It is currently 20 Jan 2018, 23:06

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

### Show Tags

15 Jun 2017, 22:41
1
KUDOS
Expert's post
00:00

Difficulty:

45% (medium)

Question Stats:

68% (02:08) correct 32% (02:22) wrong based on 78 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

_________________

Kudos [?]: 139627 [1], given: 12794

Director
Joined: 04 Dec 2015
Posts: 696

Kudos [?]: 356 [1], given: 261

Location: India
Concentration: Technology, Strategy
Schools: ISB '19, IIMA , IIMB, XLRI
WE: Information Technology (Consulting)
At a party, John collected $96 to buy p equally-priced pizzas. When [#permalink] ### Show Tags 15 Jun 2017, 23:01 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 [?]: 356 [1], given: 261 Manager Joined: 24 Dec 2016 Posts: 74 Kudos [?]: 13 [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

15 Jun 2017, 23:14
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 [?]: 13 [0], given: 83

BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 1811

Kudos [?]: 830 [0], given: 22

Location: India
WE: Sales (Retail)
At a party, John collected $96 to buy p equally-priced pizzas. When [#permalink] ### Show Tags 16 Jun 2017, 01:22 Since John bought p equally priced pizzas, with 96$,
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

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

Kudos [?]: 830 [0], given: 22

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7868

Kudos [?]: 18494 [0], given: 237

Location: Pune, India
Re: At a party, John collected $96 to buy p equally-priced pizzas. When [#permalink] ### Show Tags 16 Jun 2017, 02:23 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

_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Kudos [?]: 18494 [0], given: 237 Intern Joined: 15 Sep 2015 Posts: 15 Kudos [?]: 2 [0], given: 14 Re: At a party, John collected$96 to buy p equally-priced pizzas. When [#permalink]

### Show Tags

16 Jun 2017, 03:12
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 [?]: 2 [0], given: 14

Intern
Joined: 30 Mar 2017
Posts: 39

Kudos [?]: 13 [0], given: 47

Location: United States (FL)
Re: At a party, John collected $96 to buy p equally-priced pizzas. When [#permalink] ### Show Tags 16 Jun 2017, 03:37 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

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 [?]: 13 [0], given: 47

Manager
Joined: 06 Nov 2016
Posts: 100

Kudos [?]: 21 [0], given: 15

Location: India
GMAT 1: 710 Q49 V37
GPA: 2.8
Re: At a party, John collected $96 to buy p equally-priced pizzas. When [#permalink] ### Show Tags 16 Jun 2017, 11:53 96/p = cost before discount after discount: 96/p - 2 thus: (96/p -2)*(p+4) = 96 p = 12, price after discount:$6

Kudos [?]: 21 [0], given: 15

Retired Moderator
Joined: 12 Aug 2015
Posts: 2340

Kudos [?]: 1000 [0], given: 682

GRE 1: 323 Q169 V154

### Show Tags

17 Sep 2017, 01:04
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