Official Guide Explanation:
Problem Solving #D15

Background

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Solution and Metadata

Question: D15
Page: 22
Difficulty: 6 (Moderately Difficult)
Category 1: Arithmetic > Powers and Roots of Numbers > Powers

Explanation: First, list all the prime numbers less than 20:

2, 3, 5, 7, 11, 13, 17, 19

Next, look for ways to approximate their products in ways that are related to powers of 10:

2(5) = 10

3(7) = 2(10) (plus a little bit)

11(19) = 2(10²) (it's about the same as 10 times 20, which is 200)

13(17) = 2(10²) (like the above, it's about the same as 10 times 20)

This leaves us with:

10(2)(10)(2)(10²)(2)(10²)

More directly: 2³10⁶

2³ is 8, which we can round up to 10, especially since three of our four approximations were slightly rounded down. Finally, then, our answer is 10⁷, choice (C).

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