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Lesson: Intermediate Problem Solving - 17t01

The Roman Numeral Question, continued

[Page 17 of 27]
Before we go on we have to consider one more situation: what if our two rules of thumb for statement order conflict? For example, in the question below, Statement III appears in the largest number of answer choices, but it's also the most difficult to evaluate. What would you do?

Choose a statement order as you prefer, based on one guideline or by combining the guidelines. Use elimination to select the correct answer, then click Continue.

For which of the following expressions would the value be less if 235 were replaced by 231?

I.

II.

III.

 
None
II only
III only
I and III
II and III

Did you evaluate statements by difficulty level, say starting with Statement 1, or by representation, starting with Statement III since it appears in 3 answer choices?

There is no one way that's best for everyone in every situation. Apply your judgement based on the combination of how quickly and accurately you could evaluate the most-represented statement. For example, in this problem if you knew immediately how to evaluate Statement III, then going for that first would be smart because of the possibility of eliminating 2 or even 3 choices at once.

Let's say that's what we did.

Statement III: If 235 were replaced by 231, the denominator in this expression would get larger, and therefore the expression itself would get smaller, which is what we're looking for. So, the correct answer will include Statement III, which means that we can eliminate Choices (A) and (B).

Now we're going to have to check both of the remaining statements so we could do either next. We'll tackle Statement I first because it's the easier of the two. If you'd started with Statement I, you'd probably go on to evaluate Statement II next because it is more straightforward than III.

Statement I: When 231 is subtracted from 1,500 we get a larger number, not smaller, so we can eliminate Choice (D).

Statement II: Replacing 235 with 231 will produce a smaller denominator. Since the numerator stays the same, the expression will become larger. That means that this statement will not appear in the correct answer, so we can eliminate Choice (E), leaving us with Choice (C), the correct answer.

Note that in this case we had to evaluate all 3 statements to find the correct answer. This is often not the case; it's not unusual for the statements to be grouped so that the 4 incorrect choices are eliminated by only 2 of the statements.

So, it makes sense to develop the habit of evaluating statements based on how often they appear in the answer choices, combined with your knowledge of your personal strengths and weaknesses in terms of content (what you can evaluate quickly and confidently). This strategy also helps you when you have to guess, either because you cannot evaluate a statement or because you're running out of time.

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