Is the Average of a Set of 5 Distinct Positive Integers {a, b, 6, 4, 2} Greater than the Median?

Question: Is the average of a set of 5 distinct positive integers {a, b, 6, 4, 2} greater than the median?

1. The highest number in the set is 6
2. The lowest number in the set is 2

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 the average of a set of 5 distinct positive integers {a, b, 6, 4, 2} greater than the median?”- is the topic of GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Premier 2017 with 6 Practice Tests”. 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 comprise 15 questions which are two-fifths of the total 31 GMAT quant questions.

Solution:

From statement A, we have the highest number in the set as 6. But this statement is insufficient in itself because it limits the highest value and since we know that the value of a and b can’t be negative or 0, so we can try as a = 1 and b = 3. Now we will find out that median is 3 and average is 3.2. If we will try a = 3 and b = 5, the average will be equal to median i.e., 4.

From statement B, we have the lowest number in the set as 2. But this statement is insufficient in itself. If a and b are very large numbers, the average will be greater than the median, which will be no higher than 6. But if a = 3 and b = 5, then the average will be equal to the median.

Hence from the above two steps, we came to know that option (1) and option (2) combined is sufficient and we got that a = 3 and b = 5.

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