GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Jul 2018, 14:14

### 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

# An amusement park currently charges the same price for each ticket of

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 47037
An amusement park currently charges the same price for each ticket of [#permalink]

### Show Tags

13 Nov 2014, 09:42
00:00

Difficulty:

25% (medium)

Question Stats:

79% (02:09) correct 21% (02:52) wrong based on 151 sessions

### HideShow timer Statistics

Tough and Tricky questions: Word problems.

An amusement park currently charges the same price for each ticket of admission. If the current price of admission were to be increased by $$3$$, 12 fewer tickets could be bought for $$160$$, excluding sales tax. What is the current price of each ticket?

A. $$3$$
B. $$5$$
C. $$8$$
D. $$20$$
E. $$32$$

Kudos for a correct solution.

_________________
Manager
Joined: 10 Sep 2014
Posts: 98
Re: An amusement park currently charges the same price for each ticket of [#permalink]

### Show Tags

13 Nov 2014, 10:14
1
1
Answer A: 160/3 = 50.33 tickets. 160/6 = 25.66 tickets, difference is not 12
Answer B: 160/5= 32, 160/8 = 20, difference of 12

Intern
Joined: 05 Sep 2013
Posts: 9
Location: Georgia
Re: An amusement park currently charges the same price for each ticket of [#permalink]

### Show Tags

13 Nov 2014, 11:07
A) 160/3=53.33 not integer (eliminate)
B) 160/5=32 160/2=80 difference is not 12 (eliminate)
C) 160/8=20 160/5=32 32-20=12

Manager
Joined: 12 May 2013
Posts: 73
Re: An amusement park currently charges the same price for each ticket of [#permalink]

### Show Tags

13 Nov 2014, 11:36
2
Hey! this is how i got the answer.

160/x = (160/x) +12

Solve the equation and we will get x= -8 or x=5, the price of the ticket cannot be negative so x=5 is the correct answer.
B
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1837
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: An amusement park currently charges the same price for each ticket of [#permalink]

### Show Tags

13 Nov 2014, 20:34
3

Price ............. Quantity .................. Total

a ...................... $$\frac{160}{a}$$ ..................... 160 (Assume price = "a")

a+3 ................... $$\frac{160}{a} - 12$$ ............... 160 (Price increased by 3, sales decline by 12)

Solving the equation

$$(a+3)* (\frac{160}{a} - 12) = 160$$

$$a^2 + 3a - 40 = 0$$

a = 5
_________________

Kindly press "+1 Kudos" to appreciate

Manager
Joined: 05 Jun 2014
Posts: 63
GMAT 1: 630 Q42 V35
Re: An amusement park currently charges the same price for each ticket of [#permalink]

### Show Tags

14 Nov 2014, 02:40
Plug in is the best approach for this question to save time. Answer is B.
Intern
Joined: 04 Jul 2014
Posts: 46
Schools: Smeal" 20
Re: An amusement park currently charges the same price for each ticket of [#permalink]

### Show Tags

14 Nov 2014, 05:03
1
Bunuel wrote:

Tough and Tricky questions: Word problems.

An amusement park currently charges the same price for each ticket of admission. If the current price of admission were to be increased by $$3$$, 12 fewer tickets could be bought for $$160$$, excluding sales tax. What is the current price of each ticket?

A. $$3$$
B. $$5$$
C. $$8$$
D. $$20$$
E. $$32$$

Kudos for a correct solution.

Let price be p & no. of tickets be n.

p*n = 160
(p+3)*(n-12) = 160

If price is 3, n = 160/3, n is not a whole no. , so 3 is not the answer
If price is 5, n=32 from 1st eqn...checking with 2nd equation 8*(n-12) = 160 -> 8n = 256 -> n=32. Price $5 satisfies both equations. Hence answer B. Math Expert Joined: 02 Sep 2009 Posts: 47037 Re: An amusement park currently charges the same price for each ticket of [#permalink] ### Show Tags 14 Nov 2014, 09:32 Bunuel wrote: Tough and Tricky questions: Word problems. An amusement park currently charges the same price for each ticket of admission. If the current price of admission were to be increased by $$3$$, 12 fewer tickets could be bought for $$160$$, excluding sales tax. What is the current price of each ticket? A. $$3$$ B. $$5$$ C. $$8$$ D. $$20$$ E. $$32$$ Kudos for a correct solution. Official Solution: An amusement park currently charges the same price for each ticket of admission. If the current price of admission were to be increased by $$3$$, 12 fewer tickets could be bought for $$160$$, excluding sales tax. What is the current price of each ticket? A. $$3$$ B. $$5$$ C. $$8$$ D. $$20$$ E. $$32$$ The question asks us to determine the current price of each ticket of admission. If we let $$p$$ equal the current price per ticket, and $$n$$ equal the number of tickets that can be bought for $$160$$, we can set up some equations. First, we know that $$pn = 160$$. Second, we are told that if $$p$$ is increased by 3, then 12 fewer tickets can be bought with $$160$$. This equation also expresses how many tickets can be bought for $$160$$, giving us: $$(p + 3)(n - 12) = 160$$. Solve the first equation for $$n$$, giving: $$n = \frac{160}{p}$$. Substitute this value for $$n$$ into the second equation, solving for $$p$$: $$(p + 3)(\frac{160}{p} - 12) = 160$$ Multiply both sides by $$p$$ to get rid of the fraction: $$(p + 3)(\frac{160}{p} - 12)p = (p + 3)(160 - 12p) = 160p$$. Multiply through to get rid of the parentheses: $$160p - 12p^2 + 480 - 36p = 160p$$. Combine like terms: $$124p - 12p^2 + 480 = 160p$$. Set the equation equal to 0: $$0 = 12p^2 + 36p - 480$$.Divide both sides by 12: $$0 = p^2 + 3p - 40$$. Factor: $$0 = (p - 5)(p + 8)$$. Therefore, $$p = 5$$ or $$p = -8$$. Since the the price cannot be negative, $$p = 5$$. Answer: B. _________________ SC Moderator Joined: 22 May 2016 Posts: 1827 An amusement park currently charges the same price for each ticket of [#permalink] ### Show Tags 20 Aug 2017, 08:36 Bunuel wrote: Tough and Tricky questions: Word problems. An amusement park currently charges the same price for each ticket of admission. If the current price of admission were to be increased by $$3$$, 12 fewer tickets could be bought for $$160$$, excluding sales tax. What is the current price of each ticket? A. $$3$$ B. $$5$$ C. $$8$$ D. $$20$$ E. $$32$$ Kudos for a correct solution. A 90-second approach using answer choices (maybe quicker -- I only caught this 20 seconds in, after trying C the long way). The$160 total stays constant, but the ticket price goes up by $3. Add$3 to each answer, and you eliminate four answers very quickly: A, C, D, and E.

The new prices for those four choices do not divide evenly into $160.* Total price / price per ticket = # of tickets, which will not be a whole integer at new price. A. ($3-->$6) C. ($8-->$11) D. ($20-->$23) E. ($32-->$35) That leaves B. If brave, mark and move on. If not (raises hand), check.$160/$5 = 32 tickets sold$160/$8 = 20 tickets sold Higher price = 12 fewer tickets. Correct. Answer B * -- C and D (11 and 23) are pretty obvious. --If uncertain about A, add digits of 160; not divisible by 3, so not divisible by 6. -- For E, 35 * 2 = 70, doubled is$140. The extra is \$20 (160-140). That won't work; you can't divide 20 by 35 evenly.

_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

An amusement park currently charges the same price for each ticket of   [#permalink] 20 Aug 2017, 08:36
Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.