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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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?

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

Show Tags

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;

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

Show Tags

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)

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 = \((x-2)\) = \(6\)

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

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)

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

Show Tags

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

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

Show Tags

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?

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

Show Tags

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

Version 8.1 of the WordPress for Android app is now available, with some great enhancements to publishing: background media uploading. Adding images to a post or page? Now...

Post today is short and sweet for my MBA batchmates! We survived Foundations term, and tomorrow's the start of our Term 1! I'm sharing my pre-MBA notes...

“Keep your head down, and work hard. Don’t attract any attention. You should be grateful to be here.” Why do we keep quiet? Being an immigrant is a constant...