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IntroductionGT package Math Olympiad
Math Olympiad 1
Math Olympiad 2
Math Olympiad 3
Math Olympiad 4
Math Olympiad 5
Week 1: Number SubstitutionWeek 2: MeasurementsWeek 3: Sum, Difference & MultipleWeek 4: Fraction & DecimalsWeek 5: Quiz 1Week 6: Solve EquationWeek 7: Geometry (1)Week 8: Counting ProblemsWeek 9: Number CalculationWeek 10: Quiz 2Week 11: Percentage ProblemsWeek 12: Distance, Speed & TimeWeek 13: Work ProblemsWeek 14: Divisibility and RemainderWeek 15: Quiz 3Week 16: Least and MostWeek 17: Word Problems (1)Week 18: Number Thinking (1)Week 19: Combination & Probability (1)Week 20: Quiz 4Week 21: AlgebraWeek 22: Time ProblemsWeek 23: Average ProblemsWeek 24: Multiple & FactorWeek 25: Quiz 5Week 26: Mid-Term ExamWeek 27: Ratio ProblemsWeek 28: Number Thinking (2)Week 29: Data AnalysisWeek 30: Age ProblemsWeek 31: Quiz 6Week 32: Number SequencesWeek 33: Pattern ProblemWeek 34: "Unsolvable" EquationsWeek 35: Money ProblemsWeek 36: Quiz 7Week 37: Geometry(2)Week 38: Logical ReasoningWeek 39: Word Problem (2)Week 40: Number Thinking (3)Week 41: Quiz 8Week 42: Combination & Probability (2)Week 43: Distance, Speed & Time (2)Week 44: Challenge Geometry Questions Week 45: Sum, Difference & Multiple (2)Week 46: Quiz 9Week 47: Probability ProblemsWeek 48: Distance, Speed & Time (3)Week 49: Price & CostWeek 50: Challenge ProblemsWeek 51: Quiz 10Week 52: Final Exam
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Challenge Geometry Questions ( Week 44 Evaluation)
1.  A square has an area with a value 8 times its perimeter. How long is each side of the square?
2.  Two circles A and B are enclosed inside a larger circle C. There is no overlap between A and B, and they stretch the entire diameter of the larger circle C. The area of circle C is 100π. What is the largest possible non-shaded area inside C? Note that the diagram might not be drawn to scale.
Best GT Prep
A) 51π
B) 48π
C) 60π
D) 50
E) 50π
3.  ABCD is a rectangle. E, and F are at the same height. If the area of the rectangle ABCD is 89, what is the area sum of the shaded triangles?
Best GT Prep
A) 19.25
B) 24.25
C) 22.25
D) 21.25
E) can not be determined
4.  The sides of a triangle are all integer lengths. Two sides have the lengths of 12 and 5. What is the smallest possible perimeter of the triangle?
A) 26
B) 28
C) 25
D) 27
E) can not be determined
5.  What is the length of BE in the following diagram?
A) 17
3
 
B) 17
C) 14
D) 17
2
 
E) 16
6.  
In the figure above, point R lies on segment OP. The area of the circle with center O is 400π, and the length of the line segment OP is 17. What is the area of the circle with center Q?
A) 8
B) 9π
C) 10π
D) 11π
E) 6π
7.  
If the area of the square in the figure above is 64 and the perimeter of each of the 4 triangles is 18, what is the perimeter of the figure (a star) outlined by the solid line? Note that the figure is not drawn to scale.
A) 24
B) 40
C) 32
D) 72
E) 16
8.  In a parallelogram ABCD, if AC > BD, which of the following statement(s) must be true? Note that the diagram is not drawn to scale.


I. ∠B > ∠A
II.AB + BC > BC + CD
III.∠BDC > ∠BCA
A) II only
B) II and III
C) I and III
D) I and II
E) I only
9.  By connecting the four midpoints of each of the sides of a square, a new square is formed enclosed in the original square. If the most external square is the 1st square, the one enclosed by the first one is the 2nd square, the one enclosed by the 2nd square is the 3rd square, ... and so on. If the 7th square has a perimeter of 4, what is the area of the 1st square?
Best GT Prep
A) 128
B) 1024
C) 512
D) 16
E) 64
10.  Given two squares, if the ratio of the area of the larger square to the area of the smaller square is 17, what is the ratio of the length of the diagonal of the larger square to the length of the diagonal of the smaller?
A) 17
17
 
B) 17
C)
17
 
D) 172
E) none of the above.



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