sana.noor wrote:A certain bank has ten branches. What is the total amount of assets under management at the bank?
(1) There is an average (arithmetic mean) of 400 customers per branch. When each branch's average (arithmetic mean) 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) When the total assets per branch are added up, each branch is found to manage an average (arithmetic mean) of 160 million dollars in assets.
OA is B
I'm happy to help with this.
As usual, this is a fantastic question --- no surprise from MGMAT!
Let's start with statement #2, which is easier:
average = sum/(number of entries), or (sum) = (average)*(number of entries). If we multiply that average ($160M) by 10 banks, that will give us the sum, the total assets. This statement, all by itself, is
sufficient. That was reasonably straightforward.
Statement #1 is the hard part of this problem. The first statement is: "
There is an average (arithmetic mean) of 400 customers per branch." Let's think about that. Here's a hypothetical distribution of customers
Bank #1 = 10 customer
Bank #2 = 10 customer
Bank #3 = 10 customer
Bank #4 = 10 customer
Bank #5 = 10 customer
Bank #6 = 10 customer
Bank #7 = 10 customer
Bank #8 = 10 customer
Bank #9 = 10 customer
Bank #10 = 3910 customer
Those ten have an average of 4000 customers. Obviously, this list is unrealistic, but I showing an extreme case. Now, suppose one or two of those 10-customer banks has a single customer such as, say, Warren Buffet or Bill Gates, someone insanely rich. Then, each tiny bank with one super rich person will have a very high average.
Now, the prompt tells us:
When each branch's average (arithmetic mean) 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. So, now, the averages at all ten banks will count equally --- we're just going to find the sum and divide by ten. This means, the banks with only 10 customers will be inordinately over-represented in the average, and if the single super-rich customer happens to belong to banks #1-9, he will have a much larger effect on the overall average than if this single customer were a member of bank #10. Therefore, the final average we get from this procedure is almost completely meaningless, because different arrangements of the same total assets could result in different values of this final average. Knowing this final average tells us nothing. This statement, along and by itself, is
insufficient.
Answer = [spoiler]
(B) [/spoiler]
Does all this make sense?
Mike
