# ISEE Upper Level Quantitative : How to find the solution to an equation

## Example Questions

### Example Question #71 : Equations

Column A                                     Column B

The price of a                               $27$30 jacket that's

on sale for

10% off.

The quantity in Column A is greater.

The quantities in both columns are equal.

The quantity in Column B is greater.

There can be no relationship determined.

The quantities in both columns are equal.

Explanation:

First, calculate the price of the jacket in Column A. If the $30 jacket is on sale for 10% off, that means that it is$3 lower. (10% of $30 is$3). Therefore, the price of the jacket is \$27. The quantities in both columns are equal.

### Example Question #72 : Equations

Give the -coordinate of the point on the line of the equation  that has -coordinate 9.

None of the other responses is correct.

Explanation:

The point  is on the line of the equation . Finding the -coordinate of this point is the same as evaluating  for .. Substitute, and we get:

### Example Question #73 : Equations

Given the line of the equation , which is the greater quantity?

(A) The -coordinate of the -intercept of the line

(B) The -coordinate of the -intercept of the line

(A) and (B) are equal

It is impossible to determine which is greater from the information given

(A) is greater

(B) is greater

(A) and (B) are equal

Explanation:

The -intercept of any line is the point at which the line intersects the -axis; therefore, its -coordinate is 0. Similarly, the -coordinate of the -intercept is 0. The quantities are equal.

### Example Question #74 : Equations

Given the line of the equation , which is the greater quantity?

(A) The -coordinate of the -intercept of the line

(B) The -coordinate of the -intercept of the line

It is impossible to determine which is greater from the information given

(A) and (B) are equal

(B) is greater

(A) is greater

(A) is greater

Explanation:

The -coordinate of the -intercept of the line is 0, so to find the -coordinate, set  and solve for :

Similarly, to find the -coordinate of the -intercept, set  and solve for :

(A), the -coordinate of the -intercept of the line, is greater.

### Example Question #75 : Equations

Given the line of the equation , which is the greater quantity?

(A) The -coordinate of the -intercept of the line

(B) The -coordinate of the -intercept of the line

(A) and (B) are equal

(B) is greater

(A) is greater

It is impossible to determine which is greater from the information given

(B) is greater

Explanation:

The -coordinate of the -intercept of the line is 0, so to find the -coordinate, set  and solve for :

Similarly, to find the -coordinate of the -intercept, set  and solve for :

(B), the -coordinate of the -intercept of the line, is greater.

### Example Question #76 : Equations

Given the line of the equation , which is the greater quantity?

(A) The -coordinate of the -intercept of the line

(B) The -coordinate of the -intercept of the line

It is impossible to determine which is greater from the information given

(A) is greater

(A) and (B) are equal

(B) is greater

(B) is greater

Explanation:

The -coordinate of the -intercept of the line is 0, so to find the -coordinate, set  and solve for :

Similarly, to find the -coordinate of the -intercept, set  and solve for :

(B), the -coordinate of the -intercept of the line, is greater.

### Example Question #77 : Equations

Given the line of the equation , which is the greater quantity?

(A) The -coordinate of the -intercept of the line

(B) The -coordinate of the -intercept of the line

It is impossible to determine which is greater from the information given

(A) and (B) are equal

(B) is greater

(A) is greater

(B) is greater

Explanation:

The -coordinate of the -intercept of the line is 0, so to find the -coordinate, we set  and solve for :

Similarly, to find the -coordinate of the -intercept, we set  and solve for :

(B), the -coordinate of the -intercept of the line, is greater.

### Example Question #78 : Equations

Which is the greater quantity?

(A)

(B)

(A) is greater

(B) is greater

(A) and (B) are equal

It is impossible to determine which is greater from the information given

(A) is greater

Explanation:

so

Substitute for  in the other equation:

so (A) is greater.

### Example Question #79 : Equations

Which is the greater quantity?

(A)

(B)

(A) is greater

(B) is greater

It is impossible to determine which is greater from the information given

(A) and (B) are equal

(A) is greater

Explanation:

The first equation actually provides all of the needed information.

, so

making

### Example Question #80 : Equations

Which is the greater quantity?

(A)

(B)

(A) is greater

It is impossible to determine which is greater from the information given

(A) and (B) are equal

(B) is greater

(A) is greater

Explanation:

Add both sides of the equations as follows:

, so

, so (A) is greater.