It is currently 17 Oct 2017, 03:11

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

At a party, John collected $96 to buy p equally-priced pizzas. When

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41871

Kudos [?]: 128512 [1], given: 12179

At a party, John collected $96 to buy p equally-priced pizzas. When [#permalink]

Show Tags

New post 15 Jun 2017, 23:41
1
This post received
KUDOS
Expert's post
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

69% (02:15) correct 31% (02:14) wrong based on 71 sessions

HideShow timer Statistics

At a party, John collected $96 to buy p equally-priced pizzas. When he called the store, however, they were running a promotion for $2 off of each pizza, so he was able to buy 4 more pizzas than he expected for the same $96. How much was the cost of each pizza after the discount?

A. $6
B. $8
C. $9
D. $10
E. $12
[Reveal] Spoiler: OA

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 128512 [1], given: 12179

1 KUDOS received
Director
Director
User avatar
P
Joined: 04 Dec 2015
Posts: 696

Kudos [?]: 296 [1], given: 261

Location: India
Concentration: Technology, Strategy
Schools: ISB '19, IIMA , IIMB, XLRI
WE: Information Technology (Consulting)
GMAT ToolKit User
At a party, John collected $96 to buy p equally-priced pizzas. When [#permalink]

Show Tags

New post 16 Jun 2017, 00:01
1
This post received
KUDOS
Bunuel wrote:
At a party, John collected $96 to buy p equally-priced pizzas. When he called the store, however, they were running a promotion for $2 off of each pizza, so he was able to buy 4 more pizzas than he expected for the same $96. How much was the cost of each pizza after the discount?

A. $6
B. $8
C. $9
D. $10
E. $12


Let price per pizza be \(x.\)

Total number of pizza \(= p\)

Price of \(x\) pizza's before discount \(= $96\)

\(px = 96\) ------------ (i)

Total number of pizza after discount \(= p + 4\)

Price decrease on each pizza after discount \(= x - 2\)

Given Price of pizza's after discount is \($96\). ie;

\((p+4)(x-2) = 96\)
\(px + 4x -2p - 8 = 96\)
\(96 + 4x - 2p -8 = 96\) ---------- (Substituting value of \(px\) from (i))
\(4x - 2p - 8 = 0\)
\(4x - 2p = 8\)
\(2x - p = 4\)
\(p = 2x + 4\) ---------- (ii)

Substituting value of \(p\) from (ii) in equation (i), we get;

\((2x+ 4)x = 96\)
\(2x^2 + 4x = 96\)
\(2x^2 - 4x - 96 = 0\)
\(x^2 - 2x - 48 = 0\)
\(x^2 - 8x + 6x - 48 = 0\)
\(x(x - 8) + 6 (x - 8) = 0\)
\((x+6)(x+8) = 0\)
\(x = 8, -6\)

Price cannot be negative. Therefore price of each pizza before discount was \($8\).

Price of pizza after discount is \(8-2 = $6.\)
Answer (A).

Kudos [?]: 296 [1], given: 261

Manager
Manager
User avatar
S
Joined: 24 Dec 2016
Posts: 75

Kudos [?]: 12 [0], given: 83

Location: India
Concentration: Finance, General Management
WE: Information Technology (Computer Software)
Re: At a party, John collected $96 to buy p equally-priced pizzas. When [#permalink]

Show Tags

New post 16 Jun 2017, 00:14
Bunuel wrote:
At a party, John collected $96 to buy p equally-priced pizzas. When he called the store, however, they were running a promotion for $2 off of each pizza, so he was able to buy 4 more pizzas than he expected for the same $96. How much was the cost of each pizza after the discount?

