Question: There are twenty students in a class, all of whom scored between 0 and 100 on their final exams. If the class average was 85, how many people scored below the average score on the exam?

1. Twelve people in the class scored higher than an 85
2. The lowest eight scores added up to 640

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

Solution and Explanation:

Approach Solution (1):

S1: You can’t say anything about the number of people who scored below the average score on the exam
Suppose 12 people get 86 marks each (which could be anything between 86 and 100th both inclusive), then there can be many scenarios:

1. Out of 8 people remaining, 7 people get 85 and 1 person gets 73
2. 6- 85 marks each, 2- 158 marks (together). Similarly we can think of other combination

S2: Again many combinations:

1. Lowest 8 scores getting 80 each
2. 7 people getting 85 marks each and the last one getting 45 and so on…

Using both the statements also, we cannot answer the question. Because both the statements say the same thing: lowest 8 scores sum to less than 680. First statement says the highest 12 scores sum to more than 1020 and the second one says lowest 8 scores sum to 640. So, even both the statements together are not sufficient to answer the question.

Correct Option: E

Approach Solution (2):

It is asked that how many people have a score > 85? OR How many people have a score >= 85?

S1: 12 people have a score > 85, but it's not answering what we are looking for.
Hence insufficient

S2: Average of the lowest 8 people is 80, we can’t say how many more will fall below 85.
Hence insufficient

Combined: Solution must be less than equal to 8, but we can’t say surely because we would need proper distribution for the same.
Hence insufficient

Correct Option: E

Approach Solution (3):

S = 20
But S consists of students that scored lower than the mean, equal to the mean, and higher than the mean.
L + E + H = 20
L =?

Statement 1) We are given that H = 12, but the students who scored exactly the mean score of 85 are still unknown, so we cannot simply take 20 - 12 = 8, only L + E = 20 - 12 = 8, where E is unknown. Insufficient.

Statement 2) The lowest eight scores had a 640/8 = 80 average. It could be that 4 students had a score of 85 and 4 students had a score of 75, and thus only 4 students scored below average. It could also be that all 8 students (and more from the other 12 students) had a score of 80. Insufficient.

Combined) From statement 2 we illustrated that the number of students who scored less than 80 can differ at least between 4 and 8. From statement 1 we know that L <= 8, but we still do not have enough information. Insufficient.

Two possibilities to illustrate:

{75,75,75,75, 85,85,85,85, 85,85,85,85, 85,85,85,85, 95,95,95,95}
The average is 85 and 4 students scored below the mean.

{80,80,80,80, 80,80,80,80, 80,80,90,90, 90,90,90,90, 90,90,90,90}
The average is 85 and 10 students scored below the mean.

Correct Option: E

“There are twenty students in a class, all of whom scored between 0 and 100 on their final exams. If the class average was 85, how many people scored below the average score on the exam?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

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