Scott Woodbury-Stewart

GMAT OFFICIAL GUIDE DS – In the xy-plane, the straight-line graphs of the three equations above…

In the xy-plane, the straight-line graphs of the three equations above …

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 

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