SAT Tip of the Week: Beware of Tricky Wording in SAT Math Questions

SAT Tip of the Week - FullMany times, our talented and accomplished students report that they know all of the math concepts on the SAT and are fully capable of solving all of the problems.  However, they frequently complain that they make “dumb” or “careless” mistakes on the SAT and lose points.  While some of these mistakes seem silly in hindsight, many of the questions on the SAT are designed to lure students into tricks and traps or force errors if the students are not paying close attention to the wording.

One of the most frequently missed nuances of wording on the SAT math section has to do with the phrases “must be true” and “could be true.”  This is a small change in wording and is very easy to miss but can have real repercussions on how you answer the question.  It’s especially important to pay attention to this kind of nuanced wording on the SAT if you want to reach that goal of getting a perfect 2400 score.

When a question says “must be true”, it means “ALWAYS true” not just sometimes true.  It is a very strict definition and must work all the time for all cases.  But when a question says “could be true”, it is a lower burden of proof and as long as you find just ONE instance where it is true, then it meets the criteria of “could be true” even if all of the other cases you think of are not true.

Let’s take a look at the following example:

U = {3/5, 7/5, 2, 5, 15/2, 8}

W = {3/5, 7/3, 5, 8}

If x is both a member of set U and W above, which of the following must be true?

  1. x = 5
  2. x is an integer
  3. 5x is an integer

 

(A)  None of the above

(B)  II only

(C)  III only

(D)  II and III only

(E)   I, II, and III

Note that the question stem uses the wording “must be true.”  This means that the statement must be true for all cases and all circumstances.  Let’s go through and test each one, but before we do, it would be useful to write out all the terms that are members of both U and W or the “intersection” of the two sets:  U ? W = {3/5, 5, 8}

  1. x = 5 —This is only true for one of the terms, so it is not “always” true. Therefore it does not meet the criteria of “must be true.”  Eliminate answer choice E.
  2. x is an integer — This is only true for the terms 5, and 8 but not for 3/5, so again, this does not meet the strict criteria of “must be true.”  Eliminate answer choices B and D.
  3. 5x is an integer — If we multiply each term by 5, we get {3, 15, 24}.  Yes, they are all integers so this one checks out for all of the terms.  This is our only “must be true” statement so the correct answer to this question is C.

Note how this question changes if the question stem instead said:

If x is both a member of set U and W above, which of the following could be true?

That change in wording now allows for roman numerals I and II to pass the less stringent criteria of “could be true” since we can come up with at least one case in each instance where the statement could be true.  As a result, the correct answer choice is no longer C but is then E – I, II and III.

Be aware of this kind of subtle wording on the SAT to make sure you are applying the correct reasoning and logic to these kinds of questions.  When you come across a question that says “must be true” or “could be true.”  Underline it on your test so that you know to pay close attention!

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Jason Sun is the Director of College Prep for Veritas Prep. When he’s not in the office, he can be found competing in swing dance competitions or defending his title as a table tennis champion. 

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