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Geometry
N/A
What is the number of 360-degree rotations that a bicycle wheel made while rolling 100 meters in a straight line without slipping?
(1) The diameter of the bicycle wheel, including the tire, was 0.5 meter.
(2) The wheel made twenty 360-degree rotations per minute.
N/A
In triangle PQR, if PQ = x, QR = x + 2, and PR = y, which of the three angles of triangle PQR has the greatest degree measure?
(1) y = x+ 3
(2) x = 2
N/A
If l and w represent the length and width, respectively, of the rectangle above, what is the perimeter?
(1) 2l + w = 40
(2) l + w= 25
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N/A
What is the radius of the circle above with center O?
(1) The ratio of OP to PQ is 1 to 2.
(2) P is the midpoint of chord AB.
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N/A
Is the perimeter of square S greater than the perimeter of equilateral triangle T?
(1) The ratio of the length of a side of S to the length of a side of T is 4:5.
(2) The sum of the lengths of a side of S and a side of T is 18.
N/A
In the triangle above, does a^2 + b^2 = c^2 ?
(1) x + y = 90
(2) x = y
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N/A
In the figure above, if lines k and m are parallel, what is the value of x ?
(1) y = 120
(2) z = 60
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N/A
In the figure above, segments PR and QR are each parallel to one of the rectangular coordinate axes. Is the ratio of the length of QR to the length of PR equal to 1?
(1) c = 3 and d = 4.
(2) a = -2 and b = -1.
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N/A
If P and Q are each circular regions, what is the radius of the larger of these regions?
(1) The area of P plus the area of Q is equal to
90Ï
90
ð
.
(2) The larger circular region has a radius that is 3 times the radius of the smaller circular region.
N/A
In the figure above, segments RS and TU represent two positions of the same ladder leaning against the side SV of a wall. The length of TV is how much greater than the length of RV?
(1) The length of TU is 10 meters.
(2) The length of RV is 5 meters.
DS48602.01
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N/A
In the figure above, what is the measure of angle ABC?
(1) BX bisects angle ABY and BY bisects angle XBC.
(2) The measure of angle ABX is 40°.
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N/A
The inside of a rectangular carton is 48 centimeters long, 32 centimeters wide, and 15 centimeters high. The carton is filled to capacity with k identical cylindrical cans of fruit that stand upright in rows and columns, as indicated in the figure above. If the cans are 15 centimeters high, what is the value of k?
(1) Each of the cans has a radius of 4 centimeters.
(2) Six of the cans fit exactly along the length of the carton.
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N/A
What is the area of the rectangular region above?
(1) l + w = 6.
(2) d^2 = 20
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N/A
If P, Q, and R are three distinct points, do line segments PQ and PR have the same length ?
(1) P is the midpoint of line segment QR.
(2) Q and R lie on the same circle with center P.
N/A
The length of the edging that surrounds circular garden K is 1/2 the length of the edging that surrounds circular garden G. What is the area of garden K (Assume that the edging has negligible width.)
(1) The area of G is
25Ï
25
ð
square meters.
(2) The edging around G is
10Ï
10
ð
meters long.
(1) The area of G is
25Ï
25
ð
square meters.
(2) The edging around G is
10Ï
10
ð
meters long.
N/A
Quadrilateral RSTU shown above is a site plan for a parking lot in which side RU is parallel to side ST and RU is longer than ST. What is the area of the parking lot?
(1) RU = 80 meters
(2) TU =
20
10
â
â
â
20
10
meters
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N/A
In the figure above, what is the length of AD?
(1) AC = 6
(2) BD = 6
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N/A
The figure above represents a circle graph of Company H's total expenses broken down by the expenses for each of its five divisions. If O is the center of the circle and if Company H's total expenses are $5,400,000, what are the expenses for Division R ?
(1) x = 94
(2) The total expenses for Divisions S and T are twice as much as the expenses for Division R.
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605-655 (Medium)
Figures X and Y above show how eight identical triangular pieces of cardboard were used to form a square and a rectangle, respectively. What is the ratio of the perimeter of X to the perimeter of Y?
555-605 (Medium)
On a scale drawing, a rectangle 1 inch by 1 1 3 inches represents the floor of a room and the indicated scale is 1 inch equals 15 feet. How many square tiles 6 inches on a side will be needed to cover this floor?