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A customer using a certain telephone calling plan pays a fee

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A customer using a certain telephone calling plan pays a fee  [#permalink]

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New post Updated on: 19 Jul 2015, 03:53
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A customer using a certain telephone calling plan pays a fee of $25 per month, and then receives a discount of 40% on the regular charge for all calls made to country A. If calls to country A are regularly charged at $1.60 per minute for the first 3 minutes, and $0.80 per minute for each minute thereafter, what is the maximum the customer could have saved over regular prices if he was charged for 1 hour of calls made to country A in a certain month?

A. $8.75
B. $12
C. $13.40
D. $17.40
E. $24.40

Originally posted by gayathri on 08 Nov 2004, 13:20.
Last edited by Bunuel on 19 Jul 2015, 03:53, edited 1 time in total.
Added the OA.
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Re: A customer using a certain telephone calling plan pays a fee  [#permalink]

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New post 09 Nov 2004, 01:07
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gayathri wrote:
A customer using a certain telephone calling plan pays a fee of $25 per month, and then receives a discount of 40% on the regular charge for all calls made to country A. If calls to country A are regularly charged at $1.60 per minute for the first 3 minutes, and $0.80 per minute for each minute thereafter, what is the maximum the customer could have saved over regular prices if he was charged for 1 hour of calls made to country A in a certain month?

1) $8.75
2) $12
3) $13.40
4) $17.40
5) $24.40


Like the other poster pointed out, the key is, what is the MAX the customer could have saved using the savings plan? Well, you save the most (in absolute dollar terms) by incurring the biggest phone bill possible. And how do you do that? You call for 3 minutes (get charged at $1.60 per minute) hang up, and then do that 20 times, since the question said you must talk for 1 hour.

So you are charged 1.60 per minute for 60 minutes = 96. This is what it normally costs you with no discount.

If you have the discount, you have to pay the $25 connection fee BUT you only pay 60% of the phone bill (40% savings): 0.6 * 96 = 57.6. So the total comes out to $25 + $57.6 = $82.6

So you save $96 - $82.6 = $13.4 or answer choice (3)
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Re: A customer using a certain telephone calling plan pays a fee  [#permalink]

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New post 08 Nov 2004, 13:45
I am not getting any number in the ans choices... let me work it out again...can u check in the meantime on the ans choices..
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New post 08 Nov 2004, 13:55
Venksune, the answer choices are rt. The question is deliberately tricky. The key phrase in the question is "what is the MAXIMUM the customer could have saved"

Its from Kaplan.
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New post 08 Nov 2004, 14:00
Yes, I clearly remember getting this one in one of their CAT test and this one is just SO wordy. It's not hard in and of itself but the difficulty level is significantly heigthened in actual exam conditions.
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New post 08 Nov 2004, 14:06
Getting 13.40 (96-82.6). Sleepy..I type 32.4 earlier..why did I do that?
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New post 01 May 2005, 14:51
gayathri wrote:
OA is $13.40


I was reviewig the old postings. i found this question discussed here. But OA should be $24.40.

It was discussed later too and explained nicely by Honghu.

gayathri wrote:
A customer using a certain telephone calling plan pays a fee of $25 per month, and then receives a discount of 40% on the regular charge for all calls made to country A. If calls to country A are regularly charged at $1.60 per minute for the first 3 minutes, and $0.80 per minute for each minute thereafter, what is the maximum the customer could have saved over regular prices if he was charged for 1 hour of calls made to country A in a certain month?

1) $8.75
2) $12
3) $13.40
4) $17.40
5) $24.40
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A customer using a certain telephone calling plan pays a fee  [#permalink]

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New post 01 Feb 2016, 00:05
3
2
A customer using a certain telephone calling plan
  • pays a fee of $25 per month
  • receives a discount of 40% on the regular charge for all calls made to country A.

Regular call charges to country A
    $1.60 per minute for the first 3 minutes, and
    $0.80 per minute for each minute

what is the maximum the customer could have saved over regular prices if he was charged for 1 hour of calls made to country A in a certain month?

for maximum he could have saved, we need find max he could have spent without having a plan.
so we assume all calls are of duration less than 3 minutes i.e., charge is 1.6 per min.
we have an hour thus 60 minutes.

charge=60*1.6=96
charge after applying the discount=\(96*(1-\frac{40}{100})\)=57.6
plan fee=25
Total charges=25+57.6=82.6
Regular total charge as calculated above could have been 96-82.6=13.4
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Re: A customer using a certain telephone calling plan pays a fee  [#permalink]

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New post 16 Jun 2016, 19:19
Nevernevergiveup wrote:
A customer using a certain telephone calling plan
  • pays a fee of $25 per month
  • receives a discount of 40% on the regular charge for all calls made to country A.

