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Math Expert V
Joined: 02 Sep 2009
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The price of a phone call consists of a standard connection fee, which  [#permalink]

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Difficulty:   15% (low)

Question Stats: 85% (02:14) correct 15% (02:33) wrong based on 131 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 _________________ MBA Section Director V 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 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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Joined: 21 Jan 2015
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Concentration: Strategy, Marketing
GMAT 1: 620 Q48 V28 GMAT 2: 690 Q49 V35 WE: Sales (Consumer Products)
Re: The price of a phone call consists of a standard connection fee, which  [#permalink]

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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  G 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 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 V 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 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 _________________ Target Test Prep Representative D 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 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 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 P 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 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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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
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Re: The price of a phone call consists of a standard connection fee, which  [#permalink]

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