Economists work with supply and demand curves that show the price P

Question

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.

Show Spoiler

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.

gmatophobia · Accepted Answer

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

Jake7Wimmer · Answer

Bunuel  isn't geometry not supposed to be on the focus exam? This came up in Mock 4 for me.

Bunuel · Answer

Coordinate geometry/functions is still tested on the GMAT.

Dbrunik · Answer

consider just re reading the short graphing section in the official guide. its short and sweet

KarishmaB · Answer

Supply curve is P = aQ + b This is the equation of a line in its most usual form y = ax + b. To define it, we need the values of a and b (slope and y intercept) P is the Y axis and Q is the X axis Demand Curve is P = \frac{k}{Q} This is the reciprocal function and is a curve. To define it, we just need the value of k. The point (10, 5) lies on both of them. This means that 5 = 10a + b (cannot get a and b from this one equation) and 5 = k/10 (can get k = 50 from this) We need the value of a and b now. (1) The point (8,1) is on the supply curve. Now we have another point through which the line passes. We know that 2 points are sufficient to uniquely define a line. So a and b will have unique values. Sufficient alone. (2) The point (25,2) is on the demand curve. Not required. We already know that k = 50 and we cannot get a and b from this Not sufficient alone Answer (A) GMAT-Club-Forum-g0hgg3vn.png

bumpbot · Answer

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Economists work with supply and demand curves that show the price P

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