Weighted-Averages

The SBC GMAT Files

Weighted-Averages
Staff, Test Prep New York/Test Prep San Francisco

Fast forward to the future. You scored brilliantly on the GMAT, got an MBA from a top-tier school, and have become a credit analyst for a multi-national bank.  Tom the Toy Factory has applied for credit at your bank and your simple task today is to assess the interest that your bank is going to charge them over the money they borrow. Here is your Manager Bob, your boss giving you instructions about the company policy of doing this credit analysis. The only data we have about Bob is that he tends to play with the system, and tends to cut male patrons some slack.

Bob: Call the company. For every male employee charge 4% interest and for every female charge 4.5% interest. Then, just average it.

Oops, he had only 15 seconds to give you the instructions and he’s then off to a meeting.

You call the company and they tell you there are 10 male employees and 15 female.

Step 1:  Organize the data: This step is crucial for most GMAT questions. With simpler questions, it helps you speed your thinking and/or calculations. With complex problems, it organizes and guides your thinking to avoid the traps. We suggest you not under-estimate the importance of this step.

Males Females Total
Number (Quantity) 10 15 25
Interest Charged ( Value of each Quantity) 4 4.5 W.A.

Step 2: Calculate total number of People: 10 males + 15 females = 25 people. When practicing problems, double-check that you are not adding up the weights that each carry. A useful question is “Whose weight is more/ less?”  Whatever the answer, use its counterpart and the answer together. Here, females are charged more interest. The female counterpart is the male employee. So, add the number of females and males. Simple!

Step 3: Calculate the ratios: Ratios are basically how much of the total are male and how much of the total are female.

Step 4: Multiply each ratio by the quantity. The simple formula to handle this calculation is:
= (10/25)*4 + (15/25)*4.5
= 1.6 + 2.7 = 4.3

So, the interest your company will charge Tom the Toy factory for borrowing money is 4.5% since they have more females.

Alright, buddy, the dream is over. Back to being a GMAT-student. On to the conceptual part. The rest of the article is important. Please read it. No, really, please.

Why is this called Weighted Averages? All the values in the analysis do not hold the same weight. Conceptually, a good analogy is a team meeting. In a team meeting, the senior director’s opinion bears more weight in the decision-making, whereas what the manager says bears less weight – assuming they are both developing their unbiased opinions based on their experience and a director is more experienced that a manager.

Will I be calculating these every time? Not every time. That is why conceptual understanding is important. Data Sufficiency questions often do not require you to calculate. And, that is why step one is often more important.

How can they make such questions difficult? If you know any 2 of the 3 following, you can calculate or estimate the third. By using different combinations, such questions can be made difficult.
a. The ratio of the weights of different quantities. (Here, 4/25 is one ratio, 4.5/15 is another ratio)
b. The values of the quantities. (Here, 10 and 15 are the quantities of people)
c. The weighted average.

Common tricks that GMAT likes:
a. Not using the word ‘average’ anywhere in the question or answer options. How to beat it? Basically, there are two sub-groups being mixed to form a single large group AND the weight each group holds is different. Here, two groups (males and females) are being combined to charge them a single interest rate AND individually these groups have different weights.

b. Extraneous data: Not very often, but they may throw in irrelevant data. Here, if they gave you the ratio of two interest rates, chances are some students get distracted and use those numbers somewhere in the calculations. How to beat it? Step one! Organize your data. If you have organized your data properly, chances of identifying and discarding such distractors increase.

c. Complicated numbers: Hear this, if Zuckerberg purchased 2 pens for $249 and three other for $349, what is the average price for each? How to beat it? First, look at the answer options. It is likely that one or two are out of range: $499 or $240. Discard those options. Second, look closely at the data points. $249 and $349 are exactly $100 away. Reduce the lower data point to zero. So, the upper data point will become $100. Keep all other data points the same and mentally calculate like usual.

(0*2 + 100*3) / 5 = 300/5 = 60.

Now, add $60 to the lower number $249. You get $309. That is the EXACT answer. Zuckerberg owned!

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