IMO Level 1- Mathematics Olympiad (SOF) Class 6: Questions 545 - 545 of 1059

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Question number: 545

» Fractions

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Question

How many parts should be shaded in the figure A to make it the same fraction as the unshaded part in the figure B?

Triangle poly1Triangle poly1: Polygon A, B, CTriangle poly2Triangle poly2: Polygon C_1, D_1, E_1Quadrilateral poly3Quadrilateral poly3: Polygon F_1, G_1, H_1, I_1Quadrilateral poly3_1Quadrilateral poly3_1: Polygon F_2, G_2, H_2, I_2Quadrilateral poly3_2Quadrilateral poly3_2: Polygon F_3, G_4, H_4, I_4Quadrilateral poly3_3Quadrilateral poly3_3: Polygon F_4, G_7, H_7, I_8Quadrilateral poly3_4Quadrilateral poly3_4: Polygon F_5, G_ {10}, H_ {10}, I_ {12} Quadrilateral poly3_5Quadrilateral poly3_5: Polygon F_7, G_ {15}, H_ {15}, I_ {19} Quadrilateral poly3_6Quadrilateral poly3_6: Polygon F_9, G_ {20}, H_ {20}, I_ {26} Quadrilateral poly3_7Quadrilateral poly3_7: Polygon F_ {11}, G_ {25}, H_ {25}, I_ {33} Segment cSegment c: Segment [A, B] of Triangle poly1Segment aSegment a: Segment [B, C] of Triangle poly1Segment bSegment b: Segment [C, A] of Triangle poly1Segment gSegment g: Segment [G, H] Segment hSegment h: Segment [H, J] Segment iSegment i: Segment [J, K] Segment jSegment j: Segment [K, G] Segment kSegment k: Segment [I, L] Segment lSegment l: Segment [M, N] Segment mSegment m: Segment [O, P] Segment nSegment n: Segment [Q, R] Segment pSegment p: Segment [S, T] Segment qSegment q: Segment [U, V] Segment rSegment r: Segment [W, Z] Segment sSegment s: Segment [A_1, B_1] Segment e_1Segment e_1: Segment [C_1, D_1] of Triangle poly2Segment c_1Segment c_1: Segment [D_1, E_1] of Triangle poly2Segment d_1Segment d_1: Segment [E_1, C_1] of Triangle poly2Segment f_1Segment f_1: Segment [F_1, G_1] of Quadrilateral poly3Segment g_1Segment g_1: Segment [G_1, H_1] of Quadrilateral poly3Segment h_1Segment h_1: Segment [H_1, I_1] of Quadrilateral poly3Segment i_1Segment i_1: Segment [I_1, F_1] of Quadrilateral poly3Segment f_2Segment f_2: Segment [F_2, G_2] of Quadrilateral poly3_1Segment g_2Segment g_2: Segment [G_2, H_2] of Quadrilateral poly3_1Segment h_2Segment h_2: Segment [H_2, I_2] of Quadrilateral poly3_1Segment i_2Segment i_2: Segment [I_2, F_2] of Quadrilateral poly3_1Segment f_3Segment f_3: Segment [F_3, G_4] of Quadrilateral poly3_2Segment g_4Segment g_4: Segment [G_4, H_4] of Quadrilateral poly3_2Segment h_4Segment h_4: Segment [H_4, I_4] of Quadrilateral poly3_2Segment i_4Segment i_4: Segment [I_4, F_3] of Quadrilateral poly3_2Segment f_4Segment f_4: Segment [F_4, G_7] of Quadrilateral poly3_3Segment g_7Segment g_7: Segment [G_7, H_7] of Quadrilateral poly3_3Segment h_7Segment h_7: Segment [H_7, I_8] of Quadrilateral poly3_3Segment i_7Segment i_7: Segment [I_8, F_4] of Quadrilateral poly3_3Segment f_5Segment f_5: Segment [F_5, G_ {10} ] of Quadrilateral poly3_4Segment g_ {10}Segment g_ {10}: Segment [G_ {10}, H_ {10} ] of Quadrilateral poly3_4Segment h_ {10}Segment h_ {10}: Segment [H_ {10}, I_ {12} ] of Quadrilateral poly3_4Segment i_ {10}Segment i_ {10}: Segment [I_ {12}, F_5] of Quadrilateral poly3_4Segment f_6Segment f_6: Segment [F_7, G_ {15} ] of Quadrilateral poly3_5Segment g_ {15}Segment g_ {15}: Segment [G_ {15}, H_ {15} ] of Quadrilateral poly3_5Segment h_ {14}Segment h_ {14}: Segment [H_ {15}, I_ {19} ] of Quadrilateral poly3_5Segment i_ {14}Segment i_ {14}: Segment [I_ {19}, F_7] of Quadrilateral poly3_5Segment f_7Segment f_7: Segment [F_9, G_ {20} ] of Quadrilateral poly3_6Segment g_ {20}Segment g_ {20}: Segment [G_ {20}, H_ {20} ] of Quadrilateral poly3_6Segment h_ {18}Segment h_ {18}: Segment [H_ {20}, I_ {26} ] of Quadrilateral poly3_6Segment i_ {18}Segment i_ {18}: Segment [I_ {26}, F_9] of Quadrilateral poly3_6Segment f_8Segment f_8: Segment [F_ {11}, G_ {25} ] of Quadrilateral poly3_7Segment g_ {25}Segment g_ {25}: Segment [G_ {25}, H_ {25} ] of Quadrilateral poly3_7Segment h_ {22}Segment h_ {22}: Segment [H_ {25}, I_ {33} ] of Quadrilateral poly3_7Segment i_ {22}Segment i_ {22}: Segment [I_ {33}, F_ {11} ] of Quadrilateral poly3_7Figure Atext1 = “Figure A”Figure Btext1_1 = “Figure B”

Image of a Triangle and Rectangle Having Some Shaded Parts

Choices

Choice (4)Response

a.

3

b.

8

c.

2

d.

12

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