Telephone Company X's monthly charge for long-distance telep

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BTGmoderatorAT: Moderator; Posts: 426; Joined: Tue Aug 22, 2017 8:48 pmFollowed by: 1 member

by BTGmoderatorAT » Tue Mar 06, 2018 7:50 am

Telephone Company X's monthly charge for long-distance telephone calls is $1.95 plus $0.10 per minute, whereas Telephone Company Y's monthly charge is $5.95 plus $0.08 per minute. For what total number of minutes of long-distance calls per month would the monthly charge for the two companies be the same?

A. 100
B. 120
C. 150
D. 180
E. 200

I'm confused how to set up the formulas here. Can any experts help?

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Source: Beat The GMAT — Problem Solving | Tue Mar 06, 2018 7:50 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Tue Mar 06, 2018 8:13 am

ardz24 wrote:Telephone Company X's monthly charge for long-distance telephone calls is $1.95 plus $0.10 per minute, whereas Telephone Company Y's monthly charge is $5.95 plus $0.08 per minute. For what total number of minutes of long-distance calls per month would the monthly charge for the two companies be the same?

A. 100
B. 120
C. 150
D. 180
E. 200

Let x = the total number of minutes of long-distance calls

Telephone Company X's monthly charge for long-distance telephone calls is $1.95 plus $0.10 per minute
So, TOTAL charge = $1.95 + $0.10(x)

Telephone Company Y's monthly charge is $5.95 plus $0.08 per minute
TOTAL charge = $5.95 + $0.08(x)

For what total number of minutes of long-distance calls per month would the monthly charge for the two companies be the same?
We want to satisfy the equation $1.95 + $0.10(x) = $5.95 + $0.08(x)
Subtract 1.95 from both sides to get: 0.1x = 4 + 0.08x
Subtract 0.08x from both sides to get: 0.02x = 4
So, x = 4/0.02
= 400/2
= 200

Answer: E

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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mbawisdom: Senior | Next Rank: 100 Posts; Posts: 94; Joined: Tue Dec 16, 2014 9:50 amFollowed by: 4 members; Location: London, UK; Thanked: 2 times; GMAT Score:770

by mbawisdom » Tue Mar 06, 2018 8:33 am

ardz24 wrote:Telephone Company X's monthly charge for long-distance telephone calls is $1.95 plus $0.10 per minute, whereas Telephone Company Y's monthly charge is $5.95 plus $0.08 per minute. For what total number of minutes of long-distance calls per month would the monthly charge for the two companies be the same?

A. 100
B. 120
C. 150
D. 180
E. 200

I'm confused how to set up the formulas here. Can any experts help?

Let x = the number of minutes

1.95 + 0.10x = 5.95 + 0.08x
0.02x = 4.00
x = 200

Answer is E.

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by [email protected] » Tue Mar 06, 2018 5:58 pm

Hi ardz24,

We're told that Telephone Company X's monthly charge for long-distance telephone calls is $1.95 plus $0.10 per minute and Telephone Company Y's monthly charge is $5.95 plus $0.08 per minute. We're asked for the total number of minutes of long-distance calls per month that would lead to the monthly charges for the two companies to be the SAME. This question can be solved by TESTing THE ANSWERS.

To start, it's worth noting that the difference in per-minute charges from the 2 companies is small (just $0.02 per minute), so we will clearly need a large number of minutes to make up for difference in the 'fixed' costs ($1.95 vs. 5.95). Two of the answers are relatively easy to 'manipulate' (Answers A and E) - so since we're looking for a large number of minutes, I'll start by TESTing Answer E first.

Answer E: 200 minutes
200 minutes on Company X's plan = $1.95 + (200)($0.10) = $1.95 + $20 = $21.95
200 minutes on Company Y's plan = $5.95 + (200)($0.08) = $5.95 + $16 = $21.95
These two totals match, so this must be the answer.

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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StefC10: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Wed Mar 07, 2018 3:57 am

by StefC10 » Wed Mar 07, 2018 4:27 am

My shortcut would be:

Breakeven questions are always the same: you have company X and company Y

X has higher fixed costs and lower variable costs
Y has lower fixed costs and higher variabel costs

You just have to calculate when the difference in fixed costs is gone, the difference is 5.95 - 1.95 = 4
You have to earn those 4 dollar by looking at the difference is variable costs, the difference is 0.10 - 0.08 = 0.02

So you have to earn the 4 dollars/euro's/whatever back by using the variable costs, this ends up being simple by calculating 4 / 0.02 = 200

Long story short, breakeven is always:

5.95 - 1.95 = 4
0.10 - 0.08 = 0.02

4 / 0.02 = 200

The other methods used are the same, i just think this is the simplest to understand

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Mon Mar 12, 2018 4:09 pm

ardz24 wrote:Telephone Company X's monthly charge for long-distance telephone calls is $1.95 plus $0.10 per minute, whereas Telephone Company Y's monthly charge is $5.95 plus $0.08 per minute. For what total number of minutes of long-distance calls per month would the monthly charge for the two companies be the same?

A. 100
B. 120
C. 150
D. 180
E. 200

We can let m = the total number of minutes for long-distance calls for the month and create the equation:

1.95 + 0.1m = 5.95 + 0.08m

0.02m = 4

m = 200

Answer: E

Jeffrey Miller
Head of GMAT Instruction
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

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