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# The price of a phone call consists of a standard connection fee, which

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Math Expert
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The price of a phone call consists of a standard connection fee, which  [#permalink]

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27 Jul 2018, 01:32
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25% (medium)

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84% (01:54) correct 16% (02:16) wrong based on 69 sessions

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The price of a phone call consists of a standard connection fee, which is constant, plus a per minute charge. A 10-minute call costs $2.90 and a 16-minute call costs$4.40. How much does a 13-minute call cost?

(A) $3.55 (B)$3.57
(C) $3.58 (D)$3.65
(E) $3.77 _________________ Senior RC Moderator Status: Perfecting myself for GMAT Joined: 22 May 2017 Posts: 759 Concentration: Nonprofit Schools: Haas '21 GPA: 4 WE: Engineering (Computer Software) Re: The price of a phone call consists of a standard connection fee, which [#permalink] ### Show Tags 27 Jul 2018, 02:50 1 Let s be the standard connection fee and c be the minute charge A 10-minute call costs$2.90 = 290 cents

=> s + 10c = 290 ------- (1)

16-minute call costs $4.40 = 440 cents => s + 16c = 440 ------- (2) Subtracting 1 from 2 6c = 150 => c = 25 Substituting the value of c in 1 => s + 250 = 290 => s = 40 13-minute call would cost => 40 + 13(25) = 365 cents =$3.65

Hence option D
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Re: The price of a phone call consists of a standard connection fee, which  [#permalink]

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27 Jul 2018, 02:58
Ans: D
As one method is already mentioned above.. Idea is same here but might be a bit short.
Given : Call cost(C ) = fixed Charge (F)+ Minutes(minutes charge) (nM) : where n is number of minutes.
so from stem:
2.90 = F+9M ----(Eq.1)
4.40 = F+15M ----(Eq.2): and we need to find F+12M = ?? ----(Eq.3)
now we can start solving and do the calculations by finding one value and then getting second or just look at the equations. if we add Eq.1 & Eq.2
2.90 = F+9M
4.40 = F+15M
---------------
7.30 = 2F + 24M : gives is 3.65 =F+12M ans..

Bunuel wrote:
The price of a phone call consists of a standard connection fee, which is constant, plus a per minute charge. A 10-minute call costs $2.90 and a 16-minute call costs$4.40. How much does a 13-minute call cost?

(A) $3.55 (B)$3.57
(C) $3.58 (D)$3.65
(E) $3.77 _________________ -------------------------------------------------------------------- The Mind is Everything, What we Think we Become. Kudos will encourage many others, like me. Please Give Kudos !! Thanks Manager Joined: 13 Feb 2018 Posts: 135 Re: The price of a phone call consists of a standard connection fee, which [#permalink] ### Show Tags 27 Jul 2018, 03:29 Let: F be be the fixed connection cost V be variable cost per minute We get two equations: F+10V=2.9 F+16v=4.4 Solve it and F=0.4 V=0.25 0.4+13*0.25=3.65 IMO Ans: D EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 12660 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: The price of a phone call consists of a standard connection fee, which [#permalink] ### Show Tags 02 Oct 2018, 21:40 Hi All, We're told that the price of a phone call consists of a standard connection fee, which is constant, plus a per minute charge, a 10-minute call costs$2.90 and a 16-minute call costs $4.40. We're asked for the cost of a 13-minute call. This question can be solved in a couple of different ways - and there's a great 'rate shortcut' that you can use to avoid some of the extra math that comes with certain approaches. Since there's a standard connection fee, we know that the difference between the costs of two calls is solely due to the number of minutes in the call. With the given information (about a 10-minute call and a 16-minute call), the difference in price comes down to the 6 minute difference in the length of the calls. Thus, the extra 6 minutes cost an extra$4.40 - $2.90 =$1.50. We're asked for the cost of a 13-minute call - which is exactly 'halfway' between those two prices. Half of $1.50 is$0.75, so we can add that to the cost of a 10-minute call to find the cost of the 13-minute call. $2.90 +$0.75 = $3.65 Final Answer: GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: The price of a phone call consists of a standard connection fee, which  [#permalink]

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03 Oct 2018, 17:59
Bunuel wrote:
The price of a phone call consists of a standard connection fee, which is constant, plus a per minute charge. A 10-minute call costs $2.90 and a 16-minute call costs$4.40. How much does a 13-minute call cost?

(A) $3.55 (B)$3.57
(C) $3.58 (D)$3.65
(E) $3.77 Letting f = the standard connection fee and n = the per-minute charge, we can create two equations, one for the 10-minute call and one for the 16-minute call:: f + 10n = 2.90 and f + 16n = 4.40 Subtracting the first equation from the second, we have: 6n = 1.50 n = 0.25 Substituting 0.25 for n into the first equation, we see that f is: f + 2.5 = 2.90 f = 0.4 So a 13-minute call costs 0.4 + 13 x 0.25 =$3.65.

Alternate solution:

If we let m = the per-minute charge, x = the number of minutes, b = the standard connection fee, and y = the total cost of an x-minute call, we will have y = mx + b. As we can see, this is a line, and the ordered pairs (10, 2.90) and (16, 4.40) are on this line. We are looking for the y-value when x = 13. We can observe that 13 is exactly halfway between 10 and 16; therefore, the y-value should be exactly halfway between 2.90 and 4.40 also. Thus y = (2.90 + 4.40)/2 = 7.30/2 = 3.65.

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The price of a phone call consists of a standard connection fee, which  [#permalink]

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04 Oct 2018, 06:52
Bunuel wrote:
The price of a phone call consists of a standard connection fee, which is constant, plus a per minute charge. A 10-minute call costs $2.90 and a 16-minute call costs$4.40. How much does a 13-minute call cost?

(A) $3.55 (B)$3.57
(C) $3.58 (D)$3.65
(E) \$3.77

$$? = f + 13c\,\,\,\,\left[ \ \right]$$

The constant fee (f) and the minute-charge (c) will be considered in CENTS. (Amounts in cents are always integers!)

$$\left\{ \matrix{ \,f + 10c = 290 \hfill \cr \,f + 16c = 440 \hfill \cr} \right.\,\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( + \right)} \,\,\,\,\,\,2f + 26c = 290 + 440\,\,\,\,\,\,\mathop \Rightarrow \limits^{{\rm{focus}}\,!} \,\,\,\,\,\,? = {{2f + 26c} \over 2} = 145 + 220 = 365\,\,\,\,\,\,\left[ {\,{\rm{cents}}\,} \right]$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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The price of a phone call consists of a standard connection fee, which &nbs [#permalink] 04 Oct 2018, 06:52
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