BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Beth has a collection of 8 boxes of clothing for a charity,

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Moderator
Posts: 2599
Joined: Sun Oct 29, 2017 2:08 pm
Followed by:2 members

Beth has a collection of 8 boxes of clothing for a charity,

by AAPL » Sat Feb 02, 2019 7:38 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

GMAT Prep

Beth has a collection of 8 boxes of clothing for a charity, and the average (arithmetic mean) number of pieces of clothing per box is c. If she replaces a box in the collections that have 12 pieces of clothing with a box that contains 22 pieces of clothing, what is the average number of pieces of clothing per box for the new collection in terms of c?

A. c-5/4
B. c+5/4
C. 8-10/c
D. 8+10/c
E. 8c-10

OA B
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
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

by Brent@GMATPrepNow » Sat Feb 02, 2019 7:57 am
AAPL wrote:GMAT Prep

Beth has a collection of 8 boxes of clothing for a charity, and the average (arithmetic mean) number of pieces of clothing per box is c. If she replaces a box in the collections that have 12 pieces of clothing with a box that contains 22 pieces of clothing, what is the average number of pieces of clothing per box for the new collection in terms of c?

A. c - 5/4
B. c + 5/4
C. 8 - 10/c
D. 8 + 10/c
E. 8c - 10

OA B

One box contains 12 items of clothing
Let t, u, v, w, x, y, z = the number of items in each of the other 7 boxes

Beth has a collection of 8 boxes of clothing for a charity, and the average (arithmetic mean) number of pieces of clothing per box is c.
We can write: (t + u + v + w + x + y + z + 12)/8 = c

If she replaces a box in the collections that has 12 pieces of clothing with a box that contains 22 pieces of clothing, what is the average number of pieces of clothing per box for the new collection in terms of c?
If we replace the box with 12 items with a box with 22 items, the NEW average = (t + u + v + w + x + y + z + 22)/8
If we replace 22 with 12 + 10, then the NEW average = (t + u + v + w + x + y + z +12 + 10)/8

USEFUL PROPERTY: (a + b)/c = a/c + b/c
We apply the above property to write: NEW average = (t + u + v + w + x + y + z +12)/8 + 10/8
Replace first fraction with c to get: NEW average = c + 10/8
Simplify remaining fraction to get: NEW average = c + 5/4

Answer: B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 2095
Joined: Tue Dec 04, 2012 3:22 pm
Thanked: 1443 times
Followed by:247 members

by ceilidh.erickson » Sat Feb 02, 2019 9:28 am
When there are variables in the answer choices in a PS problem, it's often easy to pick our own values for those variables.

With averages, it's often easiest to just treat each member of the group as the same. i.e. let's say that in this case, we have 8 identical boxes with 12 clothing items each.
So the original average c = 12.
If we have 8 boxes with an average of 12 each, the total # of clothing items = 8*12 = 96.

If we change one of those boxes from 12 to 22, we simply have 10 more clothing items total: 96 + 10 = 106 pieces of clothing.
If our new total is 106 but the number of boxes is the same at 8, the new average = 106/8 = 13.25.

To see which answer choice fits, we plug in c = 12 into each answer choice, and see which gives us our target value of 13.25.

A. c - 5/4 --> 12 - 5/4 = 10.75. No.

B. c + 5/4 --> 12 + 5/4 = 13.25. Yes.

C. 8 - 10/c --> 8 - 10/12 7.1666... No.

D. 8 + 10/c --> 8 + 10/12 8.83333.... No.

E. 8c - 10 --> 8*12 - 10 = 86. No.

The answer is B.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8086
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

by Scott@TargetTestPrep » Wed Feb 06, 2019 6:25 pm
AAPL wrote:GMAT Prep

Beth has a collection of 8 boxes of clothing for a charity, and the average (arithmetic mean) number of pieces of clothing per box is c. If she replaces a box in the collections that have 12 pieces of clothing with a box that contains 22 pieces of clothing, what is the average number of pieces of clothing per box for the new collection in terms of c?

A. c-5/4
B. c+5/4
C. 8-10/c
D. 8+10/c
E. 8c-10

OA B
The sum of Beth's original boxes is 8c.

After she replaces a 12-piece box with a 22-piece box, the new sum is 8c - 12 + 22 = 8c + 10, so the new average is:

(8c + 10)/8 = 8c/8 + 10/8 = c + 5/4

Answer: B

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

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

ImageImage
Top
Post new topic Post Reply
• Page 1 of 1