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Data Sufficiency

Data sufficiency

Data sufficiency problems don’t involve difficult concepts or formulas, it just tests your reasoning and analytical skills combined with basic mathematics. In Data Sufficiency problems you have to decide whether the given data is sufficient to answer the questions or not. The format of the question in the exam is as follows:

Understanding Answer options

In Data sufficiency problems, a question consists of two statements labeled I and II, in which a certain information is given. You have to decide whether the information given in the statements is sufficient to answer the question or not.

Data sufficiency tricks

Step 1 – Examine the Question:

What is asked? Do we have to find a value or do we have to check a relationship?

  • Before looking at the two numbered statements, take twenty to thirty seconds to consider the question by itself. Figure out what is being asked. There are usually 2 possibilities a specific number may be sought (“What is the value of y?” “How many gallons of milk is in the tank?”), or a true/false answer may be needed (“Is it true that a >7?” “Is n a prime number?”) Make sure you understand what the question is asking.

Step 2 – Consider each statement individually

  • Having figured out the nature of the question and decided, in a general way, what information is needed to answer it, look at each of the two numbered statements provided. Consider them one at a time, without reference to each other.
  • First look at statement A, then look at statement B.
  • Having gotten this far, you may already be able to pick the right answer.

If neither statement by itself is sufficient to answer the question, go on to the third stage:

Step 3 – Combine the two statements

Third, if necessary, combine the two statements. If neither of the statements by itself is sufficient to answer the question, consider whether you can answer the question by combining the information given in both statements. If so, the answer is 3; if not, the answer is 5.

Example of Data Sufficiency

Example:

A certain group of car dealerships agreed to donate x dollars to a Red Cross chapter for each card sold during a 30-day period. What was the total amount that was expected to be donated?

A).A total of 500 cars were expected to be sold.

B).60 more cars were sold than expected, so that the total amount actually donated was $28,000.

  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient
  3. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
  4. Each statement ALONE is sufficient
  5. Statements (1) and (2) TOGETHER are NOT sufficient

Solution:

The best way to approach data sufficiency questions is to take each statement individually first, before having to consider them together. To that end, let’s start with statement 1.

Statement 1: The question asks us to determine how much money will be donated to the Red Cross based on the number of cars sold at the dealership. With data sufficiency questions, we always want to start with what we know.

  • We know that 500 cars are expected to be sold, as it tell us that in statement 1. Now, we need to decide if we can figure out how much money will be donated.
  • The question tells us that x dollars will be donated for each car sold, so the equation 500x represents the total amount of the expected donation.
  • However, we don’t know the value of x, and we have no way of determining it from the information given. So, we cannot solve the equation 500x, meaning that statement 1 is NOT sufficient for us to solve this problem.

Statement 2: Just as we took statement 1 by itself, let’s take statement 2 by itself first.

  • Statement 2 tells us that 60 more cars were sold than expected. If we know that x represents the amount of money donated to the Red Cross for each car, then we know that 60x represents the amount donated beyond the expected amount, because 60 cars were sold and x dollars were donated for each car.
  • If the total amount of the donation was $28,000, then the total amount that was expected can be found using the equation $28,000 – 60x, with 60x representing the unexpected amount we found before. Since we don’t know what x represents, we can’t find the total amount of the expected donation using Statement 2 alone.
  • Now that we’ve evaluated both statements individually, it’s time to evaluate them together. The first thing I notice when I look at both statements is that both statements have x in them. That means that I can combine the statements and solve for x.
  • Combining the two statements yields me the equation 500x = 28000 – 60x. From there, I can determine the total amount of the expected donation since I can combine like terms and solve for x.
  • Notice that I don’t actually have to solve this equation. All I need to do is know that I can solve it. Since I can solve with the statements together, but not alone, my correct answer is C.