In honor of Gabby Douglas’ gold medal win, as well as the U.S. women’s gymnastics team’s all-around gold medal win, here is an Olympics-inspired Data Sufficiency problem.
A particular gymnastics tournament awards a gold, a silver, and a bronze medal in each of four events: Floor, Beam, Bars, and Vault. A platinum “Best All-Around” medal is awarded to the competitor who gains the most points from winning the other medals: 3 points for gold, 2 points for silver, 1 point for bronze. If McKenzie won the Best All-Around medal, and no one can win more than one medal in any of the four events, did she win at least one gold medal?
- All of the gold, silver, and bronze medals were won by fewer than six competitors, including McKenzie
- Another competitor in the tournament has 8 points.
(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.
Choose your answer before proceeding!
First, you may ask, “How could someone win the All-Around without winning a single gold medal?”
Easy – just imagine that McKenzie won ALL of the silver medals (8 points), and that no one else won more than one medal (the other medals are won by 8 separate people), so each person who has a gold has just 3 points, and each person who has a bronze has just 1 point.
This example – McKenzie winning all the silvers – is the easiest (or highest-point-value) way that McKenzie could win All-Around without getting any golds, so this example will be helpful in testing the statements below.
1) INSUFFICIENT. If all the medals were won by “fewer than six” people, that means a maximum of five. Let’s use examples to prove insufficiency.
First, let’s find an example (that is consistent with statement 1) where the answer to the question is YES, McKenzie won at least one gold:
McKenzie wins ALL the golds
Competitor X wins all the silvers
Competitor Y wins all the bronzes
(Obviously, many other combinations would fulfill the requirements.)
Now, let’s find an example (that is consistent with statement 1) where the answer to the question is NO, McKenzie did not win any golds:
Competitors A, B, C, and D each win one gold
McKenzie wins ALL the silver medals
Competitors A, B, C, and D each win one bronze (in different events than the ones in which they each won the gold, of course)
In this scenario, McKenzie has 8 points and everyone else has 4 points. We also fulfill the requirement of “fewer than six competitors.” Since we are able to get both a YES and a NO answer to the question while using statements consistent with statement 1, the statement is INSUFFICIENT.
2) SUFFICIENT. If another competitor has 8 points, McKenzie must have at least 9. Since “no one can win more than one medal in any of the four events,” there is no way to get 9 points without winning at least one gold.
The answer is B.
Here’s a fine point that might help you in your studies – notice that when we tested statement 1, we did NOT test examples wherein the medals are won by six or more competitors. That would not actually prove anything!
Many students make this mistake: instead of testing examples where the statement is true in order to try to get two different answers to the question, they test examples that both are and are not consistent with the statement, and then when they get different results, they conclude that the statement is insufficient because … er …different examples made different stuff happen? This is sloppy thinking.
To perform at – dare I say – an Olympic level at Data Sufficiency, be sure to remember that the statements are factual. They do not lie! Your goal when testing Data Sufficiency statements is to test examples that make the statement true, with the goal of producing different answers to the question.