Each of the questions given below consists of a statement and / or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is / are sufficient to answer the given question. Read both the statements and Give answer (a) if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question; Give answer (b) if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question; Give answer (c) if the data either in Statement I or in Statement II alone are sufficient to answer the question; Give answer (d) if the data even in both Statements I and II together are not sufficient to answer the question; Give answer (e) if the data in both Statements I and II together are necessary to answer the question. Is 500 the average score on the GMAT? I. Half of the people, who take the GMAT, score above 500 and half of the people score below 500. II. The highest GMAT score is 800 and the lowest score is 200.

### Concept & Logic This question tests the critical statistical distinction between different measures of central tendency: the arithmetic mean (average) versus the median (the literal middle value of a dataset). ### Step-by-Step Solution * **Analyze the Core Question:** We need to definitively answer YES or NO to whether the arithmetic mean is exactly 500. * **From Statement I:** This statement gives the textbook definition of the **median** score. It tells us the median is 500 (50% scored above, 50% scored below). However, the median being 500 does not guarantee the average is 500. If the top 50% of scores are clustered closely near 510, but the bottom 50% of scores are spread all the way down to 200, the extreme low scores will pull the mean significantly lower than 500. Thus, Statement I alone is not sufficient. * **From Statement II:** We are given the range extremes (maximum 800, minimum 200). Knowing the absolute highest and absolute lowest scores tells us absolutely nothing about the mathematical distribution of the thousands of scores in between those bounds. Thus, Statement II alone is not sufficient. * **Combining Statements I and II:** We know the median is 500 and the extremes are 200 and 800. The distribution could be perfectly symmetrical (mean = 500). However, the distribution could also be heavily skewed. For example, half the test takers could score 200, and half could score 800 (mean = 500). Alternatively, half could score 490, and the other half could consist of a single 800 and the rest scoring 510 (mean $\neq$ 500). Both skewed and symmetrical scenarios are possible. Thus, combined statements are not sufficient. ### Exam Strategy & Shortcut Immediately recognize the statistical definitions at play. "Half above, half below" is the explicit definition of a median. Standardized aptitude tests constantly test the trap of confusing the median with the mean. As soon as you see median data being offered to prove a mean, mark it insufficient unless a second statement explicitly dictates that the dataset forms a perfectly symmetrical distribution. ### Common Pitfall The most common mistake is assuming that real-world data always follows a normal, perfectly symmetrical bell-curve distribution where the Mean = Median = Mode. In many datasets (and intentionally tricky test questions), distributions are heavily skewed. Never assume a symmetrical distribution unless it is expressly stated. ### Final Answer **Therefore, the correct answer is Data even in both Statements together are not sufficient.**