Why Do We Care about Yes/No Data Sufficiency Questions?
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GMAT Data Sufficiency questions can seem a little mysterious. (If you’re just getting started, or if you need a refresher, here’s a great article on the basics of Data Sufficiency.) These problems are more like logic puzzles than math questions. That makes Data Sufficiency a good opportunity for those of us who want to score well on Quant, but don’t like doing math! However, you might have some questions about Data Sufficiency as you start to understand the problem type a little better. Here’s one of them: why do we categorize Data Sufficiency questions into “yes/no” and “value”?
A Data Sufficiency problem always includes a question, which appears at the top. The question is always unfair: you can never answer it without getting more information first. For instance, these could be Data Sufficiency questions:
What is the value of x?
What is the median weight, in pounds, of the 17 students in a certain class?
Claire rolled a fair 6-sided die 4 times. How many times did the die show a value of 4 or greater?
All three of those are examples of “value” questions. A value question is a question that could be answered with a number. On the other hand, yes/no Data Sufficiency questions can be answered with a “yes” or a “no”:
Is x greater than 10?
Is the median weight of the students in Classroom A equal to the median weight of the students in classroom B?
Claire rolled a fair 6-sided die 4 times and totaled the values that she rolled. Was the total of all of her rolls divisible by 10?
Before you start trying to solve any Data Sufficiency problem, you should notice whether you’re answering a yes/no question or a value question. Doing this can make the difference between confidently giving a right answer, and falling for a trap. Here’s why.
In order to answer a value question, you need to be able to calculate a specific number. You don’t actually have to do the calculation—that’s what’s so great about Data Sufficiency questions—but you do need to be able to do it. For instance, in this value Data Sufficiency problem, Statement 1 would be sufficient:
What is the value of x?
(1) x = 1,945,732156
Now, here’s a yes/no problem that uses the same statement:
Is x greater than 10?
(1) x = 1,945,732156
This problem is pretty similar to the previous one. You can calculate the value of x, so you can answer the yes/no question about whether it’s greater than 10. The statement is sufficient.
Here’s where things get weird. In order to answer a value question, you have to know the value of x. So, the statement in this problem is insufficient:
What is the value of x?
(1) x is a positive multiple of 100.
But in order to answer a yes/no question, you might not need the value at all. This statement is sufficient:
Is x greater than 10?
(1) x is a positive multiple of 100.
There are an infinite number of positive multiples of 100. You definitely can’t calculate the value of x—you can’t even get close. However, you can still answer the question. You don’t know what x is, but you do know something about it: x is 100, 200, 300, 400, 500, or some other positive multiple of 100. In other words, you know that whatever x is, it’s definitely bigger than 10. You know that the answer to the question is “yes”! So, even though the statement doesn’t let you find the value of x, it’s still sufficient.
In other words, when you’re dealing with yes/no Data Sufficiency questions, a statement doesn’t have to give you a specific value to be sufficient. As long as it gives you enough info to answer either “yes” or “no” to the question, it’s good enough. If it does give you a specific value, that’s nice, but it doesn’t have to.
So, don’t look at a question like “is x greater than 10?” and think to yourself “okay, I need to figure out what x is.” That’s a common cause of mistakes on Data Sufficiency questions. Instead, ask yourself whether the answer to the question is yes or no—without worrying about what x is.
Give this tricky yes/no Data Sufficiency question a try. Focus on answering the question with a “yes” or a “no,” not on finding specific values!
If x and y are positive integers, is xy equal to yx?
- y > x
- x and y are prime
Answer: C. Statement 1 is insufficient: if x = 2 and y = 4, the answer to the question is ‘yes’, while if x = 1 and y = 3, the answer to the question is ‘no.’ Statement 2 is insufficient as well: if x and y are equal, the answer to the question would be ‘yes,’ while otherwise, it would be ‘no.’ Combining both statements, however, lets you answer the question—the two values will never be equal if x and y are distinct primes. That’s true even though you can’t find the value of x and y at all! ?
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Chelsey Cooley
is a Manhattan Prep instructor based in Seattle, Washington. Chelsey always followed her heart when it came to her education. Luckily, her heart led her straight to the perfect background for GMAT and GRE teaching: she has undergraduate degrees in mathematics and history, a master’s degree in linguistics, a 790 on the GMAT, and a perfect 170/170 on the GRE. Check out Chelsey’s upcoming GRE prep offerings here.