Last visit was: 23 Jul 2024, 05:16 It is currently 23 Jul 2024, 05:16
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.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Date
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94580
Own Kudos [?]: 643206 [39]
Given Kudos: 86728
Send PM
Most Helpful Reply
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Own Kudos [?]: 30852 [15]
Given Kudos: 799
Location: Canada
Send PM
Intern
Intern
Joined: 07 Apr 2020
Posts: 44
Own Kudos [?]: 87 [6]
Given Kudos: 2
Send PM
General Discussion
IESE School Moderator
Joined: 11 Feb 2019
Posts: 270
Own Kudos [?]: 173 [0]
Given Kudos: 53
Send PM
Re: A person purchased a total of 2t + 1 tickets. Some of the tickets cost [#permalink]
I took a lot of time to think on how to proceed with this question. Then thought why "+1", why not "2t" or just "t".

Then realized, 2t+1 is always odd and qtn also states that number of $4 tickets is 3 more than $7 tickets.

so tried t =1==> tickets = 3; it implies all $4 tickets; price = 12 i.e. 2t+1
t=2 ==> tickets = 5;tickets = 2 + 3; one each for $4 and $7 and 3 tickets extra for $4. Price = 1 tickets for $11 and 3 extra tickets for $12; total price = 23 i.e. (2t+1)
t=3 ==>tickets = 7; tickets = 4 + 3; two each for $4 and $7 and 3 tickets extra for $4. Price = 2 tickets for $11 and 3 extra tickets for $12 ; total price = 34 i.e. (2t+1)

I combined price of $4 and $7 = $11 and it means 2 tickets combined for $11 each ($4+$7)
Intern
Intern
Joined: 27 Jan 2020
Posts: 12
Own Kudos [?]: 2 [0]
Given Kudos: 1029
Send PM
Re: A person purchased a total of 2t + 1 tickets. Some of the tickets cost [#permalink]
Enchanting wrote:
Bunuel wrote:
A person purchased a total of 2t + 1 tickets. Some of the tickets cost $4 each and the remaining tickets cost $7 each. If 3 more $4 tickets than $7 tickets were purchased, which of the following expresses the total cost, in dollars, of the 2t + 1 tickets?

A. 11t + 1
B. 11t + 12
C. 22t – 10
D. 22t + 11
E. 22t + 23



PS20417


We will solve this by substitution.
    If t = 1, then number of tickets = 3
      Number of $ 4 tickets = 3
        Cost of $ 4 tickets = 12
      Number of $ 7 tickets = 0
        Cost of $ 7 tickets =0
      Total cost =12 = 11*1+1 = 11t+1
    We are getting 11t + 1 for any value of t.
Answer: Option A.



Why did you considered all the 3 tickets as of 4$ and 0 for 7$?
I didn't get the highlighted part, can you elaborate please?
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3710
Own Kudos [?]: 17353 [2]
Given Kudos: 165
Send PM
Re: A person purchased a total of 2t + 1 tickets. Some of the tickets cost [#permalink]
2
Bookmarks
Expert Reply

Solution



Given
In this question, we are given that
    • A person purchased a total of 2t + 1 tickets.
    • Some of the tickets cost $4 each and the remaining tickets cost $7 each

To find
We need to determine
    • If 3 more $4 tickets than $7 tickets were purchased, which of the following expresses the total cost, in dollars, of the 2t + 1 tickets

Approach and Working out
Let the number of $4 tickets be x, and the number of $7 tickets be y
    • x + y = 2t + 1
    • Cost = 4x + 7y

Now, if x = y + 3
    • Cost = 4(y + 3) + 7(y) = 11y + 12
    • And, 2y + 3 = 2t + 1
      o Implies, y = t - 1

    • Thus, Cost = 11(t – 1) + 12 = 11t + 1

Thus, option A is the correct answer.

Correct Answer: Option A
Director
Director
Joined: 09 Jan 2020
Posts: 953
Own Kudos [?]: 235 [1]
Given Kudos: 432
Location: United States
Send PM
Re: A person purchased a total of 2t + 1 tickets. Some of the tickets cost [#permalink]
1
Kudos
Bunuel wrote:
A person purchased a total of 2t + 1 tickets. Some of the tickets cost $4 each and the remaining tickets cost $7 each. If 3 more $4 tickets than $7 tickets were purchased, which of the following expresses the total cost, in dollars, of the 2t + 1 tickets?

A. 11t + 1
B. 11t + 12
C. 22t – 10
D. 22t + 11
E. 22t + 23

PS20417


x = 4 dollar tickets
y = 7 dollar tickets

\(x = y + 3\)

\(x + y = 2y+ 3\)

\(2y + 3 = 2t + 1\)

\(2y = 2t - 2\)

\(y = t - 1\)

\(4x+7y\) = total cost

\(4(y+3) + 7y\)

\(4y + 12 + 7y\)

\(11y + 12\)

\(11(t-1) + 12\)

\(11t - 11 + 12 = 11t + 1\)
Senior Manager
Senior Manager
Joined: 18 Jun 2018
Posts: 334
Own Kudos [?]: 201 [1]
Given Kudos: 1283
Concentration: Finance, Healthcare
Send PM
A person purchased a total of 2t + 1 tickets. Some of the tickets cost [#permalink]
1
Bookmarks
Let t = 2, which means that we have 2(2)+1 = 5 tickets in total.

