Is 500 the Average (Arithmetic Mean) Score on the GMAT?

Question: Is 500 the average (arithmetic mean) score on the GMAT?

(1) Half of the people who take the GMAT score above 500 and half of the people score below 500.
(2) The highest GMAT score is 800 and the lowest score is 200

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.

“Is 500 the average (arithmetic mean) score on the GMAT?” – 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.

Solution and Explanation:

Approach 1

It is asked in the question whether 500 is the average (arithmetic mean) score on the GMAT or not.
There are two statements given, we have to check if they are sufficient to answer the problem or not.
In statement 1 it is given that half of the people who take the GMAT score above 500 and half of the people score below 500.
If half of the people get more than 500 and half less than 500, we cannot clearly tell exactly what the mean will be.
Considering the GMAT scores, 450 470 530 550 we will have an arithmetic mean of 500
But 450 470 520 540 will have a mean lower than 500. Hence this statement is insufficient to answer the question.

(2) The highest GMAT score is 800 and the lowest score is 200.
If the highest and lowest scores are 200 and 800, there may be a score like 600 in between.
The average of these 3 scores is not 500, whereas
if that score in between was 500, then we would get an average score of 500.
Hence, this data is insufficient to answer the question.

On combining we can't clearly tell that the average is definitely equal to 500
Consider 200 300 700 800, which has an average of 500.
But 200 200 700 800, has average lesser than 500. This however satisfies both the conditions. Hence, both of these statements are insufficient to answer the problem.

E is the correct option.

Approach 2

Statement 1: Half of the people who take the GMAT score above 500 and half of the people score below 500.

Let's suppose the number of students who take GMAT = 4
so possible sets are

200 , 300, 520 , 540 : Average = 390 : Answer to question is No
200, 300, 750, 750: Average = 500: Answer to the question is Yes

Statement 1 by itself is not sufficient

Statement 2: The highest GMAT score is 800 and the lowest score is 200
Let's suppose a number of students who take GMAT = 4
so possible sets are

200 , 300, 520 , 800 : Average = 475 : Answer to question is No
200, 500, 500 , 800: Average = 500 : The answer to question is Yes

Statement 2 by itself is not sufficient

combining 1 + 2
200 , 480 , 520 , 800 : Average = 500 : Answer to question is Yes
200 , 480 , 620 , 800 : Average = 525 : Answer to question is No

Hence E is the correct option.

Approach 3

Let us consider statement A alone. Let us assume that half of the people scored 600 and half scored 499.
So the average is not 500.

Also there is a possibility that the average is 500 when half scores above 500 and half scores below.
Hence, we do not get an unique answer.
Considering statement B:
Just by knowing the highest and the lowest score, we will not know the average.
Combining both the statements also will not provide any exact value. Hence, D is the correct answer.

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