Lesson: Data Sufficiency Challenging - 20t05

Multiple Steps: Example 2

[Page 20 of 24]

If m and n are positive integers, are m and n consecutive integers?

1)

2)

The question stem asks whether m and n are consecutive numbers. What are the two ways to represent this relationship algebraically?

m =

m =

Review Statement 1 below. Is it sufficient or insufficient? Select the correct answer and then click Continue.

1)

  Sufficient Insufficient    

Review Statement 2 below. Is it sufficient or insufficient? Select the correct answer and then click Continue.

2)

  Sufficient Insufficient    

For this statement, we don’t need to go through the steps because we recognize the expression on the right side of the equation as a "classic" algebraic identity: . So, in this case, . Once again, we have confirmation that n = m – 1 (which is the same as m = n + 1). Statement 2 is also sufficient.

This question wasn’t nearly as difficult as it first appeared, once we saw the steps we needed to take in order to reach our goal. The fastest way to get there was to look for an algebraic way to determine the relationship between n and m. We also could’ve picked numbers, though in a situation like this you have to be sure not to spend too much time trying out various pairs of consecutive integers.

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