If , 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:
- There are 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 is always true?
But rest assured – there is an efficient method for solving these 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 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 , 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 do not have to find a case where x is less than y if you can just make them equal. With that in mind, try using the one all time “game changer” number, 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 equals . 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 that it is not true. It is 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 are 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 cannot 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 have 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.