Last visit was: 24 Apr 2026, 13:13 It is currently 24 Apr 2026, 13:13
Home
Messages
Tests
Schools
Events
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 24 Apr 2026
Posts: 109,820
Own Kudos:
811,062
 [18]
Given Kudos: 105,873
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,820
Kudos: 811,062
 [18]
A certain collector sold 5/8 of her paintings, including 2/3 of her 18 Jun 2018, 21:42
Kudos
Add Kudos
18
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

45% (medium)

Question Stats:

74% (02:49) correct 26% (02:55) wrong based on 464 sessions

History

Date
Time
Result
Not Attempted Yet
A certain collector sold \(\frac{5}{8}\) of her paintings, including \(\frac{2}{3}\) of her impressionist paintings. If \(\frac{3}{5}\) of her paintings were impressionist, what fraction of the paintings that were NOT SOLD were impressionist?


A. \(\frac{1}{4}\)

B. \(\frac{3}{8}\)

C. \(\frac{2}{5}\)

D. \(\frac{8}{15}\)

E. \(\frac{5}{8}\)
ShowHide Answer
Official Answer
D
User avatar
pushpitkc
User avatar
Joined: 26 Feb 2016
Last visit: 19 Feb 2025
Posts: 2,800
Own Kudos:
6,235
 [3]
Given Kudos: 47
Location: India
GPA: 3.12
Posts: 2,800
Kudos: 6,235
 [3]
A certain collector sold 5/8 of her paintings, including 2/3 of her 18 Jun 2018, 21:55
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
A certain collector sold \(\frac{5}{8}\) of her paintings, including \(\frac{2}{3}\) of her impressionist paintings. If \(\frac{3}{5}\) of her paintings were impressionist, what fraction of the paintings that were NOT SOLD were impressionist?


A. \(\frac{1}{4}\)

B. \(\frac{3}{8}\)

C. \(\frac{2}{5}\)

D. \(\frac{8}{15}\)

E. \(\frac{5}{8}\)
Show more

Let's assume that the collector has 80 paintings.

We are told that \(\frac{5}{8}\) of the paintings (\(\frac{5}{8}*80 = 50\) paintings) are sold.

\(\frac{3}{5}\) of her paintings were impressionist -> \(\frac{3}{5}*80 = 48\) paintings were impressionist.

Of the impressionist paintings, \(\frac{2}{3}*48 = 32\) paintings are sold.

Therefore, the fraction of impressionist paintings that were not sold is \(\frac{48-32}{80-50} = \frac{16}{30} = \frac{8}{15}\)(Option D)
User avatar
EgmatQuantExpert
User avatar
e-GMAT Representative
Joined: 04 Jan 2015
Last visit: 02 Apr 2024
Posts: 3,657
Own Kudos:
20,880
Given Kudos: 165
Expert
Expert reply
Posts: 3,657
Kudos: 20,880
A certain collector sold 5/8 of her paintings, including 2/3 of her 18 Jun 2018, 22:16
Kudos
Add Kudos
Bookmarks
Bookmark this Post

Solution



Given:
    • A collector sold \(\frac{5}{8}\) of her paintings, which include \(\frac{2}{3}\) of her impressionist paintings
    • \(\frac{3}{5}\) of her paintings were impressionist

To find:
    • The fraction of the paintings that were not sold were impressionist

Approach and Working:
As we have 3 fractional terms to deal with, we can assume the total number of paintings to be the LCM (8, 3, 5) = 120 [LCM of the denominators of the fractions]
    • Total impressionist paintings = \(120 * \frac{3}{5} = 72\)
    • Number of paintings sold = \(120 * \frac{5}{8} = 75\)
      o Hence, number of paintings not sold = \(120 – 75 = 45\)

    • Number of impressionist paintings sold = \(72 * \frac{2}{3} = 48\)
      o Hence, number of impressionist paintings not sold = \(72 – 48 = 24\)

    • Therefore, the fraction of paintings that were not sold were impressionist = \(\frac{24}{45} = \frac{8}{15}\)

Hence, the correct answer is option D.