A. $6
B. $8
C. $9
D. $10
E. $12


Let the price for each pizza be x.
Thus, \(p*x = 96\) {no. of pizza*price of each pizza = Total sum of money John had}
=>\(p = \frac{96}{x}\) -- eqn. (1)


After the discount, reduced price of each pizza = \((x-2)\)
and thus, he could buy 4 extra pizza. So, no. of pizzas becomes \((p+4)\)
thus the equation changes to : (p+4)*(x-2) = 96
=>\(p+4 = \frac{96}{(x-2)}\) -- eqn (2)

Equating eqn. 1 and 2-

\(\frac{96}{(x-2)} = \frac{96}{x} + 4\)
=>\(\frac{96}{(x-2)} - \frac{96}{x} = 4\)

Taking LCM and solving results in-
\(4x(x-2) = 192\)
=> \(4x^2 - 8x = 192\)
=> \(x^2 -2x - 48 = 0\)
=> \((x-8)(x+6) = 0\)
=> \(x = 8 or -6\).

As the price cant be a negative value, \(x= 8\)
As x was the original price for the pizzas, i.e., price before discount, price after discount = \((x-2)\) = \(6\)

Option A.

Kudos [?]: 12 [0], given: 83

BSchool Forum Moderator
User avatar
P
Joined: 26 Feb 2016
Posts: 1449

Kudos [?]: 590 [0], given: 16

Location: India
Concentration: General Management, Leadership
WE: Sales (Retail)
Premium Member CAT Tests
At a party, John collected $96 to buy p equally-priced pizzas. When [#permalink]

Show Tags

New post 16 Jun 2017, 02:22
Since John bought p equally priced pizzas, with 96$,
and we assume each of the pizza cost 'c'
From the question stem pc = 96
96(when prime factorized) gives \(2^5*3\)
The cost of the pizza's cannot be \(9(3^2)\) and \(10(2*5)\). So Option C and D are out!

The second part of the question, gives us the price during promotion
(p + 4)(c - 2) = 96

Now evaluating the answer options,
Since price of pizza (after discount) is 8$, John would have bought 12 pizza's during the promotional period.
However, price before discount would be 10$ and he would have bought 8 pizza's which doesn't give us 96$ as total cost.
Hence, Option C is also not right

If price after discount is 6$, he would have bought 16 pizza's during the promotional period.
However, price before discount would be 8$ and he would have bought 12 pizza's which gives us 96$ as total revenue.
Hence, Option A is our answer


_________________

Stay hungry, Stay foolish

2017-2018 MBA Deadlines

Class of 2020: Rotman Thread | Schulich Thread
Class of 2019: Sauder Thread

Kudos [?]: 590 [0], given: 16

Expert Post
Veritas Prep GMAT Instructor
User avatar
G
Joined: 16 Oct 2010
Posts: 7668

Kudos [?]: 17324 [0], given: 232

Location: Pune, India
Re: At a party, John collected $96 to buy p equally-priced pizzas. When [#permalink]

Show Tags

New post 16 Jun 2017, 03:23
Expert's post
1
This post was
BOOKMARKED
Bunuel wrote:
At a party, John collected $96 to buy p equally-priced pizzas. When he called the store, however, they were running a promotion for $2 off of each pizza, so he was able to buy 4 more pizzas than he expected for the same $96. How much was the cost of each pizza after the discount?

A. $6
B. $8
C. $9
D. $10
E. $12


Instead of taking variables and solving the equations, this question can be best done by jumping to the options directly.

John collected $96 to buy p pizzas, each of same price. So obviously, 96 will be divisible by p, and by the un-discounted price of the pizza.
The discounted price is $2 less and bought 4 more pizzas i.e. p + 4 pizzas. The discounted price would be divisible by 96 too.

Looking at the options, 6 and 8 could be the discounted and un-discounted prices.
At $6, you would get 96/6 = 16 pizzas
At $8, you would get 96/8 = 12 pizzas (4 less)
(A match)

Hence discounted price is $6

Answer (A)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Kudos [?]: 17324 [0], given: 232

Intern
Intern
avatar
B
Joined: 15 Sep 2015
Posts: 15

Kudos [?]: 1 [0], given: 14

CAT Tests
Re: At a party, John collected $96 to buy p equally-priced pizzas. When [#permalink]

