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Sally's internet provider offers unlimited traffic

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Intern
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Joined: 07 May 2014
Posts: 20
Sally's internet provider offers unlimited traffic  [#permalink]

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New post 29 May 2014, 08:59
1
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A
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C
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E

Difficulty:

  65% (hard)

Question Stats:

44% (01:11) correct 56% (01:20) wrong based on 81 sessions

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Sally's internet provider offers unlimited traffic which costs $0.5 per day charged off at 12 a.m. The service is discontinued when client's debt exceeds $5. If today in the morning Sally makes a payment of $7, for how many days, including today, will she be connected to the internet without any additional payments, given her initial balance was $0?

(A) 15
(B) 24
(C) 25
(D) 26
(E) 13
Intern
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Re: Sally's internet provider offers unlimited traffic  [#permalink]

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New post 29 May 2014, 09:07
Since we begin on Day 1 with zero balance, does the the $0.5 charge apply today after the payment is made? The question suggests that the $0.5 charge applies at 12 midnight. If this is true, does the internet service begin immediately after payment? How would you solve this?

The original solution is provided below:

Solution 1:

Though the values are not too large, it would still take much time to simply count the number of days.

The first approach to the problem is as follows. The internet provider will charge off $0.5 until it runs out of the $7 and then until the debt exceeds $5. So, first add these sums up:

$7+$5=$12

Now we should find, how many times $0.5 fit into $12

$12∶$0.5=24

Thus, we apply 24 changes to the original sum on the first day and find, that Sally will be connected to the internet for 25 days, including today.

Solution 2:

In fact, in this problem we deal with arithmetic progression with the 1st term \(a1=7\), difference \(d=-0.5\) and the n-th term \(an=-5\).

To find n we need to use one of the formulas of arithmetic progression
\(n=\frac{an-a1}{d}+1\)

Applying the formula, we obtain

n=\(\frac{(-5)-7}{-0.5}+1\) \(=\) \(\frac{-12}{-0.5}+1\) = 24+1 = 25

The correct answer is C.
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Re: Sally's internet provider offers unlimited traffic  [#permalink]

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New post 29 May 2014, 13:22
dhirajx wrote:
Sally's internet provider offers unlimited traffic which costs $0.5 per day charged off at 12 a.m. The service is discontinued when client's debt exceeds $5. If today in the morning Sally makes a payment of $7, for how many days, including today, will she be connected to the internet without any additional payments, given her initial balance was $0?

(A) 15
(B) 24
(C) 25
(D) 26
(E) 13


day 0- payment of $7 is made in the morning (after 12 am midnight)
day 1 onwards(after 12 am midnight) internet service will begin and will run for 7*2=14 days i.e. at the end of day 15 balance will be zero.
now sally can still use the internet till her debt reaches $5 which means total of 5*2=10 days.

now the question states for how many days, including today, will she be connected to the internet without any additional payments i.e. we will have to include day0 also in our final answer. therefore total no. of days =1+14+10=25
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Re: Sally's internet provider offers unlimited traffic  [#permalink]

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New post 04 Apr 2016, 18:22
for day 1, there will be no charge.
so starting from day 2, there will be 0.5$/day charge
7$=14 days
5$=10 days
14+10+1 = 25 days
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Re: Sally's internet provider offers unlimited traffic  [#permalink]

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New post 09 Mar 2018, 11:56
"exceeds 5$" is the catch for this question.

At the end of day 24, the debt is 5$ exactly, but it has n't exceeded 5$ yet, allowing sally to continue using internet into the next day
Re: Sally's internet provider offers unlimited traffic &nbs [#permalink] 09 Mar 2018, 11:56
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