Problem Solving

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

BTGmoderatorLU wrote:Source: Manhattan Prep

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

BTGmoderatorLU wrote:Source: Manhattan Prep

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

A 10-minute call costs $2.90 and a 16-minute call costs $4.40
$4.40 - $2.90 = $1.50, and 16 minutes - 10 minutes = 6 minutes

So, the extra $1.50 paid for extra 6 minutes of calling
So, $0.75 would pay for 3 minutes of calling

How much does a 13-minute call cost?
A 10-minute call costs $2.90
So, the cost of a 13-minute call = $2.90 + $0.75 = $3.65

Answer: D

Cheers,
Brent