A school supply store sells only one kind of desk and one kind of chair,

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BTGModeratorVI: Legendary Member; Posts: 1223; Joined: Sat Feb 15, 2020 2:23 pm; Followed by:1 members

A school supply store sells only one kind of desk and one kind of chair,

by BTGModeratorVI » Fri Feb 28, 2020 10:03 am

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A school supply store sells only one kind of desk and one kind of chair, at a uniform cost per desk or per chair. If the total cost of 3 desks and 1 chair is twice that of 1 desk and 3 chairs, then the total cost of 4 desks and 1 chair is how many times that of 1 desk and 4 chairs?

A. 5
B. 3
C. 8/3
D. 5/2
E. 7/3

Answer: E
Source: Official Guide

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Source: Beat The GMAT — Problem Solving | Fri Feb 28, 2020 10:03 am

swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

Re: A school supply store sells only one kind of desk and one kind of chair,

by swerve » Sat Feb 29, 2020 5:22 am

BTGModeratorVI wrote: ↑
Fri Feb 28, 2020 10:03 am
A school supply store sells only one kind of desk and one kind of chair, at a uniform cost per desk or per chair. If the total cost of 3 desks and 1 chair is twice that of 1 desk and 3 chairs, then the total cost of 4 desks and 1 chair is how many times that of 1 desk and 4 chairs?

A. 5
B. 3
C. 8/3
D. 5/2
E. 7/3

Answer: E
Source: Official Guide

Let \(d\) be the price per desk and let \(c\) be the price per chair.

\(3d+c=2(d+3c)\)
\(3d+c=2d+6c\)
\(d=5c\)

\(\dfrac{4d+c}{d+4c} = \dfrac{21c}{9c} = \dfrac{7}{3}\quad\Longrightarrow\quad\)E

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

Re: A school supply store sells only one kind of desk and one kind of chair,

by Brent@GMATPrepNow » Mon Mar 02, 2020 7:07 am

BTGModeratorVI wrote: ↑
Fri Feb 28, 2020 10:03 am
A school supply store sells only one kind of desk and one kind of chair, at a uniform cost per desk or per chair. If the total cost of 3 desks and 1 chair is twice that of 1 desk and 3 chairs, then the total cost of 4 desks and 1 chair is how many times that of 1 desk and 4 chairs?

A. 5
B. 3
C. 8/3
D. 5/2
E. 7/3

Answer: E
Source: Official Guide

Let C = the cost of ONE chair
Let D = the cost of ONE deck

The total cost of 3 desks and 1 chair is twice that of 1 desk and 3 chairs
We can write: 3D + C = 2(D + 3C)
Expand to get: 3D + C = 2D + 6C
Subtract 2D from both sides: D + C = 6C
Subtract C from both sides: D = 5C

The total cost of 4 desks and 1 chair is how many times that of 1 desk and 4 chairs?
This is asking us to determine how many times the price of 1 desk and 4 chairs DIVIDES INTO the price of 4 desks and 1 chair

In other words, we want to find the value of (4D + C)/(D + 4C)

Since we now know that D = 5C, we can replace D with 5C to get:
(4D + C)/(D + 4C) = [4(5C) + C]/[5C + 4C]
= [20C + C]/9C
= 21C/9C
= 21/9
= 7/3

Answer: E

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8083; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

Re: A school supply store sells only one kind of desk and one kind of chair,

by Scott@TargetTestPrep » Wed Mar 04, 2020 5:09 am

BTGModeratorVI wrote: ↑
Fri Feb 28, 2020 10:03 am
A school supply store sells only one kind of desk and one kind of chair, at a uniform cost per desk or per chair. If the total cost of 3 desks and 1 chair is twice that of 1 desk and 3 chairs, then the total cost of 4 desks and 1 chair is how many times that of 1 desk and 4 chairs?

A. 5
B. 3
C. 8/3
D. 5/2
E. 7/3

Answer: E
Source: Official Guide

Let’s let D = the cost of a desk and C = the cost of a chair. We can create the equation:

3D + C = 2(D + 3C)

3D + C = 2D + 6C

D = 5C

Let’s let 4 desks and 1 chair cost K times the cost of 1 desk and 4 chairs. So, we have:

4D + C = K(D + 4C)

Substituting 5C for D, we have:

20C + C = K(5C + 4C)

21C= K(9C)

K = 21C/9C = 7/3

Answer: E

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