GMAT Club invites you to test your GRE knowledge for a chance to win! Each week, we will post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for a free Manhattan GRE Strategy guide (e-book). What are you waiting for? Get out your scrap paper and start solving! Click here to view contest & prize details This week's question:3,456 consumers each ranked three brands of toothpaste in order of preference (for instance, a person who likes Brand A most, Brand B second-most, and Brand C least would be considered to have cast a vote for the ranking “ABC”). If the chart on the left indicates the frequency of the consumers’ rankings of the three brands, then the number of people who listed Brand B as their first or second choice is what percent greater than the number of people who listed Brand C as their first or second choice?

Answer Choices:a.) 25%

b.) 50%

c.) 100%

d.) 150%

e.) 225%

Please post your answer, along with the explanation, below. Get cracking! **Edit: **This challenge is now closed.

Solution

First, let’s find out what percent of people ranked toothpastes B and C as first or second place:

34+10+19+21 = 84% of people ranked B as first or second place

9+19+7+21 = 56% of people ranked C as first or second place

We are told that 3,456 consumers participated in the study, but this is just a distractor. It is common in Data Interpretation questions that a total is given, but is not required to answer every question. A question that only asks about a percent change between two “pie slices” can be answered with percents alone.

Therefore, the question can now be rephrased as “84 is what percent greater than 56?”

Keep in mind that the question does NOT ask “84 is what percent OF 56?” Let’s examine the difference by introducing a very simple (new) example:

30 is 150% OF 20—That makes sense, because 30 is equal to 100% of 20, plus another 50% of 20.

30 is 50% GREATER THAN 20—That also makes sense, because “greater than” means “in addition to the original 20.” 30 is equal to 20, plus another half of 20. We can calculate this with the percent change formula as well:

\(Percentage Change = |\frac{Difference}{Original}| * 100\)

Back to our problem—the percent change approach will be quite helpful here. 84 is equal to 56, plus half of 56 (which is 28) added back on. Thus, 84 is 50% greater than 56. Or:

\(Percentage Change = |\frac{28}{56}| * 100 = 50%\)

Remember that the formula is “difference over original times 100”—if you want a percent increase, the “original” is the smaller number, and if you want a percent decrease, the “original” is the larger number. Here, we are clearly asked for a percent increase, so 56 is our “original.”

Again, 84 is 50% greater than 56.

The correct answer is B.

The winner of this Week's Challenge is... (drum roll).... Zynga. Congratulations! Please send me a pm with your name, email address and choice of Manhattan GRE Guide

Details on the next challenge are available in the

Weekly Challenge Master thread... Stay tuned!