y = 180. Since statement (1) does not give a value for y, you cannot answer the question using statement (1) alone. According to statement (2), y = 40; therefore, x + z = 140. Since statement (2) does not give a value for z, you cannot answer the question using statement (2) alone. Using both statements together, since x + 2y —180 and the value of y is given, you can find the value of x. Therefore, BOTH statements (1) and (2) TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.

**Numbers:** All numbers used are real numbers.

**Figures:**

- Figures conform to the information given in the question, but will not necessarily conform to the additional information given in statements (1) and (2).
- Lines shown as straight are straight, and lines that appear jagged are also straight.
- The positions of points, angles, regions, etc., exist in t h e order shown, and angle measures are greater than zero.
- All figures lie in a plane unless otherwise indicated.

**Reading Comprehension**

Each of the reading comprehension questions is based on the content of a passage. After reading the passage, answer all questions pertaining to it on the basis of what is stated or implied in the passage. For each question, select the best answer of the choices given.

**Critical Reasoning**

Each of the critical reasoning questions is based on a short argument, a set of statements, or a plan of action. For each question, select the best answer of the choices given.

**Sentence Correction**

Each of the sentence correction questions presents a sentence, part or all of which is underlined. Beneath the sentence you will ?nd ?ve ways of phrasing the underlined part. The ?rst of these repeats the original; the other four are different. Follow the requirements of standard written English to choose your answer, paying attention to grammar, word choice, and sentence construction. Select the answer that produces the most effective sentence; your answer should make the sentence clear, exact, and free of grammatical error. It should also minimize awkwardness, ambiguity, and redundancy.

Read the statement and the instructions that follow it, and then make any notes that will help you plan your response.

LOADING...