Bunuel wrote:
Bunuel wrote:
Competition Mode Question
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.
Are You Up For the Challenge: 700 Level QuestionsOFFICIAL 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.
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.