First, there are two types of Data Sufficiency questions, depending on the answer that is expected:
- Value questions: These are the questions in which the answer is a number, for example: "what is the area of triangle ABC?"
- Yes/No questions: These are the questions in which the answer is either yes or no, for example: "is the integer x prime?"
The incorrect meaning of sufficiency
The key, I think, is to understand the meaning of sufficiency. The following are common incorrect ways to understand "sufficiency":
"It helps me to answer the question"
For example, if the question asks "What is Paul's age?" and the statement says "Paul's age is between 26 and 30", it's erroneous to think that it's sufficienct because "it helps".
"I need to find one value for x"
This is what I call the "implicit question". Everytime you have a Data Sufficieny question with variables, you are inclined to think "I need to find the value of all the variables in order to give an answer". That is not true for many cases.
"It doesn't say anything"
This usually happens when students try to eyeball the question. Since they don't see an inmediate relationship between the statement and the question, they conclude that it's insufficient. It can be understood as similar to "it doesn't help"
The correct meaning of sufficiency
If you follow this rule, you will make a lot fewer simple errors and have a pretty good chance at getting the hard questions right.
For a statement to be sufficient it must give you a unique answer.
Here is what this means in the context of solving the problem:
- In a yes/no question, a sufficient statement answers "always yes" or "always no". Insufficient statements answer "sometimes yes and sometimes no".
- When you are faced with a confusing statement, try to find cases (as trivial as they may seem) that answer in different ways. Don't jump to conclusions too fast.
- When you try one value and the answer is "yes", don't assume that it's sufficient! You must demonstrate that the answer will always be yes. Conversely, when one value answers "no" don't assume that a "yes" value exists, the answer might be always no.
- In Value questions, don't try only positive integers. Identify what you can assume about the variables (integers, positive, negative, zero, fraction, decimal, etc.) and make sure to try different numbers.
- The questions asked don't always require you to know the exact value of the variables. Don't confuse sufficiency with knowing all the values. For example if the question asks if the product of the integers x and y is even, and a statement says "x is even", it is sufficient even though we don't know anything about y (because even times even or odd is always even). Always focus on the real question.
- Usually for yes/no questions, in order to demonstrate that a statement always answers yes or answers no, you will be required to use properties or algebra. If two or three values answer yes it might not always be yes (for example, if you forgot to try a decimal or a really big number). You want to get good at this in your practice sessions because during the exam you will have to rely on your intuition a bit and it might not always be practical to fully demonstrate an "always yes/no" answer.
If you memorize all of the properties and formulas for the GMAT and you don't grasp this way of solving Data Sufficiency problems, you will find yourself falling for the easy traps (which hurt your score more). Practice with this mindset of forcing you to find a unique solution in order to answer sufficient, or forcing you to find two or more solutions in order to answer insufficient.
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