Sometimes we don’t need a whole lot of discussion. We just need a problem broken down step-by-step. This question comes from the GMAT Official Guide, 13th edition, Section 6.3 #110.
“Tom, Jane, and Sue each purchased a new house. The average (arithmetic mean) price of the three houses was $120,000. What was the median price of the three houses?
(1) The price of Tom’s house was $110,000.
(2) The price of Jane’s house was $120,000.”
Step 1: Identify your target and the given information- Here our goal is to find the median home price. We’re given the average price which tell us that the total of the three sales is $360,000.
Step 2: Find paths to sufficiency- in other words, figure out what you’d need to know in order to be able to find the median. When arranged in increasing order, the median is the middle term. In order to find the middle term we’ll either need to know the values of all three terms, or be guaranteed that one of our terms is the middle one.
Step 3: Assess the first statement- If Tom’s house was $110,000 we know that the two other houses sum to $250,000. If Jane’s house was $100,000 and Sue’s house was $150,000 the median would be $110,000. Alternatively if Jane’s house was $120,000 and Sue’s house was $130,000 the median would be $120,000. Since there is more than one possibility statement 1 is insufficient.
Step 4: Assess the second statement- If Jane’s house was $120,000 we know that the two other houses sum to $240,000. On the basis of this statement alone we can’t determine the exact prices of the other two houses. Many students will stop there, call this insufficient and get this question wrong. Remember, we could also have a sufficient amount of information if we could guarantee that $120,000 was the middle value. Since the other two houses sum to $240,000 we only have two options. The first option is that that one house is less than $120,000 and one is more. If that’s the case $120,000 is our median. The only other alternative is that all three houses cost $120,000. In that situation our median is still $120,000. Statement two is sufficient.
Follow all of these steps carefully and you’re well on your way to a great score. In data sufficiency questions you especially don’t want to jump ahead to combining both statements until you’ve fully evaluated each one.