Regular call charges to country A
    $1.60 per minute for the first 3 minutes, and
    $0.80 per minute for each minute

what is the maximum the customer could have saved over regular prices if he was charged for 1 hour of calls made to country A in a certain month?

for maximum he could have saved, we need find max he could have spent without having a plan.
so we assume all calls are of duration less than 3 minutes i.e., charge is 1.6 per min.
we have an hour thus 60 minutes.

charge=60*1.6=96
charge after applying the discount=\(96*(1-\frac{40}{100})\)=57.6
plan fee=25
Total charges=25+57.6=82.6
Regular total charge as calculated above could have been 96-82.6=13.4


Hi Nevernevergiveup,

I understand that the most expensive way is making continuous 3-minute calls until you get to 60 minutes. However, using the monthly plan, the cheapest way to call is to call 1 hour straight and pay total of 25 + 40%*(1.6*3 + 0.8*57) = 45.16.

So, the maximum saving would be 96 - 45.16 = 50.84, would it not? I understand it is not an answer choice, but I think that how you must interpret the question.
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Re: A customer using a certain telephone calling plan pays a fee  [#permalink]

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New post 16 Jun 2016, 21:43
2
1
gayathri wrote:
A customer using a certain telephone calling plan pays a fee of $25 per month, and then receives a discount of 40% on the regular charge for all calls made to country A. If calls to country A are regularly charged at $1.60 per minute for the first 3 minutes, and $0.80 per minute for each minute thereafter, what is the maximum the customer could have saved over regular prices if he was charged for 1 hour of calls made to country A in a certain month?

A. $8.75
B. $12
C. $13.40
D. $17.40
E. $24.40


Discount = 40% of spending

We want to maximise discount so we will need to maximise spending. We do that by assuming that 60 calls were made of 1 min each because the first minute is the most expensive.

Max discount = (40/100)* 60 * 1.6 = (40/100)*96
This would be slightly less than 40. About 38 to 39.

Saving = (Slightly less than 40) - 25 = Slightly less than 15

Answer (C)
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Re: A customer using a certain telephone calling plan pays a fee  [#permalink]

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New post 17 Jun 2016, 20:16
VeritasPrepKarishma wrote:
gayathri wrote:
A customer using a certain telephone calling plan pays a fee of $25 per month, and then receives a discount of 40% on the regular charge for all calls made to country A. If calls to country A are regularly charged at $1.60 per minute for the first 3 minutes, and $0.80 per minute for each minute thereafter, what is the maximum the customer could have saved over regular prices if he was charged for 1 hour of calls made to country A in a certain month?

A. $8.75
B. $12
C. $13.40
D. $17.40
E. $24.40


Discount = 40% of spending

We want to maximise discount so we will need to maximise spending. We do that by assuming that 60 calls were made of 1 min each because the first minute is the most expensive.

Max discount = (40/100)* 60 * 1.6 = (40/100)*96
This would be slightly less than 40. About 38 to 39.

Saving = (Slightly less than 40) - 25 = Slightly less than 15

Answer (C)


Hi Karishma,

I posted my issue with the answer to this question already, but I was hoping you could help clarify. I understand that the most expensive way is making continuous 3-minute calls until you get to 60 minutes. However, using the monthly plan, the cheapest way to call is to call 1 hour straight and pay total of 25 + 40%*(1.6*3 + 0.8*57) = 45.16.

So, the maximum saving would be 96 - 45.16 = 50.84, would it not? I understand it is not an answer choice, but I think that how you must interpret the question.

Thank you.
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A customer using a certain telephone calling plan pays a fee  [#permalink]

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New post 17 Jun 2016, 21:42
1
TheLostBear wrote:
VeritasPrepKarishma wrote:
gayathri wrote:
A customer using a certain telephone calling plan pays a fee of $25 per month, and then receives a discount of 40% on the regular charge for all calls made to country A. If calls to country A are regularly charged at $1.60 per minute for the first 3 minutes, and $0.80 per minute for each minute thereafter, what is the maximum the customer could have saved over regular prices if he was charged for 1 hour of calls made to country A in a certain month?

