●Question 1. Sentence Correction

Direction: Correct the underlined part

Part of the proposed increase in state education spending is due to higher enrollment, since the number of students in public schools have grown steadily since the mid-1980’s and, at nearly 47 million, are at a record high.

A. enrollment, since the number of students in public schools have grown steadily since the mid-1980’s and, at nearly 47 million, are at
B. enrollment, with a number of students in public schools growing steadily since the mid-1980’s and, at nearly 47 million, reaching
C. enrollment: since students in public schools have grown steadily in number since the mid-1980’s and, at nearly 47 million, have reached
D. enrollment: the number of students in public schools has grown steadily since the mid-1980’s and, at nearly 47 million, has reached
E. enrollment: students in public schools have grown steadily in number since the mid-1980’s and, at nearly 47million, are at

●Question 2. Critical Reasoning

The traditional treatment of strep infections has been a seven-day course of antibiotics, either penicillin or erythromycin. However, since many patients stop taking those drugs within three days, reinfection is common in cases where those drugs are prescribed. A new antibiotic requires only a three-day course of treatment. Therefore, reinfection will probably be less common in cases where the new antibiotic is prescribed than in cases where either penicillin or erythromycin is prescribed.
Which of the following, if true, most strengthens the argument?

A. Some of the people who are allergic to penicillin are likely to be allergic to the new antibiotic.
B. A course of treatment with the new antibiotic costs about the same as a course of treatment with either penicillin or erythromycin.
C. The new antibiotic has been shown to be effective in eradicating bacterial infections other than strep.
D. Some physicians have already begun to prescribe the new antibiotic instead of penicillin or erythromycin for the treatment of some strep infections.
E. Regardless of whether they take a traditional antibiotic or the new one, most patients feel fully recovered after taking the drug for three days.

●Question 3. Data Sufficiency

Directions: In this problem, a question is followed by two statements containing certain data. You are to determine whether the data provided by the statements are sufficient to answer the question. Choose the correct answer based upon the statement’s data and your knowledge of mathematics.

If r,s and t are different positive integers, what is the median of r,s and t?
1) r+s+t=6
2) rs=2

A. statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question
B. statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question
C. both statements taken together are sufficient to answer the question, but neither statement alone is sufficient
D. each statement alone is sufficient
E. statements 1 and 2 together are not sufficient, and additional data is needed to answer the question

●Question 4. Problem Solving

In arranging alphabet letters, CIRCLE, how many times does at least one letter stand between C and C?
A. 180 B. 200 C. 210 D. 240 E. 250


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●Answer to Q1: D
In A, the subject ‘the number’ should be connected with the verb ‘has’, not ‘have’. And ‘students’ in B as well as in C can’t be modified by ‘reaching’ and ‘have reached’ in terms of the logical meaning. In E, the meaning of the sentence ‘students are at a record high’ is awkward. So, the answer is D.

●Answer to Q2: E
To strengthen the argument, each answer choice should assure that most patients who take traditional antibiotics such as penicillin or erythromycin stop using those drugs within just three days. Although the answer choices of A, B, C, and D are irrelevant or are adversely weakening the statement, only E is exactly pointing out the reason why most patients stop taking traditional antibiotics or the new one within three days.

●Answer to Q3: D
1) because r,s and t are different positive integers, r=1,s=2,r=3, the median is 1/2, sufficient 2) r=1, s=2, because for all t, the median is 1/2, sufficient, therefore the best answer is D.

●Answer to Q4: D
CIRCLE—(CC)IRLE=6!/2!-5!=240, therefore the best answer is D.