Betty sold 3/5 of her family’s garage sale items.

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

Betty sold 3/5 of her family’s garage sale items.

by BTGModeratorVI » Thu Nov 26, 2020 1:06 pm

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Betty sold 3/5 of her family’s garage sale items. Ernest sold 1/2 of the remaining items. What fraction of the family’s garage sale items did Ernest sell?

A. 1/10
B. 1/7
C. 1/6
D. 1/5
E. 1/3

Answer: D
Source: Princeton Review

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Source: Beat The GMAT — Problem Solving | Thu Nov 26, 2020 1:06 pm

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pm; Followed by:5 members

Re: Betty sold 3/5 of her family’s garage sale items.

by deloitte247 » Sat Nov 28, 2020 10:35 am

$$Let\ total\ garage\ items\ available\ for\ sale\ =x$$
$$Betty\ sold\ \frac{3}{5}of\ x$$
$$Remaining\ garage\ item$$
$$=>\ \frac{1}{1}x-\frac{3}{5}x$$
$$\frac{5-3}{5}\left(x\right)=\frac{2}{5}x$$
$$Earnest\ sold\ \frac{1}{2}\ of\ \frac{2}{5}x\ =>$$
$$So\ fraction\ of\ earnest\ sales\ =\ \frac{1}{2}\cdot\frac{2}{5}\cdot x$$
$$\frac{1}{5}x=\frac{1}{5}$$
$$Answer\ =\ D$$

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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: Betty sold 3/5 of her family’s garage sale items.

by Brent@GMATPrepNow » Wed Dec 02, 2020 9:24 am

BTGModeratorVI wrote: ↑
Thu Nov 26, 2020 1:06 pm
Betty sold 3/5 of her family’s garage sale items. Ernest sold 1/2 of the remaining items. What fraction of the family’s garage sale items did Ernest sell?

A. 1/10
B. 1/7
C. 1/6
D. 1/5
E. 1/3

Answer: D
Source: Princeton Review

To solve this question we can use either algebra, or we can assign a "nice value" to the number of garage sale items we started with.
Let's choose a number that works well with the given values: 3/5 and 1/2

Let's say there were 30 items for sale ORIGINALLY

Betty sold 3/5 of her family’s garage sale items.
3/5 of 30 = (3/5)(30) = 18
So, Betty sold 18 items

30 - 18 = 22
So there are now 12 items REMAINING

Ernest sold 1/2 of the remaining items.
1/2 of 12 = (1/2)(12) = 6
So, Ernest sold 6 items

What fraction of the family’s garage sale items did Ernest sell?
6/30 = 1/5

Answer: D

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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GMAT/MBA Expert

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

Re: Betty sold 3/5 of her family’s garage sale items.

by Scott@TargetTestPrep » Sat Dec 05, 2020 6:00 pm

BTGModeratorVI wrote: ↑
Thu Nov 26, 2020 1:06 pm
Betty sold 3/5 of her family’s garage sale items. Ernest sold 1/2 of the remaining items. What fraction of the family’s garage sale items did Ernest sell?

A. 1/10
B. 1/7
C. 1/6
D. 1/5
E. 1/3

Answer: D

Solution:

Since the remaining items after those that Betty sold constitute 1 - 3/5 = 2/5 of all garage sale items, Ernest sold 1/2 x 2/5 = 1/5 of all garage sale items.

Answer: D