There are 50 students in Mrs. Harrison's honors

[thouldin]

The Princeton Review
"1,012 GMAT Practice Questions"
Standard Deviation Drill (page 238)
-data sufficiency question

6. There are 50 students in Mrs. Harrison's honors English class. All students receiving a grade of 84 or higher on the final exam will be recommended for advancement to AP English. How many of Mrs. Harrison's students will be recommended for advancement?

(1) 34 of the students got between 62 and 84 on the final exam.

(2) The average score on the final exam was 73.

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Book Answer: (A)
"To find the number of students who will be recommended for advancement, you need the average score and the standard deviation. Statement (1) does not give this to you directly, but it tells you that 34/50, of 68% students got between 62 and 84 on the final exam. That means that 16% got below 62 and 16% got above 84. 16% of 50 is 8, so 8 students will be recommended for advancement. Eliminate choices (B), (C), and (E). By itself, statement (2) does nothing to tell you how many students will be recommended for advancement, so the answer is choice (A)."

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For one, the question does not state that the grades are normally distributed, so you cannot apply the standard deviation rules. Correct?

Assume the data is normally distributed, which was the author's intention. Statement (1) does say that 68% (34/50) of the students received grades between 62 and 84. I understand that 68% comprises one standard deviation above and below the mean, but I see no reason for these 34 students to be the middle 34 students of the 50 since the mean is unknown.

If 34 students received grades between 62 and 84, why cannot the other 16 grades ALL be above 84? Or all be below 62 (remember we don't know the mean)? Therefore from what I can tell, statement (1) is insufficient. Once statement (1) and (2) are considered together the mean and standard deviation are known, so the information would be sufficient making choice (C) the correct answer.

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Did I come to the correct conclusions? Thanks so much for your assistance!

[esledge]

I can find no flaw in your thinking. For the problem as written, the answer should be (E). If we were given the constraint that the test scores were normally distributed, the answer should be (C), as you say.