YES/NO Data sufficient questions !

Here are some tips for tackling one of the most challenging question types which comes in every other competitive exam: “Yes/No” Data Sufficiency questions. These require more practice (and critical thinking skills) than any other part of the test.
Let’s begin with a sample question:

If t is the sum of three consecutive positive integers, is t a multiple of 24?

(1) The smallest of the 3 integers is even.

(2) t is a multiple of 3.

The first step For Data Sufficiency is to Analyze the Question Stem. First we note that this is a Yes/No question. Because we are concerned with the sum of three consecutive positive integers, we can craft an equation by calling the smallest integer x. This makes the other integers (x + 1) and (x + 2), respectively. Therefore, the sum of the three consecutive integers can be written x + (x + 1) + (x + 2). By combining like terms we see that t = 3x + 3. We can then factor and get the equation t = 3(x + 1).

Because this is a Yes/No question, we aren’t looking for the value of t or x. What we need to know is, “Is 3(x + 1) a multiple of 24?”

“No” is not the same as insufficient data

Evaluating the statements comes next. Statement 1 tells us that the smallest integer is even. If x is even, then x + 1 will always be odd. And 3 times an odd integer is always odd as well. Odd numbers cannot have even factors, so because t is always odd, we know for certain that the answer to the question is No; t is not a multiple of 24.

Inexperienced test-takers often forget a critical fact at this point. It is easy to look at this evaluation, see that the answer is No, and conclude that Statement 1 is therefore Insufficient. “No” is the same as Insufficient, right? Without thinking critically, you could fall into this trap!

Apply critical thinking to evaluating statements

The key to correctly evaluating Yes/No Data Sufficiency  questions is to recognize that the answer itself doesn’t matter; whether the answer is definite is all that matters. Here, we know that t is ALWAYS odd, which means the answer to the question is ALWAYS NO. That is as sufficient as it gets! You don’t need anything else to have a definitive answer to the question posed.

The best way to evaluate Statement 2 would be to imagine numbers that are multiples of 3, then ask whether they are always multiples of 24 (or whether they are never multiples of 24). It doesn’t take long to see that 15 is a multiple of 3 but is not a multiple of 24. However, 24 is also a multiple of 3, and it IS a multiple of 24. So one number yields a No answer and the other yields a Yes. Because this statement leads you to two possible answers, it is Insufficient. “Could be Yes, could be No” equals Insufficient every time.

The takeaway here is that “Always No” is always Sufficient. Drill yourself on Yes/No questions to be sure this clicks; Yes/No questions require a definite answer, regardless of whether that answer is Yes or No.

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