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# The price of a phone call consists of a standard connection

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GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4750
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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The price of a phone call consists of a standard connection [#permalink]  25 Jul 2018, 17:20
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Question Stats:

88% (01:23) correct 11% (03:03) wrong based on 9 sessions
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 [Reveal] Spoiler: OA _________________ Sandy If you found this post useful, please let me know by pressing the Kudos Button Try our free Online GRE Test Manager Joined: 06 Jun 2018 Posts: 94 Followers: 0 Kudos [?]: 56 [1] , given: 0 Re: The price of a phone call consists of a standard connection [#permalink] 25 Jul 2018, 23:08 1 This post received KUDOS sandy 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

Note: In both cases Standard connection fee is a constant. So any any changes made it's due to call rate.

Now, 2.9 is for 10 mins

4.40 is for 16 mins

Change = 1.5 is for 6 mins. So, what is the call rate for per min.

1.5 / 6 = 15 /60 = 0.25

Now find out the constant : 10*0.25 = 2.5

So, standard connection rate = 2.90 - 2.05 = 0.40

So charge for 13 mins : 13*0.25 + 0.4 = 3.25 + 0.4 = 3.65

GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4750
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1665 [0], given: 396

Re: The price of a phone call consists of a standard connection [#permalink]  11 Aug 2018, 16:43
Expert's post
Explanation

Since “the price of a phone call consists of a standard connection fee, which is a constant, plus a per-minute charge,” write a formula, using variables for the unknown information. Let c equal the connection fee and r equal the per-minute rate:

$$2.90 = c + r(10)$$
$$4.40 = c + r(16)$$

Now, either substitute and solve or stack and combine the equation. Note that there is one c in each equation, so subtracting is likely to be fastest:

$$4.40 = c + 16r$$
$$- (2.90 = c + 10r)$$

$$1.50 = 6r$$

$$r = 0.25$$

The calls cost 25 cents per minute. Note that most people will next plug r back into either equation to find c, but c isn’t necessary to solve!

A 10-minute call costs $$\2.90$$. That $$\2.90$$ already includes the basic connection fee (which is a constant) as well as the per-minute fee for 10 minutes. The problem asks how much a 13-minute call costs. Add the cost for another 3 minutes ($0.75) to the cost for a 10-minute call ($2.90): $$2.90 + 0.75 = \3.65$$.

In fact, both the 10-minute and 16-minute calls include the same connection fee (which is a constant), so a shortcut can be used to solve. The extra 6 minutes for the 16-minute call cost a total of $4.40 –$2.90 = $1.50. From there, calculate the cost per minute (1.5 ÷ 6 = 0.25) or notice that 13 minutes is halfway between 10 minutes and 16 minutes, so the cost for a 13-minute call must also be halfway between the cost for a 10-minute call and the cost for a 16-minute call. Add half of$1.50, or $0.75, to$2.90 to get \$3.65.
_________________

Sandy
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Re: The price of a phone call consists of a standard connection   [#permalink] 11 Aug 2018, 16:43
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