IMO Level 1- Mathematics Olympiad (SOF) Class 6: Questions 939 - 939 of 1059

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Question number: 939

» Logical and Analytical Reasoning

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Appeared in Year: 2012

MCQ▾

Question

The given question consists of two sets of figures. Figures (I), (II), (III) and (IV) constitute the Problem set. There is a definite relationship between figure (I) and (II). Establish a similar relationship between (III) and (IV) by selecting a suitable figure from the options that would replace (? ) in the figure (IV).

Polygon poly1 Polygon poly1: Polygon [A, B, 4] Polygon poly1 Polygon poly1: Polygon [A, B, 4] Polygon poly1_1 Polygon poly1_1: Polygon [A_1, B_1,4] Polygon poly1_1 Polygon poly1_1: Polygon [A_1, B_1,4] Polygon poly1_2 Polygon poly1_2: Polygon [A_3, B_3,4] Polygon poly1_2 Polygon poly1_2: Polygon [A_3, B_3,4] Polygon poly1_3 Polygon poly1_3: Polygon [A_2, B_2,4] Polygon poly1_3 Polygon poly1_3: Polygon [A_2, B_2,4] Pentagon poly2 Pentagon poly2: Polygon E, F, G, H, I Quadrilateral poly3 Quadrilateral poly3: Polygon J, K, L, M Quadrilateral poly4 Quadrilateral poly4: Polygon P, Q, R, S Pentagon poly5 Pentagon poly5: Polygon T, U, V, W, Z Quadrilateral poly6 Quadrilateral poly6: Polygon E_1, F_1, G_1, H_1 Quadrilateral poly7 Quadrilateral poly7: Polygon K_1, L_1, M_1, N_1 Quadrilateral poly8 Quadrilateral poly8: Polygon O_1, P_1, Q_1, R_1 Triangle poly9 Triangle poly9: Polygon S_1, T_1, U_1 Circle c Circle c: Circle through Z_1 with center W_1 Segment f Segment f: Segment [A, B] of Polygon poly1 Segment g Segment g: Segment [B, C] of Polygon poly1 Segment h Segment h: Segment [C, D] of Polygon poly1 Segment i Segment i: Segment [D, A] of Polygon poly1 Segment f_1 Segment f_1: Segment [A_1, B_1] of Polygon poly1_1 Segment g_1 Segment g_1: Segment [B_1, C_1] of Polygon poly1_1 Segment h_1 Segment h_1: Segment [C_1, D_1] of Polygon poly1_1 Segment i_1 Segment i_1: Segment [D_1, A_1] of Polygon poly1_1 Segment f_2 Segment f_2: Segment [A_3, B_3] of Polygon poly1_2 Segment g_2 Segment g_2: Segment [B_3, C_3] of Polygon poly1_2 Segment h_2 Segment h_2: Segment [C_3, D_3] of Polygon poly1_2 Segment i_2 Segment i_2: Segment [D_3, A_3] of Polygon poly1_2 Segment f_3 Segment f_3: Segment [A_2, B_2] of Polygon poly1_3 Segment g_3 Segment g_3: Segment [B_2, C_2] of Polygon poly1_3 Segment h_3 Segment h_3: Segment [C_2, D_2] of Polygon poly1_3 Segment i_3 Segment i_3: Segment [D_2, A_2] of Polygon poly1_3 Segment e Segment e: Segment [E, F] of Pentagon poly2 Segment f_4 Segment f_4: Segment [F, G] of Pentagon poly2 Segment g_4 Segment g_4: Segment [G, H] of Pentagon poly2 Segment h_4 Segment h_4: Segment [H, I] of Pentagon poly2 Segment i_4 Segment i_4: Segment [I, E] of Pentagon poly2 Segment j Segment j: Segment [J, K] of Quadrilateral poly3 Segment k Segment k: Segment [K, L] of Quadrilateral poly3 Segment l Segment l: Segment [L, M] of Quadrilateral poly3 Segment m Segment m: Segment [M, J] of Quadrilateral poly3 Segment n Segment n: Segment [N, O] Segment p Segment p: Segment [P, Q] of Quadrilateral poly4 Segment q Segment q: Segment [Q, R] of Quadrilateral poly4 Segment r Segment r: Segment [R, S] of Quadrilateral poly4 Segment s Segment s: Segment [S, P] of Quadrilateral poly4 Segment t Segment t: Segment [T, U] of Pentagon poly5 Segment u Segment u: Segment [U, V] of Pentagon poly5 Segment v Segment v: Segment [V, W] of Pentagon poly5 Segment w Segment w: Segment [W, Z] of Pentagon poly5 Segment z_1 Segment z_1: Segment [Z, T] of Pentagon poly5 Segment e_1 Segment e_1: Segment [E_1, F_1] of Quadrilateral poly6 Segment f_5 Segment f_5: Segment [F_1, G_1] of Quadrilateral poly6 Segment g_5 Segment g_5: Segment [G_1, H_1] of Quadrilateral poly6 Segment h_5 Segment h_5: Segment [H_1, E_1] of Quadrilateral poly6 Segment a Segment a: Segment [I_1, J_1] Segment k_1 Segment k_1: Segment [K_1, L_1] of Quadrilateral poly7 Segment l_1 Segment l_1: Segment [L_1, M_1] of Quadrilateral poly7 Segment m_1 Segment m_1: Segment [M_1, N_1] of Quadrilateral poly7 Segment n_1 Segment n_1: Segment [N_1, K_1] of Quadrilateral poly7 Segment o_1 Segment o_1: Segment [O_1, P_1] of Quadrilateral poly8 Segment p_1 Segment p_1: Segment [P_1, Q_1] of Quadrilateral poly8 Segment q_1 Segment q_1: Segment [Q_1, R_1] of Quadrilateral poly8 Segment r_1 Segment r_1: Segment [R_1, O_1] of Quadrilateral poly8 Segment u_1 Segment u_1: Segment [S_1, T_1] of Triangle poly9 Segment s_1 Segment s_1: Segment [T_1, U_1] of Triangle poly9 Segment t_1 Segment t_1: Segment [U_1, S_1] of Triangle poly9 Segment b Segment b: Segment [U_1, V_1] Problem Set text1 = “Problem Set” (I) text1_1 = ” (I) “ (II) text1_2 = ” (II) “ (III) text1_3 = ” (III) “ (IV) text1_4 = ” (IV) “ ? text1_5 = “? “

