Last Updated on May 9, 2023
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
