All ISEE Upper Level Quantitative Resources
Example Questions
Example Question #31 : Geometry
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.
(a) is greater.
(a) and (b) are equal.
It is impossible to tell from the information given.
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.
All ISEE Upper Level Quantitative Resources
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