### All ISEE Upper Level Quantitative Resources

## Example Questions

### Example Question #11 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Refer to the above figure. Which is the greater quantity?

(a)

(b)

**Possible Answers:**

(b) is the greater quantity

(a) is the greater quantity

(a) and (b) are equal

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

**Correct answer:**

(a) is the greater quantity

Extend as seen in the figure below:

The measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles; specifically,

,

and

However, , so, by substitution,

### Example Question #12 : Geometry

Given: . . Which is the greater quantity?

(a)

(b)

**Possible Answers:**

(a) and (b) are equal

(b) is the greater quantity

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

(a) is the greater quantity

**Correct answer:**

(b) is the greater quantity

Below is the referenced triangle along with , an equilateral triangle with sides of length 10:

As an angle of an equilateral triangle, has measure . Applying the Side-Side-Side Inequality Theorem, since , , and , it follows that , so .

Also, since , by the Isosceles Triangle Theorem, . Since , and the sum of the measures of the angles of a triangle is , it follows that

Substituting and solving:

.