Let the number of $4 tickets = 4 and the number of $7 tickets = 1 (i.e. number of $4 tickets = number of $7 ticket(s) + 1)

Total $4 ticket = 4 x $4 = $16 and total of $7 ticket = 1 x $7 = $7 for a combined total of $23 (so we have to look for this in the answer choices)

Now test the options:

A: 11(2) + 1 = $23 (keep)
B: 11(2) + 12 = $34 (you can skip this one outrightly since it is $11 greater than option A)
C: 22(2) - 10 = $34 (not what we are looking for)
D: 22(2) + 11 = $55 (not what we are looking for; this one can also be skipped since we can tell that it is more than $23 w/o doing the math)
E: 22(2) + 23 = $67 (not what we are looking for; this one can also be skipped since we can tell that it is more than $23 w/o doing the math)

The answer is A.
Intern
Intern
Joined: 05 Mar 2021
Posts: 10
Own Kudos [?]: 7 [0]
Given Kudos: 41
Location: India
Schools: ISB '24
Send PM
Re: A person purchased a total of 2t + 1 tickets. Some of the tickets cost [#permalink]
Given the total number of tickets = 2t+1 (odd number of tickets)
4 dollar tickets + 7 dollar tickets = 2t +1

Given that 4 dollar ticket is 3 more than 7 dollar ticket

Therefore , subtracting 3 from 2t+1 will give the number of equal 7 and 4 dollar tickets

2t +1 -3 = 2t -2 = 2 (t-1)

we have 2 types of tickets , equally dividing 2 (t-1) i.e 2 (t-1)/2 we get t-1 tickets in 7 dollars and t-1 tickets in 4 dollars
Multiplying the cost of each type, we get
7(t-1) + 4(t-1) = 11t -11.

Remember, we subtracted 3 - 4 dollar tickets from the total number of tickets.
Add (3x4) to 11t -11

Therefore total cost = 11t -11 + 12 = 11t +1
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10135
Own Kudos [?]: 17047 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
Re: A person purchased a total of 2t + 1 tickets. Some of the tickets cost [#permalink]
Expert Reply
Put t = 2 so total tickets purchased are: 5

The number of tickets of $4: 4 [cost 4 * 4 = 16]
The number of tickets of $7: 1 [cost 7 * 1 = 7]

So, 5 tickets when t = 2, will have a total cost of $23.

2t + 1 tickets then will have total cost as in when t = 2 gives us 23: 11(t) + 1

Answer A
Senior Manager
Senior Manager
Joined: 16 Oct 2020
Posts: 262
Own Kudos [?]: 168 [0]
Given Kudos: 2383
GMAT 1: 460 Q28 V26
GMAT 2: 550 Q39 V27
GMAT 3: 610 Q39 V35
GMAT 4: 650 Q42 V38
GMAT 5: 720 Q48 V41
Send PM
Re: A person purchased a total of 2t + 1 tickets. Some of the tickets cost [#permalink]
gmatophobia ScottTargetTestPrep

I was able to recognize that "2t+1" indicates an odd number of tickets but was stumped beyond that point.

I'm not sure why there's a need to introduce additional variables x and y (as others have) when t clearly stands for the number of tickets and the answer choices are also in terms of t.

What might be the simplest way to approach this question?
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19175
Own Kudos [?]: 22696 [1]
Given Kudos: 286
Location: United States (CA)
Send PM
Re: A person purchased a total of 2t + 1 tickets. Some of the tickets cost [#permalink]
1
Kudos
Expert Reply
achloes wrote:
gmatophobia ScottTargetTestPrep

I was able to recognize that "2t+1" indicates an odd number of tickets but was stumped beyond that point.

I'm not sure why there's a need to introduce additional variables x and y (as others have) when t clearly stands for the number of tickets and the answer choices are also in terms of t.

What might be the simplest way to approach this question?


I think the simplest approach is to test answer choices. Just pick some value for t and calculate the cost of 2t + 1 tickets according to the information in the question stem. Then, substitute the value of t in the answer choices. Eliminate any answer choice that does not give you the same value as the cost you calculated. By picking different values for t if necessary (it won't be), repeat the process until all but one of the answer choices are eliminated.

For your question about using variables other than t, if you can somehow come up with the expressions t - 1 and t + 2, you can calculate 7(t - 1) + 4(t + 2) to obtain the total cost directly. However, it is not easy to come up with two expressions that add up to 2t + 1 where one of the expressions is 3 greater than the other. We simply use the variables x and y (or x and x + 3) to determine these two expressions. If you can determine these two expressions mentally, then by all means, go for it!
GMAT Club Bot
Re: A person purchased a total of 2t + 1 tickets. Some of the tickets cost [#permalink]
Moderator:
Math Expert
94580 posts