GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 11 Jul 2020, 13:06 ### 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

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.  # A person purchased a total of 2t + 1 tickets. Some of the tickets cost

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 65187
A person purchased a total of 2t + 1 tickets. Some of the tickets cost  [#permalink]

### Show Tags 00:00

Difficulty:   45% (medium)

Question Stats: 65% (02:27) correct 35% (02:38) wrong based on 62 sessions

### HideShow timer Statistics

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

_________________
GMAT Club Legend  V
Joined: 11 Sep 2015
Posts: 4959
GMAT 1: 770 Q49 V46
Re: A person purchased a total of 2t + 1 tickets. Some of the tickets cost  [#permalink]

### Show Tags

2
1
Top Contributor
2
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

These kinds of questions (Variables in the Answer Choices - VIACs) can be answered algebraically or using the INPUT-OUTPUT approach.
Enchanting has solved the question using the INPUT-OUTPUT approach, so let's solve it algebraically..

3 more \$4 tickets than \$7 tickets were purchased
Let x = the NUMBER of \$7 tickets purchased
So, x + 4 = the NUMBER of \$4 tickets purchased
So, the total NUMBER of tickets purchased = x + (x + 3) = 2x + 3

The question tells us that 2t + 1 tickets were purchased.
So, we can write: 2x + 3 = 2t + 1
Subtract 1 from both sides of the equation to get: 2x + 2 = 2t
Divide both sides by 2 to get: x + 1 = t
Subtract 1 from both sides to get: x = t - 1 we'll use this information later on!

Which of the following expresses the total COST, in dollars, of the 2t + 1 tickets?
Let's first answer this question using the variables we assigned earlier.
The cost of x tickets costing \$7 each = 7x dollars
The cost of x + 3 tickets costing \$4 each = 4(x + 3) dollars
So, the TOTAL cost = 7x + 4(x + 3)
= 7x + 4x + 12
= 11x + 12
We've now expressed the total cost in terms of x.
In order to express the total cost in terms of t, we'll use the fact that x = t - 1

Take: 11x + 12
Substitute to get: 11(t - 1) + 12
Expand: 11t - 11 + 12
Simplify: 11t + 1

Cheers,
Brent
_________________
##### General Discussion
Intern  B
Joined: 07 Apr 2020
Posts: 44
Re: A person purchased a total of 2t + 1 tickets. Some of the tickets cost  [#permalink]

### Show Tags

1
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.
IESE School Moderator S
Joined: 11 Feb 2019
Posts: 308
Re: A person purchased a total of 2t + 1 tickets. Some of the tickets cost  [#permalink]

### Show Tags

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)
_________________

Cheers,
NJ
Intern  B
Joined: 27 Jan 2020
Posts: 14
Re: A person purchased a total of 2t + 1 tickets. Some of the tickets cost  [#permalink]

### Show Tags

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.

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 V
Joined: 04 Jan 2015
Posts: 3410
Re: A person purchased a total of 2t + 1 tickets. Some of the tickets cost  [#permalink]

### Show Tags

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.

_________________ Re: A person purchased a total of 2t + 1 tickets. Some of the tickets cost   [#permalink] 30 May 2020, 21:29

# A person purchased a total of 2t + 1 tickets. Some of the tickets cost  