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If x, y and z are consecutive positive integers, and x < y < z, which of the following must be true?

1. z-x = 2

2. xyz is divisible by 6

3. x+y+z divided by 3 is an integer

 

A/ 1 only

B/2 only

C/ 1 and 2 only

D/ 2 and 3 only

E/ 1, 2 and 3

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Choose the word or set of words that, when inserted in the sentence, best fits the meaning of the sentence as a whole.

The actor on the talk show offended the host by first --- him and then refusing to temper his --- remarks.

(A)  insulting…offensive

(B)   praising… indulgent

(C)  flattering… praiseworthy

(D)  scolding… radical

(E)   hitting… abusive

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Previous Questions

In the xy-coordinate system, (√6, k) is one of the points of intersection of the graphs y = x² - 7 and y = -x² + j, where j is a constant. What is the value of j?

A) 5

B) 4

C) 3

D) 2

E) 1

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Below are 5 ways of phrasing the underlined material. Choice A repeats the original phrasing. Select the phrasing that results in the most effective sentence. Please provide supporting reason(s) for your answer.

There are so many erroneous decisions that are made by the committee chair; if I was to suggest an improvement for that committee, it would be to replace her with a more experienced committee member.

A. if I was to suggest an improvement for that committee, it would be to replace her

B. if I was to suggest an improvement for them, it would be to replace her

C. if I were to suggest an improvement for that committee, it would be to replace her

D. if I were to suggest an improvement for them, it would be to replace her

E. if I was to suggest an improvement for it, it would be to replace her

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The sum of the first 100 positive integers is 5,050. What is the sum of the first 200 positive integers?

Answer Choices:

(A) 10,100

(B) 10,200

(C) 15,050

(D) 20,050

(E) 20,100

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Which of the following underlined parts presents a mistake? If the sentence is fine, please select (E) as your answer. Please provide supporting reason(s) for your answer.

Since the endorsement by a political party is no guarantee of (A) suitability for public office, the best way (B) to evaluate candidates (C) is to examine (D) his or her public records.

(E) No error.

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Which of the following statements would provide sufficient data for us to solve the question below? Please provide supporting reason(s) for your answer.

1. What is the perimeter of an isoceles triangle XYZ?
(1) XY = 11
(2) YZ = 15

Answer Choices:
(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are not sufficient.

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