One of the more-dreaded types of GMAT Problem Solving questions is the “must be true” question with three statements; these questions often look like:

If 20x = 49y, which of the following must be true?

I. x > y

II. x^{2} > y^{2
}III. x/7 is an integer

A) I only

B) II only

C) III only

D) I and III

E) I, II, and III

These problems can be daunting, mainly because:

- They’re multiple problems in one, as you have three relationships you have to deal with.
- It can be difficult to know if something is “always true” – how many possibilities do you try before you conclude that it’s always true?

But rest assured – there’s an efficient method for these types of questions that puts all the common GMAT trap answers firmly on your side by doing what human beings do best: be critical!

The opposite of “Must Be True” is “Could be False”, so instead of trying to prove that something is always true, you can use process of elimination (and your natural inclination to be critical) by trying to find one situation in which each of the statements could be false. And the best way to do this is to go on the attack – use all the “weird” numbers that tend to trap you, as your weapons against the test. “Weird” numbers like negatives, 0, and fractions tend to give the alternative answer, so you should keep those in mind as weapons that allow you to attack that idea that a statement must be true.

In the above question, for example, your goal should be to try to disprove each statement. If you can find just one set of numbers x and y for which x is not greater than y but 20x = 49y, you can confidently eliminate statement I. So try to attack, and use the GMAT’s tendencies against it. “Equal to” is not the same thing as “greater than”, so you actually don’t have to find a case where x is less than y if you can just make them equal. With that in mind, try using one the all time “gamechanger” numbers, 0. If x and y each equal 0, the given statement is true (0 does equal 0), but both statements I and II are not, as x equals y and x-squared equals y-squared. So by going on the attack and using strange numbers to your advantage, you can quickly eliminate two statements at once. And look now at the answer choices – there isn’t a choice for “none of the above”…so the answer simply must be C.

More important than this example is the set of takeaways, so for Must Be True questions, remember:

- Go on the attack and try to find a situation for each statement in which it is not true. It’s almost always easier to find one example of a “false” than it is to systematically prove that it’s always true.
- To effectively attack, consider those “weird” numbers like negatives, nonintegers, and 0. Many fear these types of numbers as traps…but they’re also your weapons against the test.
- Consider the layout of the answer choices as an asset, too – with three statements and only five answer choices, the test can’t ask you about every possible combination, so sometimes you can save the “hardest” statement for last and end up not even having to deal with it because you’ve eliminated the other answer choices.

So don’t fear “Must Be True” questions – with some technique, strategy, and practice these questions that many feel must be feared can actually become those that you must get right.

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I always thought that different variables necessarily represent different values, so that they could not both be 0. Does the GMAT allow for x to equal y?

Hey Joshua – good question…and YES, x and y could be the same thing. Variables just stand for “some unknown number”, and since we don’t know which number each variable stands for we can’t assume that they’re different.

Take, for example, an equation that shows up pretty frequently with Data Sufficiency questions:

x – y = 0

That one guarantees that x = y, so it’s certainly possible that they’re the same, UNLESS the question says that “for unique integers x and y” or something like that – “unique” means “different”, so look out for that designation.

I think the question must lack of precision, because if x = 49/20 (= 2,45) and y =1, the third option would not be correct 2,45 / 7 = 0,35 is not an integer !!!

Something is wrong somewhere.

If there wasn’t any other precision in the question, such as “knowing that x and y are integers”, then I think there is a problem with using 0 as the same value for x and y. This because you can get different answers.

For example, if you use negative numbers (non integers) instead of 0 (what I did when solving this question), such as x = -1 and y = -20/49, you eliminate the first and the third one, leaving the second one ‘always’ true, because if you use negative values, abs(X) must be greater than abs(Y), which is what the second statement says.

hi

thanks for the post. please can you elaborate how C is the answer.

x= 49/20 y

x/7 = 7/20y

How can we be sure that value of x/7 will always be integer. What if y =1,2, or 3? It wont be an integer. am i missing something?