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Buy "All-In-One Standard ($149)", get free Daily quiz (2 mon). Coupon code : SPECIAL # At a party, John collected$96 to buy p equally-priced pizzas. When

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Math Expert
Joined: 02 Sep 2009
Posts: 52938
At a party, John collected $96 to buy p equally-priced pizzas. When [#permalink] ### Show Tags 15 Jun 2017, 22:41 1 1 00:00 Difficulty: 65% (hard) Question Stats: 67% (02:30) correct 33% (02:52) wrong based on 109 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 _________________ Director Joined: 04 Dec 2015 Posts: 740 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]

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15 Jun 2017, 23:01
1
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 $$8-2 = 6.$$
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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. Senior PS Moderator Joined: 26 Feb 2016 Posts: 3341 Location: India GPA: 3.12 At a party, John collected$96 to buy p equally-priced pizzas. When  [#permalink]

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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 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 _________________ You've got what it takes, but it will take everything you've got Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 8883 Location: Pune, India Re: At a party, John collected$96 to buy p equally-priced pizzas. When  [#permalink]

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16 Jun 2017, 02:23
2
1
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 Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options > Intern Joined: 15 Sep 2015 Posts: 16 Re: At a party, John collected$96 to buy p equally-priced pizzas. When  [#permalink]

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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
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Joined: 30 Mar 2017
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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?
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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
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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
Intern
Joined: 06 Sep 2018
Posts: 37
GMAT 1: 760 Q50 V44
GMAT 2: 740 Q48 V44

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03 Oct 2018, 16:51
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

We can let the price of each pizza before the discount = n and create the equations:

pn = 96

p = 96/n

and

(p + 4)(n - 2) = 96

pn + 4n - 2p - 8 = 96

Substituting p = 96/n into the second equation, we have:

(96/n)n + 4n - 2(96/n) - 8 = 96

96 + 4n - 192/n - 8 = 96

4n - 8 - 192/n = 0

Multiplying by n, we have:

4n^2 - 8n - 192 = 0

n^2 - 2n - 48 = 0

(n - 8)(n + 6) = 0

n = 8 or n = -6

Since the price of a pizza can’t be negative, n = 8. However, this is the price before the discount. The price of each pizza after the discount is 8 - 2 = 6 dollars.

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