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Fish181
Joined: 13 Dec 2023
Last visit: 22 Jan 2025
Posts: 135
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Status:Applying in R1 of 2024 to t15
Affiliations: University of Tennessee
Location: United States (CO)
Concentration: Strategy, Finance
GMAT Focus 1: 605 Q76 V84 DI80 
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WE:Analyst (Consumer Packaged Goods)
GMAT Focus 2: 615 Q78 V86 DI78
Posts: 135
07 Apr 2024, 11:03
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
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Question Stats:
70% (02:14) correct
30%
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wrong
based on 539
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Economists work with supply and demand curves that show the price P of goods as a function of the quantity Q of those goods supplied or demanded. For a certain product, the supply curve is \(P = aQ + b\) and the demand curve is \(P = \frac{k}{Q}\), where \(a\), \(b\), and \(k\) are nonzero constants. The point at which these curves intersect in the (\(Q, P\)) coordinate plane is referred to as the equilibrium point, and for this product the equilibrium point is (10,5). For this product, what are the values of \(a\), \(b\), and \(k\)?
(1) The point (8,1) is on the supply curve.
(2) The point (25,2) is on the demand curve.
GMAT-Club-Forum-t7g4m62o.png [ 75.93 KiB | Viewed 3050 times ]
(1) The point (8,1) is on the supply curve.
(2) The point (25,2) is on the demand curve.
Attachment:
GMAT-Club-Forum-t7g4m62o.png [ 75.93 KiB | Viewed 3050 times ]
07 Apr 2024, 11:35
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Fish181
Supply Curve = \(P = aQ + b\)
Demand Curve = \(P = \frac{k}{Q}\)
The point at which these curves intersect in the (\(Q, P\)) coordinate plane is referred to as the equilibrium point, and for this product the equilibrium point is (10,5)
Inference: Point (10,5) lies on the demand and supply curves.
From the equation of the supply curve ⇒ \(5 = 10a + b\)
From the equation of the demand curve ⇒ \(5 = \frac{k}{10}\) ⇒ k = 50
Question: For this product, what are the values of \(a\), \(b\), and \(k\)
We already have the value of k, we need to find the value of \(a\) and \(b\)
Statement 1
(1) The point (8,1) is on the supply curve.
As point (8,1) lies on the supply curve, the point should satisfy the supply curve equation.
\(1 = 8a + b\)
From the question premise, we know that \(5 = 10a + b\)
Using both equations we can find the value of \(a\) and \(b\).
This statement alone is sufficient to find the value of \(a\), \(b\), and \(k\). We can eliminate B, C, and E.
Statement 2
(2) The point (25,2) is on the demand curve.
As point (25,2) lies on the demand curve, the point should satisfy the demand curve equation.
\(2 = \frac{k}{25}\)
\(k = 50\)
We already know this information from the question premise, hence the statement doesn't provide any new details. The statement alone is not sufficient to find the value of \(a\) and \(b\).
Eliminate D.
Option A
General Discussion
28 Apr 2024, 11:16
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Bunuel isn't geometry not supposed to be on the focus exam? This came up in Mock 4 for me.
