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

## Example Questions

### Example Question #11 : How To Find The Solution To An Equation

Explanation:

First, rewrite the quadratic equation in standard form by distributing the  through the product on the left and collecting all of the terms on the left side:

Use the  method to factor the quadratic expression ; we are looking to split the linear term by finding two integers whose sum is  and whose product is . These integers are , so:

Set each expression equal to 0 and solve:

or

The solution set is .

### Example Question #681 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Consider the line of the equation

Which is the greater quantity?

(a) The -coordinate of the -intercept

(b) The -coordinate of the -intercept

(a) and (b) are equal

(b) is greater

(a) is greater

It is impossible to tell from the information given

(b) is greater

Explanation:

(a) To find the -coordinate of the -intercept, substitute :

(b) To find the -coordinate of the -intercept, substitute :

(b) is the greater quantity.

### Example Question #13 : How To Find The Solution To An Equation

Which is the greater quantity?

(a)

(b) 0

(a) and (b) are equal

(a) is greater

(b) is greater

It is impossible to tell from the information given

(a) is greater

Explanation:

can be rewritten as a compound statement:

or

Solve both:

or

Either way, , so (a) is the greater quantity

### Example Question #14 : How To Find The Solution To An Equation

Consider the line of the equation

Which is the greater quantity?

(a) The -coordinate of the -intercept

(b) The -coordinate of the -intercept

(a) is greater

(b) is greater

(a) and (b) are equal

It is impossible to tell from the information given

(b) is greater

Explanation:

(a) To find the -coordinate of the -intercept, substitute :

(b) To find the -coordinate of the -intercept, substitute :

This makes (b) the greater quantity

### Example Question #15 : How To Find The Solution To An Equation

refers to the greatest integer less than or equal to .

and  are integers. Which is greater?

(a)

(b)

(a) is greater

It is impossible to tell from the information given

(b) is greater

(a) and (b) are equal

(a) and (b) are equal

Explanation:

If  is an integer, then  by definition.

Since , and, by closure,  are all integers,

and , making (a) and (b) equal.

### Example Question #16 : How To Find The Solution To An Equation

Consider the line of the equation .

Which is the greater quantity?

(a) The -coordinate of the -intercept.

(b) The -coordinate of the -intercept.

(a) and (b) are equal.

(b) is greater.

It is impossible to tell from the information given.

(a) is greater.

(a) is greater.

Explanation:

(a) To find the -coordinate of the -intercept, substitute :

(b) To find the -coordinate of the -intercept, substitute :

Therefore (a) is the greater quantity.

### Example Question #17 : How To Find The Solution To An Equation

Which is the greater quantity?

(a)

(b)

(a) is greater.

(a) and (b) are equal.

It is impossible to tell from the information given.

(b) is greater.

It is impossible to tell from the information given.

Explanation:

Each can be rewritten as a compound statement. Solve separately:

or

Similarly:

Therefore, it cannot be determined with certainty which of  and  is the greater.

### Example Question #11 : How To Find The Solution To An Equation

Which is the greater quantity?

(a)

(b)

It is impossible to tell from the information given.

(a) is greater.

(a) and (b) are equal.

(b) is greater.

It is impossible to tell from the information given.

Explanation:

If , then either  or  . Solve for  in both equations:

or

Therefore, either (a) and (b) are equal or (b) is the greater quantity, but it cannot be determined with certainty.

### Example Question #691 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Which is the greater quantity?

(a)

(b)

(b) is greater

(a) and (b) are equal

(a) is greater

It is impossible to tell from the information given

(a) and (b) are equal

Explanation:

### Example Question #20 : How To Find The Solution To An Equation

Consider the line of the equation .

Which is the greater quantity?

(a) The -coordinate of the -intercept

(b) The -coordinate of the -intercept

(b) is greater.

(a) and (b) are equal.

It is impossible to tell from the information given.

(a) is greater.