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Lesson: Data Sufficiency Challenging - 14t01

Tough Content: Example 2

[Page 14 of 24]

Take a look at this question. Again, the first thing we’ll do is evaluate the question stem.

If a and b are positive integers and a + b > ab, what is the value of a?

1)

2) ab ? a

Focus on the question stem. Do you recognize the math concept that this is testing? Type it into the Text Box, and click Continue.

This question is testing rules.

Countinue

Normally, the product of two positive integers is greater than their sum (e.g., 5 × 2 > 5 + 2), so a statement like a + b > ab should immediately make you wonder what possible values of a and/or b could make this inequality true. Once again, let's think about the likely suspects: 0, 1 and –1.

We know from the question stem that both a and b are positive, so that scratches 0 and –1. But what about 1? Let’s try out a few examples:

1 + 1 > 1 × 1

1 + 2 > 1 × 2

1 + 3 > 1 × 3

Notice that these inequalities are all true. Also note that the question stem didn’t prohibit the possibility that a and b could have the same value. So either a or b (or maybe both) must equal 1 in order for the inequality a + b > ab to be true.

Aha! Now we can see the real question here: Is a = 1? That’s what we’ll be looking for as we evaluate each statement.

Countinue

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