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15 Jun 2017, 23:41
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Difficulty:

65% (hard)

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 16 Jun 2017, 00:01 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 $$8-2 = 6.$$ Answer (A). Manager 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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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.
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At a party, John collected $96 to buy p equally-priced pizzas. When [#permalink] ### Show Tags 16 Jun 2017, 02:22 Since John bought p equally priced pizzas, with 96$,
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

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Re: At a party, John collected $96 to buy p equally-priced pizzas. When [#permalink] ### Show Tags 16 Jun 2017, 03:23 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)
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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? Current Student 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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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 Current Student 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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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
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02 Oct 2018, 14:46
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 03 Oct 2018, 17:51 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. Answer: A _________________ # Scott Woodbury-Stewart Founder and CEO Scott@TargetTestPrep.com 122 Reviews 5-star rated online GMAT quant self study course 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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