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Median


Set A consists of integers -9, 8, 3, 10, and J; Set B consists of integers -2, 5, 0, 7, -6, and T. If R is the median of Set A and W is the mode of set B, and R^W is a factor of 34, what is the value of T if J is negative?

(A) -2
(B) 0
(C) 1
(D) 2
(E) 5

Solution

This problem demonstrates a helpful note about statistics problems – quite often the key to solving a stats problem is something other than stats: number properties, divisibility, algebra, etc. The statistics nature of these problems is often just a way to make a simpler problem look more difficult.

Here, the phrase “factor of 34? should stand out to you, as there are only four factors of 34, so you can narrow down the possibilities pretty quickly to 1, 2, 17, and 34. And because the number in question must be an exponential term that becomes a factor of 34, it’s even more limited: 2, 17, and 34 can only be created by one integer exponent – “itself” to the first power.

The base of that exponent is going to be the median of Set A, and because we know that the median of Set A will be 3 (a negative term for variable J means that 3 will be the middle term), the question becomes that much clearer. 3^W can only be a factor of 34 if it’s set equal to 1, and the only way to do that is for W to be 0. REMEMBER: anything to the power of...


GMAT StatisticsEven if you fear statistics by its reputation, it is one of the easiest sections in the GMAT because a standard set of questions is asked and anyone who understands the fundamentals that I shall describe will be able to ace the questions. The three most basic topics in stats are mean, mode, and median. Usually, the GMAT will go one step further into range and standard deviation.

Mean: Mean is the average. Let’s say there are two numbers: 6 and 8. The mean would be:
(6+8)/2 =14/2 =7. If you analyze the number 7, it makes sense that it is average of 6 and 8. Using the same approach, the mean of n numbers a1,a2,a3…….an would be (a1+a2+a3…..+an)/n. If you remember this formula, you should be able to do well with mean questions. We shall discuss some of the standard questions in subsequent blogs, but for right now, remember the key formula and start doing some mean and average questions from Grockit games.

Mode: Let’s say that you are given a set of numbers, such as {4,3,7,9,9,11,10}. In order to find the mode, you have to arrange the numbers in ascending...




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