y = ax - 5
y = x + 6
y = 3x + b
In the xy-plane, the straight-line graphs of the three equations above each contain the point (p,r). If a and b are constants, what is the value of b?
(1) a = 2
(2) r = 17
D
OG The straight-line graphs of the three equations
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AbeNeedsAnswers wrote:y = ax - 5
y = x + 6
y = 3x + b
In the xy-plane, the straight-line graphs of the three equations above each contain the point (p,r). If a and b are constants, what is the value of b?
(1) a = 2
(2) r = 17
D
We can begin by substituting p and r for x and y, respectively, in the three 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 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.
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
We see that p = 11. Now we can 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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Hi AbeNeedsAnswers,
We're given the equations for 3 lines (and those equations are based on 4 unknowns: 2 variables and the 2 'constants' A and B):
Y = (A)(X) - 5
Y = X + 6
Y = 3X + B
We're told that the three lines all cross at one point on a graph (p,r). We're asked for the value of B. While this question looks complex, it's actually built around a 'system' math "shortcut" - meaning that since we have 3 unique equations and 4 unknowns, we just need one more unique equation (with one or more of those unknowns) and we can solve for ALL of the unknowns:
1) A =2
With this information, we now have a 4th equation, so we CAN solve for B.
Fact 1 is SUFFICIENT
2) R = 17
This information tell us the x co-ordinate where all three lines will meet, so it's the equivalent of having X=17 to work with. This 4th equation also allows us to solve for B.
Fact 2 is SUFFICIENT
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
We're given the equations for 3 lines (and those equations are based on 4 unknowns: 2 variables and the 2 'constants' A and B):
Y = (A)(X) - 5
Y = X + 6
Y = 3X + B
We're told that the three lines all cross at one point on a graph (p,r). We're asked for the value of B. While this question looks complex, it's actually built around a 'system' math "shortcut" - meaning that since we have 3 unique equations and 4 unknowns, we just need one more unique equation (with one or more of those unknowns) and we can solve for ALL of the unknowns:
1) A =2
With this information, we now have a 4th equation, so we CAN solve for B.
Fact 1 is SUFFICIENT
2) R = 17
This information tell us the x co-ordinate where all three lines will meet, so it's the equivalent of having X=17 to work with. This 4th equation also allows us to solve for B.
Fact 2 is SUFFICIENT
Final Answer: D
GMAT assassins aren't born, they're made,
Rich