On Jane's credit card account, the average daily balance for a 30-day billing cycle is the average of the daily balances at the end of each of the 30 day. At the beginning of a certain 30-day billing cycle, Jane's credit card account had a balance of $600. Jane made a payment of $300 on the account during the billing cycle. If no other amounts were added to or subtracted from the account during the billing cycle, what was the average daily balance on Jane's account for the billing cycle?
(1) Jane's payment was credited on the 21st day of the billing cycle.
(2) Average daily balance through the 25th day of the billing cycle was $540
Please so explain how to solve them within 2 mins...Thanks
Tough Mean Problem
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Here we have $600 balance for the whole 30day period cycle and Jane made a payment of $300 during billing cycle.nandy1984 wrote:On Jane's credit card account, the average daily balance for a 30-day billing cycle is the average of the daily balances at the end of each of the 30 day. At the beginning of a certain 30-day billing cycle, Jane's credit card account had a balance of $600. Jane made a payment of $300 on the account during the billing cycle. If no other amounts were added to or subtracted from the account during the billing cycle, what was the average daily balance on Jane's account for the billing cycle?
(1) Jane's payment was credited on the 21st day of the billing cycle.
(2) Average daily balance through the 25th day of the billing cycle was $540
Please so explain how to solve them within 2 mins...Thanks
let's say Jane's payment day is: n, Avg.daily balance will be ( n - 1 )600 + ( 30 -(n - 1))300 / 30
from stat(1): it's mention 21st day as a billing cycle i.e. n = 24, then we can obviously determine the avg.daily balance!
Sufficient.
from stat(2): here it's Avg.balance counted on 25th day of billing cycle, i.e. 540
i.e. 600 ( n - 1 ) + ( 25 - (n - 1) )300 / 25 = 540
well, it's clear that we can solve for n, Hence sufficient.
Answer: D!
Note: Here the trick is once you have those equations, then stop worrying about calculations.
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nandy1984 wrote:On Jane's credit card account, the average daily balance for a 30-day billing cycle is the average of the daily balances at the end of each of the 30 day. At the beginning of a certain 30-day billing cycle, Jane's credit card account had a balance of $600. Jane made a payment of $300 on the account during the billing cycle. If no other amounts were added to or subtracted from the account during the billing cycle, what was the average daily balance on Jane's account for the billing cycle?
(1) Jane's payment was credited on the 21st day of the billing cycle.
(2) Average daily balance through the 25th day of the billing cycle was $540
Please so explain how to solve them within 2 mins...Thanks
Explanation:
We need to find the average daily balance on Jane's account for the whole month. It is given in the question that no other amounts were added to or subtracted from the account during the billing cycle, so the balance remains unchanged, that is $300, for the remaining month. This means that we can reword the question as "On which day did Jane make the payment?"
Statement 1 directly gives the answer to the question, which is the 21st day of the billing cycle; SUFFICIENT.
Statement 2: Let us assume that Jane makes the payment on Nth day.
Then for N - 1 days, the balance was $600.
For 25 - (N - 1) or 26 - N days, the balance was $300.
The average balance = [(N - 1)600 + (26 - N)300]/25 = 540, which can be solved to find the value of N; hence SUFFICIENT.
The correct answer is D.
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Almost no math is needed. Please check my explanation here:
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My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
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