A. $8.75
B. $12
C. $13.40
D. $17.40
E. $24.40


Discount = 40% of spending

We want to maximise discount so we will need to maximise spending. We do that by assuming that 60 calls were made of 1 min each because the first minute is the most expensive.

Max discount = (40/100)* 60 * 1.6 = (40/100)*96
This would be slightly less than 40. About 38 to 39.

Saving = (Slightly less than 40) - 25 = Slightly less than 15

Answer (C)


Hi Karishma,

I posted my issue with the answer to this question already, but I was hoping you could help clarify. I understand that the most expensive way is making continuous 3-minute calls until you get to 60 minutes. However, using the monthly plan, the cheapest way to call is to call 1 hour straight and pay total of 25 + 40%*(1.6*3 + 0.8*57) = 45.16.

So, the maximum saving would be 96 - 45.16 = 50.84, would it not? I understand it is not an answer choice, but I think that how you must interpret the question.

Thank you.


Hi,
But in that case the initial expenditure will not be 96 but (1.6*3 + 0.8*57) = 50.4.....
so the saving is 50.4 - 45.16 nearly 5....


As the savings are 40% of expenditure, we have to make the expenditure the MAX, so we take that each call was of 1 minute each and he paid 1.6 * 60 = 96..
and then due to the plan he had to pay 25 + .6*96 = 57.6 +25 = 82.6..
and savings = 96-82.6 = 13.4
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Re: A customer using a certain telephone calling plan pays a fee  [#permalink]

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New post 17 Jun 2016, 21:51
1
chetan2u wrote:
TheLostBear wrote:
VeritasPrepKarishma wrote:
Discount = 40% of spending

We want to maximise discount so we will need to maximise spending. We do that by assuming that 60 calls were made of 1 min each because the first minute is the most expensive.

Max discount = (40/100)* 60 * 1.6 = (40/100)*96
This would be slightly less than 40. About 38 to 39.

Saving = (Slightly less than 40) - 25 = Slightly less than 15

Answer (C)


Hi Karishma,

I posted my issue with the answer to this question already, but I was hoping you could help clarify. I understand that the most expensive way is making continuous 3-minute calls until you get to 60 minutes. However, using the monthly plan, the cheapest way to call is to call 1 hour straight and pay total of 25 + 40%*(1.6*3 + 0.8*57) = 45.16.

So, the maximum saving would be 96 - 45.16 = 50.84, would it not? I understand it is not an answer choice, but I think that how you must interpret the question.

Thank you.


Hi,
But in that case the initial expenditure will not be 96 but (1.6*3 + 0.8*57) = 50.4.....
so the saving is 50.4 = 45.16 nearly 5....


As the savings are 40% of expenditure, we have to make the expenditure the MAX, so we take that each call was of 1 minute each and he paid 1.6 * 60 = 96..
and then due to the plan he had to pay 25 + .6*96 = 57.6 +25 = 82.6..
and savings = 96-82.6 = 13.4


Thank you chetan2u. I think my issue with the question is that the stem does not explicitly say we have to follow the same way of calling to country A in both regular and discount methods. I guess I am just reading into the question too much, but your way of putting it makes sense.
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Re: A customer using a certain telephone calling plan pays a fee  [#permalink]

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New post 06 Aug 2016, 16:07
This problem was difficult for me to answer because it was not clear.

More specifically the following points were ambiguous:
1) The $25 fee only applies to the discount, and not BOTH cases
2) The charge for the first 3 minutes is PER PHONE CALL.

This leads me to ask if this is an actual GMAT question. The difficulty of this question comes from the interpretation, which is vague.
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Re: A customer using a certain telephone calling plan pays a fee  [#permalink]

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New post 07 Oct 2017, 06:03
VeritasPrepKarishma wrote:
gayathri wrote:
A customer using a certain telephone calling plan pays a fee of $25 per month, and then receives a discount of 40% on the regular charge for all calls made to country A. If calls to country A are regularly charged at $1.60 per minute for the first 3 minutes, and $0.80 per minute for each minute thereafter, what is the maximum the customer could have saved over regular prices if he was charged for 1 hour of calls made to country A in a certain month?

