Official Guide Explanation:
Problem Solving #118




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Solution and Metadata

Question: 118
Page: 77
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Fractions >
Category 2: Word Problems > Other >
Category 3: Algebra > Equations >

Explanation: This is an excellent question on which to assign a value to the unknown quantity, in this case the total number of pizza. Since we'll be looking for (1/8) and (1/3) of the number of pizzas, the total pizzas should be divisible by both of those numbers. Say that p = 24. In that case, the mushroom pizzas, (1/8) of the total, are (1/8)(24) = 3, leaving 21 non - mushroom pizzas. (1/3) of the remaining 21 pizzas are pepperoni, so there are (1/3)(21) = 7 pepperoni pizzas. If n of the pizzas are pepperoni, that means n = 7. The number of mushroom pizzas was 3, so using n = 7, we need to find which answer choice results in 3:

(A) (3/8)n = ((3(7))/8) = (21/8)

(B) (3/7)n = ((3(7))/7) = 3 (looks good)

(C) (7/16)n = ((7(7))/16) = (49/16)

(D) (7/8)n = ((7(7))/8) = (49/8)

(E) 3n = 3(7) = 21

Since (B) is the only choice that results in 3, the number of mushroom pizzas when there are 7 pepperoni pizzas, (B) must be correct.

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