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
The price of a phone call consists of a standard connection
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Let C = price of connection feeswerve 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 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
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Brent
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$$? = f + 13c\,\,\,\,\left[ \$ \right]$$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
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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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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich
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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::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
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
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