Today’s post comes courtesy of Veritas Prep GMAT instructor and BTG expert, Bill Robinson.
If you’re a product of the 90’s like I am, you may have fond memories of the Nickelodeon game show Legends of the Hidden Temple. Described as “the thinking man’s Double Dare” by absolutely no one, the game featured six teams performing physical challenges and answering questions based on history, mythology, and geology. After three rounds, one team won the opportunity to enter the Hidden Temple in search of a historical artifact (such as Harriet Tubman’s walking stick or Icarus’s broken wing) and the grand prize. While there are no prizes on the GMAT, one Hidden Temple challenge illustrates an important Data Sufficiency concept.
After entering the Hidden Temple, contestants are inevitably faced with the Shrine of the Silver Monkey. The statue is composed of three pieces, which must be found and assembled in the proper order (feet, body, head) before he or she can move on to the next room. As a perceptive viewer, I noticed that many contestants wasted time by trying to find all three pieces before they attempted to assemble them. In contrast, the most effective approach seemed to be finding and assembling each piece before moving onto the next one
Similarly, Data Sufficiency questions provide us with three useful pieces of information: the question stem and the two statements. Our goal is to assemble them into something that will allow us to answer the question, and we should aim to do so as quickly as possible. To that end, many students read the question stem and immediately jump to the statements. Unfortunately, this is akin to Hidden Temple contestants trying to find all three pieces of the Silver Monkey before assembling the statue. Instead, we should work with the feet (the question stem) before moving onto the body and head (the statements) of the statue.
By starting with the question stem, we are both saving time (the work we do with the stem applies equally to both statements) and making better use of the information provided (the stem often contains keys that are missed by many test takers). Ideally, we should know exactly what we need before we work with the statements. This is especially important on word problems:
For its grand opening, a gym decided to sell individual and partner memberships at a discount for its first year in business. If the gym charged $375 for each individual membership and sold 3 times as many partner memberships as individual memberships, what was the gym’s total revenue from the sale of memberships?
From the stem, we can set up an equation for revenue: TR = IR + PR, where TR=total revenue, IR=individual revenue, and PR=partner revenue. We know that for each type of membership, revenue is equal to the price multiplied by the number of memberships. IR=375i where i=number of individual memberships, and PR=xp where x=price of a partner membership and p=number of partner memberships. We can even go a step farther since we know how the relationship between the number of partner and individual memberships sold: p=3i. Bringing all of our information together, our equation is TR = 375i + x3i. We can see that the statements must fill in two variables: partner price and the number of individual memberships. Let’s look at Statement 1:
1) The cost of each partner membership was $500.
It’s fairly obvious that we now have a value for x, but i still remains unknown. Statement 1 is insufficient. What about Statement 2?
2) The revenue from individual memberships was 1/5 of the total revenue from all memberships.
We know that IR (or 375i) equals , which we can simplify to TR=1875i. We end up with the same problem (i is unknown) that we did in Statement 1, so Statement 2 is also insufficient.
When we combine the statements, we don’t learn anything new. Each statement has the same problem, so there’s no way for us to find a value for i, and as a result we can’t find a value for total revenue. Even with both statements, we do not have sufficient information to solve.
As we can see, spending time with the base of our statue makes fitting the other two pieces easier. Identifying what we need makes our work with the statements much more efficient. The sooner we can put the statue together, the more time we have for the harder challenges that await us later on in the Hidden Temple.