nbrianco wrote:
and what if the members of S are negative numbers? nothing in the question states that S is composed of at least one positive number... am I mistaken? in that case, we need both statements: answer is C ... (????????)
Hi and welcome to GMAT Club! Below is an answer to your doubt.
Is the mean of set S greater than its median?First of all:
The median of a set with odd # of terms
is just a middle term (when ordered in ascending/descending order).
The median of a set with even # of terms
is the average of two middle terms (when ordered in ascending/descending order).
Next, one of the most important properties of evenly spaced set (aka arithmetic progression):
In any evenly spaced set the arithmetic
mean (average) is equal to the median and can be calculated by the formula
mean=median=\frac{a_1+a_n}{2}, where
a_1 is the first term and
a_n is the last term. Given the set
\{7,11,15,19\},
mean=median=\frac{7+19}{2}=13.
(1) All members of S are consecutive multiples of 3 --> S is an evenly spaced set, thus its mean equals to its median. Sufficient.
To address your question, lets check whether it's true if S consists with negative numbers:
{-6, -3} --> mean=-4.5=median;
{-9, -6, -3} --> mean=-6=median;
{-6, -3, 0, 3} --> mean=-1.5=median.
(2) The sum of all members of S equals 75. Clearly insufficient.
Answer: A.
For more on this topic check Number Theory chapter of Math Book:
math-number-theory-88376.htmlHope it helps.
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