Correctly Solve “Must Be True” Questions

by on January 9th, 2013

One of the more-feared 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:

  1. There are  multiple problems in one, as you have three relationships you have to deal with.
  2. 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 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 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 x^2 equals y^2. 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:

  1. 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.
  2. 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.
  3. 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.

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  • The answer C is correct only if it is mentioned in the question that x and y are integers and that is not the case here. For example, x can be 24.5 and y can be 10. This combination satisfies the equation in the question. But 24.5 is not divisible by 7.

  • x is equal to 1/20 and y is equal to 1/49, then "C" is not the right answer. 

  • @Nithiya is 100% correct... I was also thinking in terms of fraction and found that if we consider x and y as fractions C is also not correct. 

    If x = 1/{49(p)}
    y = 1/{20(p)}

    where p is any number so it can give us many fraction values for which x/7 is not an integer. 

    So please mention in the question that x, y belongs to integer.

  • None of the following must be true ;)

  • 20x = 49y, which is x/y = 49/20, which is x/y >1 which says x>y , but then x2 >Y2 so A and B can be true, so the question has a problem !!

    • I think its A, becuase for -x>-y, x2 need not be greater than y eg: -2>-3, but then 4<9; so A is the answer 100%

  • I is the correct answer

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