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

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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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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 _________________ MBA Section Director Affiliations: GMATClub Joined: 22 May 2017 Posts: 2598 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 2 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. Senior Manager Joined: 13 Feb 2018 Posts: 450 GMAT 1: 640 Q48 V28 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: 15281 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 _________________ Contact Rich at: Rich.C@empowergmat.com The Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★ Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 8109 Location: United States (CA) Re: The price of a phone call consists of a standard connection fee, which [#permalink] Show Tags 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. Answer: D _________________ Scott Woodbury-Stewart Founder and CEO Scott@TargetTestPrep.com 122 Reviews 5-star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button. GMATH Teacher Status: GMATH founder Joined: 12 Oct 2010 Posts: 935 The price of a phone call consists of a standard connection fee, which [#permalink] Show Tags 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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Re: The price of a phone call consists of a standard connection fee, which  [#permalink]

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10 Jan 2019, 10:40
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Top Contributor
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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 Let C = price of connection fee Let M = the price PER MINUTE A 10-minute call costs$2.90
We can write: C + 10M = 2.90

A 16-minute call costs $4.40. We can write: C + 16M = 4.40 How much does a 13-minute call cost? So far, we have: C + 10M = 2.90 C + 16M = 4.40 ONE (slower) approach would be to solve the system for C and M, and then calculate the cost of a 13-minute call. The FASTER approach is to recognize that something great happens when we ADD the two equations We get: 2C + 26M = 7.30 Now divide both sides by 2 to get: C + 13M = 3.65 Since C + 13M represents the TOTAL cost of a 13-minute call, we can conclude that a 13-minute call costs$3.65

Cheers,
Brent
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Re: The price of a phone call consists of a standard connection fee, which   [#permalink] 10 Jan 2019, 10:40
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