A. $8.75
B. $12
C. $13.40
D. $17.40
E. $24.40


Discount = 40% of spending

We want to maximise discount so we will need to maximise spending. We do that by assuming that 60 calls were made of 1 min each because the first minute is the most expensive.

Max discount = (40/100)* 60 * 1.6 = (40/100)*96
This would be slightly less than 40. About 38 to 39.

Saving = (Slightly less than 40) - 25 = Slightly less than 15

Answer (C)


We have got a discount of 40 % then don't u think we should do 60/100*96

Kindly explain..

Thanks
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Re: A customer using a certain telephone calling plan pays a fee  [#permalink]

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New post 24 Dec 2017, 06:47
2
TheLostBear wrote:
chetan2u wrote:
TheLostBear wrote:
Hi Karishma,

I posted my issue with the answer to this question already, but I was hoping you could help clarify. I understand that the most expensive way is making continuous 3-minute calls until you get to 60 minutes. However, using the monthly plan, the cheapest way to call is to call 1 hour straight and pay total of 25 + 40%*(1.6*3 + 0.8*57) = 45.16.

So, the maximum saving would be 96 - 45.16 = 50.84, would it not? I understand it is not an answer choice, but I think that how you must interpret the question.

Thank you.


Hi,
But in that case the initial expenditure will not be 96 but (1.6*3 + 0.8*57) = 50.4.....
so the saving is 50.4 = 45.16 nearly 5....


As the savings are 40% of expenditure, we have to make the expenditure the MAX, so we take that each call was of 1 minute each and he paid 1.6 * 60 = 96..
and then due to the plan he had to pay 25 + .6*96 = 57.6 +25 = 82.6..
and savings = 96-82.6 = 13.4


Thank you chetan2u. I think my issue with the question is that the stem does not explicitly say we have to follow the same way of calling to country A in both regular and discount methods. I guess I am just reading into the question too much, but your way of putting it makes sense.



I am also having the same doubt. If we want to show the max savings possible, we shall take the max expenditure
+discount and minimum expenditure +discount(which will be made by having a straight 1 hour call.)

Experts please explain
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New post 13 Dec 2018, 09:13
I don't understand why you have to add 25 to the discount BUT not the charge without the discount. This doesn't make sense to me.
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Re: A customer using a certain telephone calling plan pays a fee  [#permalink]

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New post 13 Dec 2018, 23:30
2
you paid $25 to get the 40% discount plan. So you will spend maximum amount to utilize the plan.

your target is to get max bill. and that will achieved by talking at maximum rates( 3 minutes talk per call). if you talk more than 3 minutes you will be charged less.

to get max bill you will made at least 20 call of 3 minutes each.

monthly bill without plan-
=1.6*3*20
=96-----------(1)

monthly bill with discount plan-
= 96*0.6(40% discount)
=57.6---------(2)

savings= (1)-(2)
=96-57.6
=38.4------------(3)

but you already paying $25 for the plan

max savings= 38.4-25
=13.4

answer is (c)
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Re: A customer using a certain telephone calling plan pays a fee  [#permalink]

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New post 14 Dec 2018, 08:46
aa008 wrote:
you paid $25 to get the 40% discount plan.

aa008, ah ok. It's clear now, thanks!
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Re: A customer using a certain telephone calling plan pays a fee  [#permalink]

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New post 13 Jan 2019, 20:49
The point where I stumbled in this question (I am guessing others did too) is the understanding that 1) regular charge occurs for every call made. So, in every call, duration is divided in two parts (3min & over 3min). This is opposed to what I took as $1.6 for 3 min and $0.8 for rest 57 min in 1 hour of calls. This would have been fine if we were to show minimum bill arising from regular charges.

Two observations that I should have actually heeded to correct my above error are:
1) We are asked to calculate for 1 hour of CALLS and not for a call of 1 hour duration. Thus multiple calls can take place.
2) We need to maximise the savings. Hence the bill from regular charges should be the highest. This will happen only when every call that is made is less than or equal to 3 minutes because only then will we be charged $1.6 per minute for the 60 minutes of calling.

Rest of the problem solving is pretty standard. However, this was tricky question because of the notes mentioned above!
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Re: A customer using a certain telephone calling plan pays a fee   [#permalink] 13 Jan 2019, 20:49

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