A certain bank has ten branches. What is the total amount of assets un

There are 10 branches in the bank.
Total amount of assets =(a) Total number of branches *(b)Total customer per branch *(c) Assets per customer.

From statement (1), (a) Total number of branches = 10
(b) Total customer per branch = 400
(c) Asset per customer = 4,00,000 , therefore statement (1) is sufficient.

From statement (2), (a) Total number of branches = 10
(b+c) Total asset per branch = 160,000,000, Therefore statement (2) is sufficient.
Answer:D

From the question statement, we know that the bank has ten branches. We are trying to find the total amount of assets under management at the bank. Since we know the number of branches of the bank, if we are able to calculate the total assets managed by each branch, we will be able to answer the question.

From statement I alone, 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.” – Lot of data, let us try to break it down.

Let the total asset under management in branch #1 be \(T_1\). Since each branch has 400 customers,

Average assets under management per customer in branch#1 = \(\frac{T_1 }{ 400}\).

Similarly, for the other branches, it will be \(\frac{T_2 }{ 400}\), \(\frac{T_3}{400}\) and so on. When we add this and divide it by 10, we get,

\(\frac{T_1+T_2+T_3+… + T_{10} }{ 4000}\). The statement says that this is equal to $400,000. Equating, we get,

\(T_1+T_2+T_3+…… + T_{10}\) = $1600,000,000 i.e. $1600 million. Therefore, statement I alone is sufficient to find the total amount of assets under management at the bank.
Answer options B, C and E can be eliminated. Possible answer options can be A or D.

From statement II alone, the bank has a total of 4000 customers (this works out to 400 customers per branch on an average, which is the same data given in statement I). Also, each branch is found to manage $160 million of assets on average. Therefore, the total assets under management is equal to $160 million multiplied by 10 i.e. $1600 million, which is the same value we got from statement I alone as well.

Statement II alone is sufficient. Answer option A can be eliminated.

The correct answer option is D.

Hope that helps!

Ans (B)

#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.

individual sum of money per branch is not know and total money per customer given 4*10^5 , but total amount of assets is not know or can be found out
insufficient
#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.
total avg of amount per bank is found to be 160 million , which is our answer
IMO B ; sufficient



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.

OFFICIAL EXPLANATION:

(1) INSUFFICIENT: When the average assets under management (AUM) per customer of each of the 10 branches are added up and the result is divided by 10, the value that is obtained is the simple average of the 10 branches’ average AUM per customer. Multiplying this number by the total number of customers will not give us the total amount of assets under management. The reason is that what is needed here is a weighted average of the average AUM per customer for the 10 branches. Each branch’s average AUM per customer needs to be weighted according to the number of customers at that branch when computing the overall average AUM per customer for the whole bank.

(2) SUFFICIENT: The average of $160 million in assets under management per branch spoken about here was NOT calculated as a simple average of the 10 branches’ average AUM per customer as in statement 1. This average was found by adding up the assets in each bank and dividing by 10, the number of branches (“the total assets per branch were added up…”). To regenerate that original total, we simply need to multiply the $160 million by the number of branches, 10. (This is according to the simple average formula: average = sum / number of terms)

The correct answer is B.

Hey Bunuel. I am not able to understand why statement 1 is insufficient? If we multiple total customer (4000) with Avg asset per customer (40,000), we should get the answer. Please explain.

This solution is incorrect, because you do not know that "each branch has 400 customers". You only know that there is "an average of 400 customers per branch". Those mean different things.

Statement 1 is not sufficient because it describes a weighted average situation, and we don't know how the average is weighted. If at a university, there are two classes, and in one class the average grade is 90 and in the other the average is 70, you can't conclude that the overall average at the university is 80. That is only true if the two classes are equal in size; in any other situation, the overall average will be closer to the average of the larger class.

The numbers in this particular question are irritating, but we can see why Statement 1 is not sufficient. It's certainly possible each branch has 400 customers, and then the bank manages $1.6 billion in assets. But we could also have this situation:

9 branches have 1 customer each, and manage $(4,000,000/9) each in assets
1 branch has 3991 customers and manages $0 in assets

Then we have 4000 customers in total, as required, and if we add up the assets per customer at each branch, we get $4,000,000, as required. But now the bank manages only $4 million in total assets, not $1.6 billion. So we can get very different answers depending on the sizes of the branches, and Statement 1 is not sufficient.

Statement 2 tells you directly the bank manages $1.6 billion, so the answer is B.

Dear IanStewart


We are so lucky to have you in this forum. I got the answer correct but still find misleading the highlighted part above. When we divide the aforementioned sum by 10, then the resultant amount is not per customer, but per branch. The way the last sentence is written seems to imply that each branch has exactly one customer - a contradictory implication.

I would be much grateful, if you could comment on my thoughts. Many thanks beforehand.

Yes, you're right, the number Statement 1 describes is not "per customer", since we never divide by 4000, the total number of customers. It's a bit awkward to describe the precise unit of that $400,000 figure, since it's computed in a strange way, but really it's "the average of each branch's average assets per customer", which, as you correctly point out, is an average taken 'per branch', not 'per customer'. The question would be better-written if it simply omitted the phrase "per customer" at the end, since it serves no purpose besides to confuse matters (since it is incorrectly used).

­

I was referring to Crackverbal explaination and it does make sense to have D as answer. Can you tell me where am I missing?


From the question statement, we know that the bank has ten branches. We are trying to find the total amount of assets under management at the bank. Since we know the number of branches of the bank, if we are able to calculate the total assets managed by each branch, we will be able to answer the question.

From statement I alone, 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.” – Lot of data, let us try to break it down.

Let the total asset under management in branch #1 be T1�1. Since each branch has 400 customers,

Average assets under management per customer in branch#1 = T1400�1400.

Similarly, for the other branches, it will be T2400�2400, T3400�3400 and so on. When we add this and divide it by 10, we get,

T1+T2+T3+…+T104000�1+�2+�3+…+�104000. The statement says that this is equal to $400,000. Equating, we get,

T1+T2+T3+……+T10�1+�2+�3+……+�10 = $1600,000,000 i.e. $1600 million. Therefore, statement I alone is sufficient to find the total amount of assets under management at the bank.
Answer options B, C and E can be eliminated. Possible answer options can be A or D.

I also thought the same but the correct seems to be option B and every other person is presenting the reasoning how the answer B is correct, please help me in this

The answer is B, not D. This is explained in the discussion above. Please review carefully.

Took me sometime to figure out what's going on here. Sharing an alternate explanation hoping it will help others.

Statement 1:
Given:
Avg number of customers per branch = 400
Branch’s average assets under management per customer = 400,000

Let's understand how the 400,000 is calculated
Let assets be A1, A2, A3... per branch
Number of customers be C1, C2, C3... per branch (Note even though the avg customer is 400, C1, C2, C3,... need not be all the same)
Branch’s average assets under management per customer = (A1/C1 + A2/C2 + ....+ A10/C10)/10 = 400,000

A1/C1 + A2/C2 + ....+ A10/C10 = 4000,000

We can say that the Total number of customers = 400*10 = 4000

To calculate Total amount of assets under management at the bank = Assets per customer * Total customers
= Assets per customer * 4000 (We don't have this value)
Assets per customer = Total assets across customers and banks/ Total customers, but the calculation above isn't the same, so we cannot use the 4000,000 value

Insufficient

Statement 2:
This is straight up
Total amount of assets under management at the bank = Number of banks * Avg assets per branch
= 10 * 160 M
= 1600 M

Note, the total number of customers here is irrelevant

Answer is B