Online Question Bank : Word Problems : #7

I wonder if you could help me understand how to work with statement (1) for this example.

I started with (2) which is easier and ended up not knowing how to work with (1) but I decided to chose answer D.

It turned out the correct answer was just B.

A certain bank has ten branches. What is the total amount of assets under management at the bank?

(1) There is an average of 400 customers per branch. When each branch’s average assets under management per customer is computed, these values are added together and this sum is divided by 10. The result is $400,000 per customer.

(2) The bank has a total of 4,000 customers. When the total assets per branch are added up, each branch is found to manage, on average, 160 million dollars in assets.

This is a 700-800 level question, so your process was exactly what you should do on the real test - you won't get every problem right, so giving yourself a 50-50 shot on a hard problem is really good. This is such a hard question that I wouldn't spend too much time worrying about it.

Given only that there are 10 branches. You already know how to deal with statement 2 so I'll only address statement 1.

Statement 1 is a classic "weighted average" scenario. In weighted averages, the different things that we are averaging do not have equal weight in the final calculation - this requires a more complicated formula than a simple average. Try an extreme example to understand this: I have one branch which manages $100 per customer... for just one customer. Another branch manages $1 per customer... for 50 customers. I wouldn't just calculate {$100 + $1} / 2 = $50.50; logically, it doesn't make sense that the average would be $50.50 if I had 1 customer @ $100 and 50 customers @ $1. Instead, I'd calculate [$100(1) + $1(50)] / 51 = $2.94; this number now actually makes logical sense - it should be pretty small.

This is essentially what statement 1 is saying - except with bigger numbers and trickier wording. The statement describes a calculation in which I take the average per customer for each branch (in the above case, $100 and $1) and just do a simple average. A simple average would give me $50.50 per customer. But that doesn't make logical sense - this should be a weighted average, as described above.