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by Ashishkapoor7 » Wed Jun 06, 2012 6:26 am
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.
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by dimochka » Wed Jun 06, 2012 12:30 pm
1. There are on average 400 customers per branch. Given 10 branches, we have 4,000 customers in total. The second number sounds like the average asset amount per customer, and so this would be sufficient, but in reality it's incorrect and quite tricky.

Here's how the question wants you to compute to get this wrong:
Bank #1 has X customers (lets say 1). Their average assets under management are $400k
Bank #2 has Y customers (let's say 799), whose average assets under management are also $400k
Banks 3-10 have the remaining customers (3,200), each averaging to $400k.

Net assets = 1 * 400 + 799 * 400 + 3,200 * 400 = (1+799+3200)*400 = 1,600,000,000

But it won't always be 1.6bn; here's a counter-example that shows why this does not work:
Bank #1 has one customer with $500k. Average assets under management are $500k
Bank #2 has 799 customers, with average assets in this bank being $300k
Banks 3-10 have the remaining 3,200 customers, and in each bank the average is $400k (for easy calculations).

Net assets = 500k * 1 + 300k * 799 + 400k * 3200 = 1,520,200,000
Notice that we're still adhering to the rules: (500k + 300k + 8*400k) / 10 = 400k.

Case 1 is not sufficient because this is a weighted average question, and you cannot add averages together unless they're weighted equally.

2) Sufficient. We have 10 branches, each manages 160mm, so all together the assets are worth 1.6bn.
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