ISEE Upper Level Quantitative : Geometry
Study concepts, example questions & explanations for ISEE Upper Level Quantitative
All ISEE Upper Level Quantitative Resources
Example Questions
Example Question #61 : Circles
Figure NOT drawn to scale
In the above diagram, 
Which is the greater quantity?
(a)
(b)
(a) and (b) are equal
It is impossible to determine which is greater from the information given
(b) is the greater quantity
(a) is the greater quantity
(a) and (b) are equal
These inscribed angles being congruent, the arcs they intercept, 
Example Question #13 : How To Find The Angle Of A Sector
Figure NOT drawn to scale
In the above diagram, 
Which is the greater quantity?
(a)
(b)
(b) is the greater quantity
It is impossible to determine which is greater from the information given
(a) and (b) are equal
(a) is the greater quantity
(a) is the greater quantity
Example Question #1 : Quadrilaterals
Three of the interior angles of a quadrilateral measure 
This quadrilateral cannot exist.
The measures of the angles of a quadrilateral have sum 
The measure of the fourth angle is 
Example Question #2 : Quadrilaterals
In a certain quadrilateral, three of the angles are 
A quadrilateral has four angles totalling 
Example Question #2 : Quadrilaterals
The angles of Quadrilateral A measure
The angles of Pentagon B measure
Which is the greater quantity?
(A)
(B)
(A) is greater
(B) is greater
(A) and (B) are equal
It is impossible to determine which is greater from the information given
(B) is greater
The sum of the measures of the angles of a quadrilateral is 
and
Example Question #3 : Quadrilaterals
Three of the interior angles of a quadrilateral measure
This quadrilateral cannot exist.
The measures of the angles of a quadrilateral have sum
The measure of the fourth angle is
Example Question #1 : Quadrilaterals
Which is the greater quantity?
(a) The perimeter of a square with sidelength 1 meter
(b) The perimeter of a regular pentagon with sidelength 75 centimeters
(a) is greater.
(b) is greater.
(a) and (b) are equal.
It is impossible to tell from the information given.
(a) is greater.
(a) One meter is equal to 100 centimeters; a square with this sidelength has perimeter 
(b) A regular pentagon has five congruent sides; since the sidelength is 75 centimeters, the perimeter is 
This makes (a) greater.
Example Question #202 : Plane Geometry
Square 1 is inscribed inside a circle. The circle is inscribed inside Square 2.
Which is the greater quantity?
(a) Twice the perimeter of Square 1
(b) The perimeter of Square 2
(b) is greater.
(a) and (b) are equal.
(a) is greater.
It is impossible to tell from the information given.
(a) is greater.
Let 
Since the perimeter of a square is four times its sidelength, Square 1 has perimeter 
Example Question #1 : Squares
Five squares have sidelengths one foot, two feet, three feet, four feet, and five feet.
Which is the greater quantity?
(A) The mean of their perimeters
(B) The median of their perimeters
It is impossible to tell which is greater from the information given
(A) is greater
(A) and (B) are equal
(B) is greater
(A) and (B) are equal
The perimeters of the squares are
The mean of the perimeters is their sum divided by five;
The median of the perimeters is the value in the middle when they are arranged in ascending order; this can be seen to also be 12 feet.
The quantities are equal.
Example Question #2 : Quadrilaterals
Four squares have sidelengths one meter, one meter, 120 centimeters, and 140 centimeters. Which is the greater quantity?
(A) The mean of their perimeters
(B) The median of their perimeters
(B) is greater
(A) and (B) are equal
(A) is greater
It is impossible to tell which is greater from the information given
(A) is greater
First find the perimeters of the squares:
The mean of the perimeters is their sum divided by four:
The median of the perimeters is the mean of the two values in the middle, assuming the values are in numerical order:
The mean, (A), is greater.
All ISEE Upper Level Quantitative Resources
