linfongyu wrote:If the range of the set containing the numbers x, y, and z is 8, what is the value of the smallest number in the set?
1) The average of the set containing the numbers x, y, z, and 8 is 12.5
2) The mean and the median of the set containing the numbers x, y, and z are equal.
[spoiler]OA: C. I disagree and think that it should be A.[/spoiler]
Range is the distance between the smallest and largest numbers in the set.
For the sake of simplicity, let's say that x is the smallest number and z is the biggest.
From the original, then, we know that z - x = 8. The question is "what's the value of x?".
1) (x + y + z + 8)/4 = 12.5
We now have 2 equations and 3 unknowns. There's no way to combine them to solve for x: insufficient.
2) with an odd number of terms, the median is the middle term. By our previous definition, that's y. So:
y = (x + y + z)/3
We now have 2 equations and 3 unknowns. There's no way to combine them to solve for x: insufficient.
Combined:
We now have 3 equations and 3 unknowns - ding ding - sufficient, choose (C).
The "n linear equations" rule is the most powerful data sufficiency tool known to GMATkind; the better you understand the rule (including all of its subtleties), the fewer calculations you'll need to make on Test Day.