Show Tags

New post 16 Jun 2017, 04:12
We can do 'plug-in answers' as well. If total no. of pizzas is p, then price per pizza is 96/p. Price after discount is 96/p-2. Plug in for 10: 96/p-2 = 10, => p = 8. Now, originally price per pizza was 96/8 = 12 (rs2 off) but 96/10 = 9.6 (not four extra pizzas). So we look at a lesser no. Plug-in for 6, 96/p-2 = 6, => p = 12. Now price per pizza = 96/12 = 8. (rs 2 off) and 96/6 = 16, which is 4 extra pizzas. Ans is A

Kudos [?]: 1 [0], given: 14

Intern
Intern
avatar
B
Joined: 30 Mar 2017
Posts: 39

Kudos [?]: 12 [0], given: 47

Location: United States (FL)
GMAT ToolKit User
Re: At a party, John collected $96 to buy p equally-priced pizzas. When [#permalink]

Show Tags

New post 16 Jun 2017, 04:37
VeritasPrepKarishma wrote:
Bunuel wrote:
At a party, John collected $96 to buy p equally-priced pizzas. When he called the store, however, they were running a promotion for $2 off of each pizza, so he was able to buy 4 more pizzas than he expected for the same $96. How much was the cost of each pizza after the discount?

A. $6
B. $8
C. $9
D. $10
E. $12


Instead of taking variables and solving the equations, this question can be best done by jumping to the options directly.

John collected $96 to buy p pizzas, each of same price. So obviously, 96 will be divisible by p, and by the un-discounted price of the pizza.
The discounted price is $2 less and bought 4 more pizzas i.e. p + 4 pizzas. The discounted price would be divisible by 96 too.

Looking at the options, 6 and 8 could be the discounted and un-discounted prices.
At $6, you would get 96/6 = 16 pizzas
At $8, you would get 96/8 = 12 pizzas (4 less)
(A match)

Hence discounted price is $6

Answer (A)



That's how I went about it, however my concern was assuming that the $96 had to be divisible by both p and p+4 (especially the latter). They wouldn't have to say that there was any $ left over after in either case, right?

Kudos [?]: 12 [0], given: 47

Manager
Manager
avatar
B
Joined: 06 Nov 2016
Posts: 91

Kudos [?]: 17 [0], given: 15

GMAT 1: 710 Q50 V36
Re: At a party, John collected $96 to buy p equally-priced pizzas. When [#permalink]

Show Tags

New post 16 Jun 2017, 12:53
96/p = cost before discount
after discount: 96/p - 2

thus: (96/p -2)*(p+4) = 96

p = 12,
price after discount: $6
Answer OA

Kudos [?]: 17 [0], given: 15

BSchool Forum Moderator
User avatar
P
Joined: 12 Aug 2015
Posts: 2213

Kudos [?]: 836 [0], given: 595

GMAT ToolKit User Premium Member CAT Tests
Re: At a party, John collected $96 to buy p equally-priced pizzas. When [#permalink]

Show Tags

New post 16 Jun 2017, 20:45
Excellent Question Bunuel.

Here is what I did on this one ->


Cost 1 = Cost 2

96 => (96/p - 2 ) (p+4)
Solving this we get => p=12 or p=-16

Hence p=12

So the cost after the discount would be 96/12 - 2 => 8-2 => 6

Hence A

Great Question :)
_________________

Give me a hell yeah ...!!!!!

Kudos [?]: 836 [0], given: 595

Intern
Intern
avatar
B
Joined: 29 Jul 2012
Posts: 17

Kudos [?]: 1 [0], given: 21

At a party, John collected $96 to buy p equally-priced pizzas. When [#permalink]

Show Tags

New post 17 Sep 2017, 02:04
Price after discount as per options given are: 6, 8, 9, 10, 12
Price before discount: 8,10,11,12,14
Price after discount and before discount should divide 96. Combination of 6 and 8 does it, therefore answer is A

Kudos [?]: 1 [0], given: 21

At a party, John collected $96 to buy p equally-priced pizzas. When   [#permalink] 17 Sep 2017, 02:04
Display posts from previous: Sort by

At a party, John collected $96 to buy p equally-priced pizzas. When

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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®.