GMAT Quantitative Reasoning: Data Sufficiency Example Problem #1

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This week we will turn our attention to a GMAT Data Sufficiency question. Because the instructions regarding Data Sufficiency questions are highly specific we have included them.

GMAT Data Sufficiency Instructions: Each of the data sufficiency questions below consist of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are ­sufficient for answering the question. Using the data given in the statement plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of counterclockwise) you are to fill in oval:

  1. if statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;
  2. if statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;
  3. if BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient;
  4. if EACH statement ALONE is sufficient to answer the question asked;
  5. if statements (1) and (2) together are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

What is the average (arithmetic mean) of 3x and 6y? 

(1)    x + 2y = 7

(2)    x + y = 5 

When solving data sufficiency questions, it’s important to recognize what information is needed to solve the problem.  In this example, the question is asking for the average of 3x and 6y. Remember that an average is found by dividing the sum by the number of terms.

Average = Sum/Number of terms

In this case, the number of terms is two, 3x and 6y.

Average = (3x + 6y) / 2

This means that if we can find the sum of 3x and 6y, we can find the average. It’s not important to find the values of x and y separately. We just need to know the value of that sum. It would be very tempting to start this problem by combining both of our statements together and solving for x and y. However, in a data sufficiency problem you should always start by looking at each statement on its own. Now, let’s look at the statements.

You can modify this equation to find the value of 3x + 6y. Multiply both sides of the equation by 3.

x + 2y = 7

3(x + 2y) = 3(7)

3x + 6y = 21

We now know that the value of 3x + 6y is 21. This means that the average of 3x + 6y is 21/2, or 11.5. The first statement is sufficient.

Again, look at each statement by itself. The equation is x + y = 5. Since there are two variables and only one equation (again, forget about the first one), there’s no way to solve for x and y. There’s also no way to modify this equation to find the sum of 3x + 6y. This statement is not sufficient.

Since the first statement is sufficient and the second is not, the answer is (A).

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