Answer: D
User avatar
nigina93
User avatar
Joined: 31 Jul 2017
Last visit: 23 Jul 2025
Posts: 162
Own Kudos:
342
Given Kudos: 347
Location: Tajikistan
Posts: 162
Kudos: 342
A certain collector sold 5/8 of her paintings, including 2/3 of her 19 Jun 2018, 04:12
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I picked number to start with. to selected easy number, i multiplied denominators of all fractions, 8*3*5=120, so total nu of painings assumed is 120. She sold a total of 75 painings, while she owned a total of 72 impressionist paintings, out of which she sold 2/3 or 48. So she has the remaining of 24 impress. painings, while total nu is 120-75, 45. so it is 24/45
User avatar
GMATGuruNY
User avatar
Joined: 04 Aug 2010
Last visit: 02 Apr 2026
Posts: 1,347
Own Kudos:
3,905
 [1]
Given Kudos: 9
Schools:Dartmouth College
Expert
Expert reply
Posts: 1,347
Kudos: 3,905
 [1]
A certain collector sold 5/8 of her paintings, including 2/3 of her 19 Jun 2018, 05:17
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
A certain collector sold \(\frac{5}{8}\) of her paintings, including \(\frac{2}{3}\) of her impressionist paintings. If \(\frac{3}{5}\) of her paintings were impressionist, what fraction of the paintings that were NOT SOLD were impressionist?


A. \(\frac{1}{4}\)

B. \(\frac{3}{8}\)

C. \(\frac{2}{5}\)

D. \(\frac{8}{15}\)

E. \(\frac{5}{8}\)
Show more
s

Every painting is EITHER sold OR not sold.
Every painting is EITHER impressionist OR not impressionist.
For an either/or problem, use a DOUBLE-MATRIX to organize the data.

Let S = sold, NS = not sold, I = impressionist and NI = not impressionist.
Let the total number of paintings = the LCM of the 3 denominators in the prompt = 8*3*5 = 120.
The following matrix is yielded:



A certain collector sold \(\frac{5}{8}\) of her paintings.
Since total sold = \(\frac{5}{8} * 120 = 75\), the following matrix is yielded:



\(\frac{3}{5}\) of her paintings were impressionist.
Since total impressionist = \(\frac{3}{5} * 120 = 72\), the following matrix is yielded:



A certain collector sold...\(\frac{2}{3}\) of her impressionist paintings.
Since \(\frac{2}{3}\) of the 72 impressionist paintings = \(\frac{2}{3} * 72 = 48\), the following matrix is yielded:



What fraction of the paintings that were NOT SOLD were impressionist?
In the resulting matrix:
\(\frac{(impressionist-not-sold)}{(total-not-sold)} = \frac{24}{45} = \frac{8}{15}\).

Show Spoiler
D
User avatar
vivapopo
User avatar
Joined: 19 Jul 2017
Last visit: 06 Jun 2020
Posts: 32
Own Kudos:
6
 [1]
Given Kudos: 1,158
Posts: 32
Kudos: 6
 [1]
A certain collector sold 5/8 of her paintings, including 2/3 of her 26 Mar 2019, 13:53
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
A certain collector sold \(\frac{5}{8}\) of her paintings, including \(\frac{2}{3}\) of her impressionist paintings. If \(\frac{3}{5}\) of her paintings were impressionist, what fraction of the paintings that were NOT SOLD were impressionist?


A. \(\frac{1}{4}\)

B. \(\frac{3}{8}\)

C. \(\frac{2}{5}\)

D. \(\frac{8}{15}\)

E. \(\frac{5}{8}\)
Show more

HELLO!
LCM (8, 3, 5) = 120
Sold=120*5/8=75
Impression=120*3/5=72
Imp sold=72*2/3=48
Imp unsold =72-48=24
Unsold=120-75=45
Fr=24/45=8/15
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,975
Own Kudos:
1,117
Posts: 38,975
Kudos: 1,117
A certain collector sold 5/8 of her paintings, including 2/3 of her 23 Dec 2025, 12:44
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109820 posts
Krunaal
Tuck School Moderator
853 posts