Last visit was: 24 Apr 2026, 03:02 It is currently 24 Apr 2026, 03:02
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
805+ (Hard)|   Word Problems|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 24 Apr 2026
Posts: 109,803
Own Kudos:
810,923
 [24]
Given Kudos: 105,868
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: 109,803
Kudos: 810,923
 [24]
A charity sells 140 benefit tickets for a total of 2001. Some tickets 18 Mar 2019, 02:33
1
Kudos
Add Kudos
23
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

95% (hard)

Question Stats:

43% (03:08) correct 57% (03:16) wrong based on 130 sessions

History

Date
Time
Result
Not Attempted Yet
A charity sells 140 benefit tickets for a total of 2001. Some tickets sell for full price (a whole dollar amount), and the rest sells for half price. How much money is raised by the full-price tickets?


(A) 782
(B) 986
(C) 1158
(D) 1219
(E) 1449
ShowHide Answer
Official Answer
A
Most Helpful Reply
User avatar
BrentGMATPrepNow
User avatar
Major Poster
Joined: 12 Sep 2015
Last visit: 31 Oct 2025
Posts: 6,733
Own Kudos:
36,454
 [11]
Given Kudos: 799
Location: Canada
Expert
Expert reply
Posts: 6,733
Kudos: 36,454
 [11]
A charity sells 140 benefit tickets for a total of 2001. Some tickets 18 Mar 2019, 17:12
9
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
Bunuel
A charity sells 140 benefit tickets for a total of 2001. Some tickets sell for full price (a whole dollar amount), and the rest sells for half price. How much money is raised by the full-price tickets?


(A) 782
(B) 986
(C) 1158
(D) 1219
(E) 1449
Show more

Let x = # of tickets sold for FULL PRICE
So, 140-x = # of tickets sold for HALF PRICE (since 140 tickets were sold in total)

Let y = the FULL PRICE cost
So, y/2 = the HALF PRICE cost

A charity sells 140 benefit tickets for a total of $2001
We can write: (amount raised by FULL-price tickets) + (amount raised by HALF-price tickets) = $2001
Substitute values to get: xy + (y/2)(140 - x) = $2001
Expand to get: xy + 70y - xy/2 = $2001
Multiply both sides by 2 to get: 2xy + 140y - xy = $4002
Simplify to get: xy + 140y = $4002

How much money is raised by the full-price tickets?
IMPORTANT: xy = the money is raised by the full-price tickets.
So our goal is to find the value of xy

We already know that xy + 140y = $4002
Subtract 140y from both sides to get: xy = $4002 - 140y

Since we're told the price of a full-price ticket is an INTEGER value (i.e., "a whole dollar amount"), we know that the units digit of 140y is 0
So, xy = $4002 - (some number with units digit 0)
So, xy must have units digit 2
Check the answer choices ... only answer choice A has units digit 2

Answer: A

Cheers,
Brent
General Discussion
avatar
ZulfiquarA
avatar
Joined: 06 Apr 2021
Last visit: 29 Nov 2025
Posts: 61
Own Kudos:
40
 [1]
Given Kudos: 38
Posts: 61
Kudos: 40
 [1]
A charity sells 140 benefit tickets for a total of 2001. Some tickets 08 Sep 2021, 23:44
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
If it wasn't A I would definitely skip and move forward because this kind of question takes time if you aren't an algebric genius. I will share what I did to solve this.
No. of tickets: 140
Sales from tickets of a price that is a whole no.: Let's take A 782
Factorize 782: 2*17*23
The price cannot be 2 because 17*23 will far exceed the 140 no. of tickets so the tickets sold at a whole number can be either 34 tickets @ 23$ or 23 tickets @ 34$
When you sell 34 tickets @ 23$ the other number of tickets that is 106 would be sold @ 11.5 which gives 1219$
I chose A and it took me more than 3 minutes
User avatar
GMATGuruNY
User avatar
Joined: 04 Aug 2010
Last visit: 02 Apr 2026
Posts: 1,347
Own Kudos:
3,905
Given Kudos: 9
Schools:Dartmouth College
Expert
Expert reply
Posts: 1,347
Kudos: 3,905
A charity sells 140 benefit tickets for a total of 2001. Some tickets 02 May 2023, 11:37
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
A charity sells 140 benefit tickets for a total of 2001. Some tickets sell for full price (a whole dollar amount), and the rest sells for half price. How much money is raised by the full-price tickets?


(A) 782
(B) 986
(C) 1158
(D) 1219
(E) 1449
Show more

Average price per ticket \(= \frac{revenue}{quantity} = \frac{2001}{140}\) ≈ 14.3
Implication:
A full-price ticket must cost MORE than $14.30, while a half-price ticket must cost LESS than $14.30.

Total revenue = 2001 = 3*23*29.
Since the price of a full-price ticket must be an INTEGER value greater than 14.3, the prime-factorization above implies that a full-price ticket probably costs either $23 or $29, yielding the following options:
Full-price = 29, half-price = 14.5
Full-price = 23, half-price = 11.5
Since a half-price ticket must cost less than $14.30, only the green option is viable.

Let F = the number of full-price tickets and H = the number of half-price tickets.
Since the total revenue is $2001, we get:
23F + 11.5H = 2001
46F + 23H = 4002

Since a total of 140 tickets are sold, we get:
F + H = 140
23F + 23H = 3220

Subtracting the red equation from the blue equation, we get:
23F = 782
F = 34
Success!
The number of full-price tickets is an integer.

The equation in green indicates that the total revenue yielded by the $23 full-price tickets = 782.

Show Spoiler
A
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,966
Own Kudos:
1,117
Posts: 38,966
Kudos: 1,117
A charity sells 140 benefit tickets for a total of 2001. Some tickets 18 Nov 2025, 08:58
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
109802 posts
Krunaal
Tuck School Moderator
853 posts