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Lesson: Data Sufficiency Challenging - 20t03

Multiple Steps: Example 2

[Page 20 of 24]

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

1) m2 = n2 + n + m

2) n2 = m2 - 2m + 1

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    

If m and n are consecutive, then we can replace m in the expression with one of n – 1 or n + 1 without violating the equation. If they’re not, the equation won’t work if we do so. So, let’s try n – 1:

Is ? Well, if we work out both sides of the equation, we get . These are not equal, so we know that .

Now let’s try n + 1:

Is ? Well, if we work out both sides of the equation, we get . These are equal, so we know that m = n + 1, which means that m and n are indeed consecutive. Statement 1 is therefore sufficient.

Let’s look at Statement 2.

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Countinue

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