On the day of the performance of a certain play, each ticket

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pm; Followed by:23 members

On the day of the performance of a certain play, each ticket

by BTGmoderatorDC » Fri Dec 13, 2019 1:42 am

On the day of the performance of a certain play, each ticket that regularly sells for less than $10.00 is sold for half price plus $0.50, and each ticket that regularly sells for $10.00 or more is sold for half price plus $1.00. On the day of the performance, a person purchases a total of y tickets, of which x regularly sell for $9.00 each and the rest regularly sell for $12.00 each. What is the amount paid, in dollars, for the y tickets ?

(A) 7y - 2x
(B) 12x - 7y
(C) (9x +12y)/3
(D) 7y + 4x
(E) 7y + 5x

OA A

Source: Official Guide

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Source: Beat The GMAT — Problem Solving | Fri Dec 13, 2019 1:42 am

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by Brent@GMATPrepNow » Fri Dec 13, 2019 6:49 am

BTGmoderatorDC wrote:On the day of the performance of a certain play, each ticket that regularly sells for less than $10.00 is sold for half price plus $0.50, and each ticket that regularly sells for $10.00 or more is sold for half price plus $1.00. On the day of the performance, a person purchases a total of y tickets, of which x regularly sell for $9.00 each and the rest regularly sell for $12.00 each. What is the amount paid, in dollars, for the y tickets ?

(A) 7y - 2x
(B) 12x - 7y
(C) (9x +12y)/3
(D) 7y + 4x
(E) 7y + 5x

OA A

Source: Official Guide

GIVEN: A TOTAL of y tickets are sold

GIVEN: x tickets regularly sell for $9.00 each. The SALE price = $9/2 + $0.50 = $5
So, these x tickets will cost a total of 5x dollars

GIVEN: The remaining tickets regularly sell for $12.00 each. The SALE price = $12/2 + $1.00 = $7
If there are y tickets in TOTAL, and x tickets have a sale price of $5 per ticket, the remaining y-x tickets have a sale price of $7 per ticket
So, these y-x tickets will cost a total of 7(y-x) dollars

So the TOTAL amount paid for all white tickets = 5x + 7(y-x)
= 5x + (7y - 7x)
= 7y - 2x

Answer: A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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by [email protected] » Fri Dec 13, 2019 9:50 am

Hi All,

This question can be solved by TESTing VALUES.

This prompt tells us some specific changes that occur to the price of a show ticket if you buy the ticket on the day of the show:
1) If the regular price is LESS than $10, then the ticket sells for HALF the price + $0.50
2) If the regular price is GREATER than/equal to $10, then the ticket sells for HALF the price + $1.00

We're told that someone purchases Y tickets on the day of the show; X of the tickets normally sell for $9, while the rest sell for $12. We're asked for the price paid for these tickets.

Looking at the Answers, I can see that they're different enough from one another that I can TEST really small numbers for Y and X.

IF....
Y = 2 tickets
X = 1 ticket that normally costs $9
The other (1) ticket normally costs $12

With the discounts, the prices would be....
(1/2)(9) + $0.50 = $4.50 = $0.50 = $5.00
(1/2)(12) + $1.00 = $6.00 + $1.00 = $7.00

Total Price = $12, when Y = 2 and X = 1

Answer A: 7(2) - 2(1) = 12 This IS a MATCH
Answer B: 12(1) - 7(2) = -2 NOT a match
Answer C: [9(1) + 12(2)]/3 = 11 NOT a match
Answer D: 7(2) + 4(1) = 18 NOT a match
Answer E: 7(2) + 5(1) = 19 NOT a match

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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by Scott@TargetTestPrep » Fri Jan 10, 2020 1:08 pm

BTGmoderatorDC wrote:On the day of the performance of a certain play, each ticket that regularly sells for less than $10.00 is sold for half price plus $0.50, and each ticket that regularly sells for $10.00 or more is sold for half price plus $1.00. On the day of the performance, a person purchases a total of y tickets, of which x regularly sell for $9.00 each and the rest regularly sell for $12.00 each. What is the amount paid, in dollars, for the y tickets ?

(A) 7y - 2x
(B) 12x - 7y
(C) (9x +12y)/3
(D) 7y + 4x
(E) 7y + 5x

OA A

Source: Official Guide

Since x tickets are regularly sold for $9 each, now they are sold for 4.5 + 0.5 = $5 each. Thus, the cost of the x discounted tickets is 5x. Similarly, since the rest of the tickets, i.e., (y - x) tickets, are regularly sold for $12 each, now they are sold for 6 + 1 = $7 each. The cost of the (y - x) discounted tickets is 7(y - x). Therefore, the total amount, in dollars, paid for the y tickets is:

5x + 7(y - x) = 5x + 7y - 7x = 7y - 2x

Answer: A

Scott Woodbury-Stewart
Founder and CEO
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