Andrew bought pizzas for his swim team. Pepperoni pizzas

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Wed Oct 03, 2018 12:44 am

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Andrew bought pizzas for his swim team. Pepperoni pizzas cost $13 and combination pizzas cost $17 and he bought only pepperoni or combination pizzas. He spent a total of $184 on pizzas. How many pizzas did he buy?

(A) 12
(B) 13
(C) 14
(D) 15
(E) 16

OA A

Source: Princeton Review

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nonplus2: Junior | Next Rank: 30 Posts; Posts: 25; Joined: Mon May 07, 2018 8:47 am; Location: India; GMAT Score:610

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by nonplus2 » Wed Oct 03, 2018 1:06 am

BTGmoderatorDC wrote:Andrew bought pizzas for his swim team. Pepperoni pizzas cost $13 and combination pizzas cost $17 and he bought only pepperoni or combination pizzas. He spent a total of $184 on pizzas. How many pizzas did he buy?

(A) 12
(B) 13
(C) 14
(D) 15
(E) 16

OA A

Source: Princeton Review

Let the price per unit of Pepperoni pizzas = $x and price per unit of combination pizzas = $y
Using the information from the question prompt, we have:
13*x + 17*y =184 or
x = (184-17*y)/13
Since both x and y are integers, we can plug in value of y starting from 1 till we have x as an integer.
When y = 7, we have x = (184-119)/13 => 65/13 = 5

So, Andrew bought 5 Pepperoni pizzas and 7 combination pizzas. A total of 5 + 7 = 12 pizzas

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Ash Mo: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Wed Oct 03, 2018 10:34 am

answer

by Ash Mo » Wed Oct 03, 2018 10:43 am

This question can be solved by algebra.
Let the number of pepperoni pizzas =x
and let the number of combination pizzas=y

Now , we can write
13x+17y=184
x= (184-17y)/13

From here , we have to plug in different values of y to ensure that x becomes an integer.
We observe that this happens when y=7 , resulting in x=5

Thus, the total number of pizzas = x+y = 12

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8136; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Thu Oct 04, 2018 6:43 pm

BTGmoderatorDC wrote:Andrew bought pizzas for his swim team. Pepperoni pizzas cost $13 and combination pizzas cost $17 and he bought only pepperoni or combination pizzas. He spent a total of $184 on pizzas. How many pizzas did he buy?

(A) 12
(B) 13
(C) 14
(D) 15
(E) 16

Letting p = the number of pepperoni pizzas bought and c = the number of combination pizzas bought, wee can create the equation:

13p + 17c = 184

13p = 184 - 17c

p = (184 - 17c)/13

We can see we can buy at most 10 combination pizzas. (If the value of c were more than 10, then the number of pepperoni pizzas bought would be negative.)

If c = 10, then p = (184 - 170)/13 = 14/13, which is not an integer.

If c = 9, then p = (184 - 153)/13 = 31/13, which is not an integer.

If c = 8, then p = (184 - 136)/13 = 48/13, which is not an integer.

If c = 7, then p = (184 - 119)/13 = 65/13 = 5, which is an integer.

Therefore, a total of 7 + 5 = 12 pizzas are bought.

Answer: A

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Fri Oct 05, 2018 5:46 am

This question illustrates the difference between the abstract math and real world math.
From the given information, we're able to create ONE equation: 13p + 17c = 184
In high school, we learned that, if we're given 1 equation with 2 variables, we cannot find the value of either variable, so what's different with this question? How are we able to find an answer?
Well, this question requires us to restrict the variables to positive integers within a certain range of values and, given this restriction, there is only one solution.

Here's a related question: https://www.beatthegmat.com/stamps-t288085.html

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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by [email protected] » Fri Oct 05, 2018 10:36 am

Hi All,

We're told that Andrew bought pizzas for his swim team; pepperoni pizzas cost $13 each, combination pizzas cost $17 each and he bought only pepperoni or combination pizzas (spending a total of $184 on pizzas). We're asked for the TOTAL number of pizzas he bought. This question can be solved in a number of different ways, but it has a great 'pattern-matching' shortcut that get you to the correct answer without too much math.

To start, it's worth noting that the combined cost of 1 pepperoni pizza and 1 combination pizza is $13 + $17 = $30. With a total of $184 of pizzas, (6)($30) = $180 is fairly close to that total. Notice that it's $4 less than what we need it to be... which is exactly the difference in price between a combination pizza and a pepperoni pizza.

So, if we buy 6 pepperoni pizzas and 6 combination pizzas, we'll spend $180 in total. If we 'swap' one pepperoni pizza for one combination pizza, then we'll end up spending 4 MORE dollars, for a total of $184. That would be 5 pepperoni pizzas and 7 combination pizzas --> a total of 12 pizzas.

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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