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## Official Guide Explanation:Problem Solving #118

Background

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Quantitative Review (2nd ed.). Click the links on the question number, difficulty level, and categories to find explanations for other problems.

These are the same explanations that are featured in my "Guides to the Official Guide" PDF booklets. However, because of the limitations of HTML and cross-browser compatibility, some mathematical concepts, such as fractions and roots, do not display as clearly online.

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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