DS question from princeton

[rakaisraka]

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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Hi rakaisraka,

This question can be dealt with in a couple of different ways - if you're comfortable with the concept of 'averages', you might be able to answer this question on a 'conceptual' level with very little 'math.' Here's how you can TEST VALUES, and use a little logic, to get to the solution:

We're told that there are 50 students in a class. We're asked for the number of students who scored 84 or higher on the final exam.

Fact 1: 34 of the students scored between 62 and 84.

IF....
ALL 34 of these students scored 80, then none of them got 84 or higher. That leaves us with 16 OTHER students, but we don't know how ANY of them scored. It's possible that ALL 16 scored 84 or higher (then the answer to the question is 16), but it's also possible that ALL 16 scored lower than 62 (then the answer to the question is 0).
Fact 1 is INSUFFICIENT

Fact 2: The average score on the final exam was 73.

This means that (73)(50) = 3650 total points were scored

IF....
25 students scored 72 and 25 students scored 74, then the average is 73 (and the answer to the question is 0).

IF...
1 students scored 84, then the other 49 students accounted for the remaining 3566 points (and the answer to the question is 1).
Fact 2 is INSUFFICIENT

Combined, we know...
34 of the students scored between 62 and 84.
The average score on the final exam was 73 (so 3650 total points were scored)

IF....
34 students scored 70, then the other 16 students had to account for the remaining 1270 points

IF....
1 scored 100, and the other 15 scored 78 (the answer to the question is 1)
2 scored 100, and the other 14 scored the remaining 1070 points (the answer to the question is 2)
Combined, INSUFFICIENT.

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

[Max@Math Revolution]

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==> This is one of the most common "2 by 2" questions in gmat and we have the below table.





In this case the original condition is a+b=50 and we have 4variables (a,b,c,d) with 1 equations(a+b=50). Since we need to match the number of variables and equations, we need 3 more equations and since we have 1 each in 1) and 2), we lack 1 equation thus E is likely the answer.

Using 1) & 2), 1) is not much of a use here while in 2) gives us (ac+bd)/50=73. This doesn't help us much either, and we can't find the number of students with recommendations. Therefore the answer is E.


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