Copper pipe costs $x$ cents per foot in $8$-foot lengths, and $x + y$ cents per foot in shorter lengths. What is

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M7MBA: Moderator; Posts: 2058; Joined: Sun Oct 29, 2017 4:24 amFollowed by: 5 members; Thanked: 1 times

by M7MBA » Thu Oct 29, 2020 12:46 pm

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Copper pipe costs $x$ cents per foot in $8$-foot lengths, and $x + y$ cents per foot in shorter lengths. What is the lowest possible price, in cents, of $51$ feet of pipe in terms of $x$ and $y?$

A. $51(x + y)$
B. $51x$
C. $48x + 3y$
D. $48(x + y)$
E. $51x + 3y$

Answer: E

Source: Princeton Review

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Source: Beat The GMAT — Problem Solving | Thu Oct 29, 2020 12:46 pm

swerve: Legendary Member; Posts: 2545; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

Re: Copper pipe costs $x$ cents per foot in $8$-foot lengths, and $x + y$ cents per foot in shorter lengths. What

by swerve » Fri Oct 30, 2020 5:53 am

M7MBA wrote: ↑
Thu Oct 29, 2020 12:46 pm
Copper pipe costs $x$ cents per foot in $8$-foot lengths, and $x + y$ cents per foot in shorter lengths. What is the lowest possible price, in cents, of $51$ feet of pipe in terms of $x$ and $y?$

A. $51(x + y)$
B. $51x$
C. $48x + 3y$
D. $48(x + y)$
E. $51x + 3y$

Answer: E

Source: Princeton Review

$51=8 \cdot 6 + 3$

So we need $6$ bars of $8$-foot length, which costs $48x$ and $3$-foot shorter bars, which costs $3(x+y)$

$48x+3(x+y)=51x+3y\Longrightarrow$ E

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jhavyom: Junior | Next Rank: 30 Posts; Posts: 16; Joined: Fri Oct 02, 2020 9:16 am

Re: Copper pipe costs $x$ cents per foot in $8$-foot lengths, and $x + y$ cents per foot in shorter lengths. What

by jhavyom » Sun Nov 01, 2020 12:33 am

M7MBA wrote: ↑
Thu Oct 29, 2020 12:46 pm
Copper pipe costs $x$ cents per foot in $8$-foot lengths, and $x + y$ cents per foot in shorter lengths. What is the lowest possible price, in cents, of $51$ feet of pipe in terms of $x$ and $y?$

A. $51(x + y)$
B. $51x$
C. $48x + 3y$
D. $48(x + y)$
E. $51x + 3y$

Answer: E

Source: Princeton Review

51 foot = 48 foot + 3 foot
Since 48 is a multiple of 8, price for 48 foot = 48x
Now, price for remaining 3 foot, 3(x+y)

Total cost = 48x + 3(x+y) = 51x + 3y

Choice E is the answer.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8155; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: Copper pipe costs $x$ cents per foot in $8$-foot lengths, and $x + y$ cents per foot in shorter lengths. What

by Scott@TargetTestPrep » Thu Nov 05, 2020 2:39 pm

M7MBA wrote: ↑
Thu Oct 29, 2020 12:46 pm
Copper pipe costs $x$ cents per foot in $8$-foot lengths, and $x + y$ cents per foot in shorter lengths. What is the lowest possible price, in cents, of $51$ feet of pipe in terms of $x$ and $y?$

A. $51(x + y)$
B. $51x$
C. $48x + 3y$
D. $48(x + y)$
E. $51x + 3y$

Answer: E

Solution:

For 51 feet of pipe, the cheapest option is to buy six 8-foot pipes and one 3-foot pipe. Therefore, the lowest possible price, in cents, of 51 feet of pipe, is:

6 * 8 * x + 1 * 3 * (x + y) = 48x + 3x + 3y = 51x + 3y

Answer: E

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