Four Images in Which Two Are Related to Each Other

Find the figure in (IV) that is related to (III) by using the relationship of (I) and (II)

Choices

Choice (4) Response

a.

Quadrilateral poly1 Quadrilateral poly1: Polygon A, B, C, D Triangle poly2 Triangle poly2: Polygon E, F, G Quadrilateral poly3 Quadrilateral poly3: Polygon L, M, N, O Circle k Circle k: Circle through K with center J Segment a Segment a: Segment [A, B] of Quadrilateral poly1 Segment b Segment b: Segment [B, C] of Quadrilateral poly1 Segment c Segment c: Segment [C, D] of Quadrilateral poly1 Segment d Segment d: Segment [D, A] of Quadrilateral poly1 Segment g Segment g: Segment [E, F] of Triangle poly2 Segment e Segment e: Segment [F, G] of Triangle poly2 Segment f Segment f: Segment [G, E] of Triangle poly2 Segment h Segment h: Segment [H, I] Segment l Segment l: Segment [L, M] of Quadrilateral poly3 Segment m Segment m: Segment [M, N] of Quadrilateral poly3 Segment n Segment n: Segment [N, O] of Quadrilateral poly3 Segment o Segment o: Segment [O, L] of Quadrilateral poly3

Image That is Related to (III): Choice A

Find the right figure in (IV) that is related to (III) by using the relationship of (I) and (II)

b.

Quadrilateral poly1 Quadrilateral poly1: Polygon A, B, C, D Triangle poly2 Triangle poly2: Polygon E, F, G Quadrilateral poly3 Quadrilateral poly3: Polygon L, M, N, O Circle k Circle k: Circle through K with center J Segment a Segment a: Segment [A, B] of Quadrilateral poly1 Segment b Segment b: Segment [B, C] of Quadrilateral poly1 Segment c Segment c: Segment [C, D] of Quadrilateral poly1 Segment d Segment d: Segment [D, A] of Quadrilateral poly1 Segment g Segment g: Segment [E, F] of Triangle poly2 Segment e Segment e: Segment [F, G] of Triangle poly2 Segment f Segment f: Segment [G, E] of Triangle poly2 Segment h Segment h: Segment [H, I] Segment l Segment l: Segment [L, M] of Quadrilateral poly3 Segment m Segment m: Segment [M, N] of Quadrilateral poly3 Segment n Segment n: Segment [N, O] of Quadrilateral poly3 Segment o Segment o: Segment [O, L] of Quadrilateral poly3

Image That is Related to (III): Choice B

Find the right figure in (IV) that is related to (III) by using the relationship of (I) and (II)

c.

Quadrilateral poly1 Quadrilateral poly1: Polygon A, B, C, D Triangle poly2 Triangle poly2: Polygon E, F, G Quadrilateral poly3 Quadrilateral poly3: Polygon L, M, N, O Circle k Circle k: Circle through K with center J Segment a Segment a: Segment [A, B] of Quadrilateral poly1 Segment b Segment b: Segment [B, C] of Quadrilateral poly1 Segment c Segment c: Segment [C, D] of Quadrilateral poly1 Segment d Segment d: Segment [D, A] of Quadrilateral poly1 Segment g Segment g: Segment [E, F] of Triangle poly2 Segment e Segment e: Segment [F, G] of Triangle poly2 Segment f Segment f: Segment [G, E] of Triangle poly2 Segment h Segment h: Segment [H, I] Segment l Segment l: Segment [L, M] of Quadrilateral poly3 Segment m Segment m: Segment [M, N] of Quadrilateral poly3 Segment n Segment n: Segment [N, O] of Quadrilateral poly3 Segment o Segment o: Segment [O, L] of Quadrilateral poly3

Image That is Related to (III): Choice C

Find the right figure in (IV) that is related to (III) by using the relationship of (I) and (II)

d.

Quadrilateral poly1 Quadrilateral poly1: Polygon A, B, C, D Triangle poly2 Triangle poly2: Polygon E, F, G Quadrilateral poly3 Quadrilateral poly3: Polygon L, M, N, O Circle k Circle k: Circle through K with center J Segment a Segment a: Segment [A, B] of Quadrilateral poly1 Segment b Segment b: Segment [B, C] of Quadrilateral poly1 Segment c Segment c: Segment [C, D] of Quadrilateral poly1 Segment d Segment d: Segment [D, A] of Quadrilateral poly1 Segment g Segment g: Segment [E, F] of Triangle poly2 Segment e Segment e: Segment [F, G] of Triangle poly2 Segment f Segment f: Segment [G, E] of Triangle poly2 Segment l Segment l: Segment [L, M] of Quadrilateral poly3 Segment m Segment m: Segment [M, N] of Quadrilateral poly3 Segment n Segment n: Segment [N, O] of Quadrilateral poly3 Segment o Segment o: Segment [O, L] of Quadrilateral poly3 Segment h Segment h: Segment [P, Q]

Image That is Related to (III): Choice D

Find the right figure in (IV) that is related to (III) by using the relationship of (I) and (II)