Official Guide Explanation:
Data Sufficiency #156




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Solution and Metadata

Question: 156
Page: 287
Difficulty: 6 (Moderately Difficult)
Category 1: Algebra > Exponents >
Category 2: Arithmetic > Powers and Roots of Numbers > Powers
Category 3: Algebra > Inequalities > other

Explanation: Statement (1) is insufficient: 5k + 1 = 5k51, so we can simplify the inequality:

5k51 > 3,000

5k > ((3,000)/5)

5k > 600

If 5k is greater than 600, it is unknown whether it is less than 1,000.

Statement (2) is sufficient: even without manipulating the equation, you can recognize that it is an equation with one variable, so you can solve for that variable. Regardless of what that variable is, you can find the value of 5k and determine whether it is less than 1,000. Choice (B) is correct.

For those interested, here's how to solve the equation in (2) for 5k:

5k - 1 = 5k-500

500 = 5k-5k - 1

500 = 5k-5k5-1

500 = 5k(1 - 5-1)

500 = 5k(1 - (1/5))

500 = 5k((4/5))

5k = 500((5/4)) = (2500/4) = 625

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