Can understand this bank problem

[carl]

I cannot unnderstand the explanation of this example:

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.

Can somebody please help?

[adbce]

I think, the answer is 'D'. Here's why.

The question is based on averages -> Average = Sum / number of entities

1) Says - average of 400 customers and there are 10 banks - so, a total of 4000 customers, each customer holding 400,000 - which would be 16 million in total assets. SUFFICIENT

2) Basically states the same as the first statement but much more clearly. SUFFICIENT.

What is the OA ?

[StaceyKoprince]

It's often better if you can detail what you do and don't understand about the problem; that way, we can give a really detailed explanation about the part that's confusing you. I'll give an overall explanation and if any part of it doesn't make sense, please let me know which part.

This is a very difficult problem. If you understand how weighted averages work, then that's the easiest way to do this, but that's a tough topic - and I assume that's where you're struggling, because that's how the official explanation describes this. So let's look at some formulas.

There are ten branches. Each branch manages some amount of money. How much do they all manage together?

(1) avg 400 customers/branch. There are 10 branches (given), so there are 400*10 = 4,000 total customers. Branch per-cust averages for each branch are then averaged together. This second average works out to $400k per customer. What does this mean? Here are some possibilities

Let's call the branches A, B, C, D, E, F, G, H, I, and J. An average is the sum of something divided by the number of items. The per-cust $ average at Branch A, then, is <sum$A> / <#custA>. The per-cust $ average at Branch B is <sum$B> / <#custB>. And I'm going to abbreviate these further as sA for "sum of $ in branch A" and cA for "# of customers at branch A." Good so far? These ten figures are then averaged, meaning we do this: [sA/cA + sB/cB + ... sJ/cJ] / 10 = 400,000.

We're also told in statement 1 that: [cA + cB + ... cJ] / 10 = 400.

We were asked to find: sA + sB + ... sJ. So let's see what we can substitute here.

Now, the above formulas are ridiculously long and complicated, so let's just pretend there are only 2 banks and see what we can do. This is data sufficiency, so if I can do it with 2, I can do it with 10 (and if I can't, I can't). I'm still going to keep the 400 and 400,000 numbers the same.

[cA + cB] / 2 = 400
[sA/cA + sB/cB] / 2 = 400,000

Okay, now go substitute the first equation into the second. Er. It's not just a straight substitution, is it? Those pesky cA and cB variables are tied into the sA and sB variables in the second equation. Could I separate them out? In other words, get [cA+cB] all by itself without any other cA or cB terms anywhere in the problem?

I can't. You can play around with it for a little while if you like, to convince yourself, but there isn't a way to do this. So statement 1 is not sufficient.

(Simple averages are not the same as weighted averages and doing two simple averages will not return the same result as a weighted average. Statement 1 does two simple average calculations but the problem requires a weighted average calculation because the number of customers at each bank is not the same. So the info isn't sufficient.)

(2) (does not tell us total # of customers - transcription above is wrong) only tells us: sA + sB + ... sJ = 160,000,000. That's what we were asked for; sufficient.

[sudaif]

Stacey - what if each bank branch had 400 customers exactly?
Would statement 1 be sufficient then?

[tim]

Yes statement 1 would then be sufficient. It's a good idea to take that information and plug it into Stacey's analysis to see for yourself why this is the case..

[sudaif]

thx Stacey and Tim. Stacey, your explanation was quite helpful :)

[tim]

You're welcome!