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17 May 2018, 12:07
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A
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Difficulty:
55%
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Question Stats:
70% (02:37) correct
30%
(02:52)
wrong
based on 211
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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
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
alldaytestprep
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Joined: 08 May 2018
Last visit: 24 Apr 2023
Posts: 98
Given Kudos: 1
Affiliations: All Day Test Prep
Location: United States (IL)
Schools: Booth '20 (A)
GMAT 1: 770 Q51 V49
GRE 1: Q167 V167
GPA: 3.58
Expert reply
Updated on: 18 May 2018, 07:42
Originally posted by alldaytestprep on 17 May 2018, 14:16.
Last edited by alldaytestprep on 18 May 2018, 07:42, edited 1 time in total.
Last edited by alldaytestprep on 18 May 2018, 07:42, edited 1 time in total.
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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
Pepperoni = P
Combo = C
13P + 17C = 184
P & C each have to be integers. The max C can be is 10 since anything more would give value for 17C greater than 184. So I would find corresponding values of P starting from C = 10, C = 9, C = 8...etc and stop once I get to a pair that works.
C = 10 ---> 13P = 14 ---> P isn't an integer
C = 9 -----> 13P = 21 ----> P isn't an integer
C = 8 ---> 13P = 48 ----> P isn't an integer
C = 7 ---> 13P = 65 -----> P = 5 ---> WE DONE.
C = 7
P = 5
----> C + P = 12
Answer: A
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Pepperoni = P
Combo = C
13P + 17C = 184
P & C each have to be integers. The max C can be is 10 since anything more would give value for 17C greater than 184. So I would find corresponding values of P starting from C = 10, C = 9, C = 8...etc and stop once I get to a pair that works.
C = 10 ---> 13P = 14 ---> P isn't an integer
C = 9 -----> 13P = 21 ----> P isn't an integer
C = 8 ---> 13P = 48 ----> P isn't an integer
C = 7 ---> 13P = 65 -----> P = 5 ---> WE DONE.
C = 7
P = 5
----> C + P = 12
Answer: A
18 May 2018, 07:00
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SidR
We have only one equation with 2 variables. The added information that helps find a unique value for number of Pepperoni and Combination pizza is the fact that both numbers have to be non-negative integers.
The only way to find the answer is through iteration as shown by arosman
