Last Updated on May 10, 2023
GMAT OFFICIAL GUIDE DS
Solution:
We can begin by substituting p and r in for x and y, respectively, in the 3 given equations.
1) r = ap – 5
2) r = p + 6
3) r = 3p + b
Statement One Alone:
a = 2
We can substitute 2 for a in the equation r = ap – 5. Thus, we have
r = 2p – 5
Next we can set equations 1 and 2 equal to each other.
2p – 5 = p + 6
p = 11
Since p = 11, we see that r = 11 + 6 = 17
Finally, we can substitute 11 in for p and 17 for r in equation 3. This gives us:
17 = 3(11) + b
17 = 33 + b
-16 = b
Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.
Statement Two Alone:
r = 17
We can substitute r into all three equations, and we have:
1) 17 = ap – 5
2) 17 = p + 6
3) 17 = 3p + b
Thus, we see that p = 11. We can next substitute 11 for p in equation 3 to determine a value for b.
17 = 3(11) + b
-16 = b
Statement two alone is also sufficient to answer the question.
Answer: D
