### All ISEE Upper Level Quantitative Resources

## Example Questions

### Example Question #1 : Equilateral Triangles

is an equilateral triangle. Points are the midpoints of , respectively. is constructed.

Which is the greater quantity?

(a) The area of

(b) Twice the area of

**Possible Answers:**

(b) is greater.

It is impossible to tell from the information given.

(a) is greater.

(a) and (b) are equal.

**Correct answer:**

(a) is greater.

Explanation:

If segments are constructed in which the endpoints form the midpoints of the sides of a triangle, then four triangles, congruent to each other and similar to the larger triangle, are formed. Therefore, one of these triangles - specifically, - would have one-fourth the area of . This means has more than twice the area of .

Note that the fact that the triangle is equilateral is irrelevant.

Tynisha

Certified Tutor

Certified Tutor

Georgia State University, Bachelor in Arts, Political Science and Government. Thomas M Cooley Law School, Juris Doctor, Busin...

Jessica

Certified Tutor

Certified Tutor

Swarthmore College, Bachelor in Arts, Philosophy. Harvard University, Master of Arts, Theology.