GMAT OFFICIAL GUIDE DS

Solution:

We are given that region R consists of all of the points (x,y) such that 2x + 3y [Symbol] 6, and we need to determine whether the point (r, s) is in the region R. That is, is 2r + 3s [Symbol] 6? Notice that no information about the values of r or s are provided in the question stem. Therefore, if the statement is sufficient to answer the question, the inequality 2r + 3s [Symbol] 6 has to hold true for all values of r and s that satisfy the condition(s) given in the statement.

Statement One Alone:

3r + 2s = 6

We see that there are infinitely many values of r and s that satisfy the equation. For example, (r, s) could be (2, 0) or it could be (0, 3). If (r, s) = (2, 0), then 2r + 3s [Symbol] 6 would be true since 2(2) + 3(0) = 4 [Symbol] 6. However, if (r, s) = (0, 3), then 2r + 3s [Symbol] 6 would be false since 2(0) + 3(3) = 9 > 6. Thus, statement one is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

r [Symbol] 3 and s [Symbol] 2

We see that there are infinitely many values of r and s that satisfy the inequalities. For example, (r, s) could be (2, 0) or it could be (2, 1). If (r, s) = (2, 0), then 2r + 3s [Symbol] 6 would be true since 2(2) + 3(0) = 4 [Symbol] 6. However, if (r, s) = (2, 1), then 2r + 3s [Symbol] 6 would be false, since 2(2) + 3(1) = 7 > 6. Thus, statement two is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

From statement one we have 3r + 2s = 6 and from statement two we have r [Symbol] 3 and s [Symbol] 2. Therefore, we have to find values for r and s that satisfy both statements. For example,
(r, s) = (2, 0) satisfies both statements and it would make 2r + 3s [Symbol] 6 true also. On the other hand (r, s) = (1, 3/2) satisfies both statements but it would make 2r + 3s [Symbol] 6 false since 2(1) + 3(3/2) = 6.5 > 6. Thus, the two statements together are not sufficient to answer the question.

Answer: E

About The Author

Jeffrey Miller is the head GMAT instructor for Target Test Prep. Jeff has more than fourteen years of experience in the business of helping students with low GMAT scores hurdle the seemingly impossible and achieve the scores they need to get into the top 20 business school programs in the world, including HBS, Stanford, Wharton, and Columbia. Jeff has cultivated many successful business school graduates through his GMAT instruction, and will be a pivotal resource for many more to follow.