Official Guide Explanation:
Data Sufficiency #93

Background

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Solution and Metadata

Question: 93
Page: 280
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Descriptive Statistics > Average
Category 2: Arithmetic > Properties of Integers > Factors and Multiples

Explanation: While at first glance, this question has five variables, the fact that the variables are consecutive even integers simplifies matters. In fact, there is only one variable, and all the others can be expressed in terms of that one. The five are:

p,p + 2,p + 4,p + 6,p + 8

q = p + 2, and so on. The average of the five integers is the middle number (the median), as is the case whenever a set of numbers are equally spaced. Thus, if we can find p, we can find the median, p + 4.

Statement (1) is sufficient. q = p + 2, and s = p + 6, so we know that:

p + 2 + p + 6 = 24

2p + 8 = 24

2p = 16

p = 8

Statement (2) is also sufficient. Again, we can substitute expressions containing p for q and r:

q = p + 2

s = p + 4

(((p + 2) + (p + 4))/2) = 11

2p + 6 = 22

2p = 16

p = 8

Choice (D) is correct.

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