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Question Stats: 68% (02:32) correct 32% (02:52) wrong based on 112 sessions

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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

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At a party, John collected $96 to buy p equally-priced pizzas. When [#permalink] Show Tags 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 $$8-2 = 6.$$ Answer (A). Manager  S Joined: 24 Dec 2016 Posts: 95 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]

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

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

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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? Current Student S Joined: 06 Nov 2016 Posts: 102 Location: India GMAT 1: 710 Q50 V36 GPA: 2.8 Re: At a party, John collected$96 to buy p equally-priced pizzas. When  [#permalink]

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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 Current Student D Joined: 12 Aug 2015 Posts: 2568 Schools: Boston U '20 (M) GRE 1: Q169 V154 Re: At a party, John collected$96 to buy p equally-priced pizzas. When  [#permalink]

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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

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Hello! Is there any easy way to realize when a problem is going to become a quadratic when attempted algebraically? Thank you!
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Re: At a party, John collected $96 to buy p equally-priced pizzas. When [#permalink] Show Tags 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. Answer: A _________________ Scott Woodbury-Stewart Founder and CEO Scott@TargetTestPrep.com See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: At a party, John collected$96 to buy p equally-priced pizzas. When   [#permalink] 03 Oct 2018, 17:51
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