### All ISEE Upper Level Quantitative Resources

## Example Questions

### Example Question #71 : Equations

Column A Column B

The price of a $27

$30 jacket that's

on sale for

10% off.

**Possible Answers:**

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.

**Correct answer:**

The quantities in both columns are equal.

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.

**Possible Answers:**

None of the other responses is correct.

**Correct answer:**

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

**Possible Answers:**

(A) and (B) are equal

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

(A) is greater

(B) is greater

**Correct answer:**

(A) and (B) are equal

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

**Possible Answers:**

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

(A) and (B) are equal

(B) is greater

(A) is greater

**Correct answer:**

(A) is greater

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

**Possible Answers:**

(A) and (B) are equal

(B) is greater

(A) is greater

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

**Correct answer:**

(B) is greater

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

**Possible Answers:**

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

(A) is greater

(A) and (B) are equal

(B) is greater

**Correct answer:**

(B) is greater

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

**Possible Answers:**

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

(A) and (B) are equal

(B) is greater

(A) is greater

**Correct answer:**

(B) is greater

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)

**Possible Answers:**

(A) is greater

(B) is greater

(A) and (B) are equal

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

**Correct answer:**

(A) is greater

so

Substitute for in the other equation:

so (A) is greater.

### Example Question #79 : Equations

Which is the greater quantity?

(A)

(B)

**Possible Answers:**

(A) is greater

(B) is greater

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

(A) and (B) are equal

**Correct answer:**

(A) is greater

The first equation actually provides all of the needed information.

, so

making .

### Example Question #80 : Equations

Which is the greater quantity?

(A)

(B)

**Possible Answers:**

(A) is greater

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

(A) and (B) are equal

(B) is greater

**Correct answer:**

(A) is greater

Add both sides of the equations as follows:

, so

, so (A) is greater.