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The price of a phone call consists of a standard connection

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The price of a phone call consists of a standard connection

by swerve » Thu Jan 10, 2019 7:48 am

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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

The OA is D

Source: Manhattan Prep
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by Brent@GMATPrepNow » Thu Jan 10, 2019 9:29 am
swerve 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

Answer: D

Cheers,
Brent
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The price of a phone call consists of a standard connection

by fskilnik@GMATH » Thu Jan 10, 2019 9:53 am
swerve 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
Source: Manhattan Prep
$$? = f + 13c\,\,\,\,\left[ \$ \right]$$
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.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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by [email protected] » Thu Jan 10, 2019 11:28 am
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: D

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Rich
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by Scott@TargetTestPrep » Mon Jan 21, 2019 5:39 pm
swerve 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 (This is the per-minute charge)

Substituting 0.25 for n into the first equation, we see that f is:

f + 2.5 = 2.90

f = 0.4 (This is the fixed fee)

So a 13-minute call costs 0.4 + 13 x 0.25 = $3.65.

Answer: D

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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