IMO Level 1- Mathematics Olympiad (SOF) Class 4: Questions 539 - 539 of 614

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Question number: 539

» Logical Reasoning

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Question

Each of the following questions consists two sets of figures. Figures P, Q, R and S constitute the problem set. There is a definite relationship between figures P and Q. Establish a similar relationship between figures R ans S by choosing a suitable figure (S) from the set of alternatives.

Problem set:

Polygon poly2 Polygon poly2: Polygon [E, F, 6] 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 a_1 Segment a_1: Segment [A_1, B_1] of Quadrilateral poly1_1 Segment b_1 Segment b_1: Segment [B_1, C_1] of Quadrilateral poly1_1 Segment c_1 Segment c_1: Segment [C_1, D_1] of Quadrilateral poly1_1 Segment d_1 Segment d_1: Segment [D_1, A_1] of Quadrilateral poly1_1 Segment a_2 Segment a_2: Segment [A_2, B_2] of Quadrilateral poly1_2 Segment b_2 Segment b_2: Segment [B_2, C_2] of Quadrilateral poly1_2 Segment c_2 Segment c_2: Segment [C_2, D_2] of Quadrilateral poly1_2 Segment d_2 Segment d_2: Segment [D_2, A_2] of Quadrilateral poly1_2 Segment a_3 Segment a_3: Segment [A_3, B_3] of Quadrilateral poly1_3 Segment b_3 Segment b_3: Segment [B_3, C_3] of Quadrilateral poly1_3 Segment c_3 Segment c_3: Segment [C_3, D_3] of Quadrilateral poly1_3 Segment d_3 Segment d_3: Segment [D_3, A_3] of Quadrilateral poly1_3 Segment f Segment f: Segment [E, F] of Polygon poly2 Segment g Segment g: Segment [F, G] of Polygon poly2 Segment h Segment h: Segment [G, H] of Polygon poly2 Segment i Segment i: Segment [H, I] of Polygon poly2 Segment j Segment j: Segment [I, J] of Polygon poly2 Segment k Segment k: Segment [J, E] of Polygon poly2 Segment k_1 Segment k_1: Segment [K, L] of Quadrilateral poly3 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, K] of Quadrilateral poly3 Segment v Segment v: Segment [T, U] of Triangle poly5 Segment t Segment t: Segment [U, V] of Triangle poly5 Segment u Segment u: Segment [V, T] of Triangle poly5 Point P P = (0.86,3.2) Point P P = (0.86,3.2) Point S S = (-1.22,3.28) Point S_1 S_1 = (-0.66,3.28) Point S_2 S_2 = (0.46,3.34) Point S_3 S_3 = (1.28,3.34) Point S_4 S_4 = (3.24,3.22) Point W W = (3.64,3.22) ? text1 = “? “ W text2 = “W” X text2_1 = “X” Y text2_2 = “Y” Z text2_3 = “Z”

Figure W, X, and Y Are Given

Find the missing figure Z

Choices

Choice (4) Response

a.

Polygon poly2 Polygon poly2: Polygon [E, F, 6] Segment a_2 Segment a_2: Segment [A_2, B_2] of Quadrilateral poly1_2 Segment b_2 Segment b_2: Segment [B_2, C_2] of Quadrilateral poly1_2 Segment c_2 Segment c_2: Segment [C_2, D_2] of Quadrilateral poly1_2 Segment d_2 Segment d_2: Segment [D_2, A_2] of Quadrilateral poly1_2 Segment f Segment f: Segment [E, F] of Polygon poly2 Segment g Segment g: Segment [F, G] of Polygon poly2 Segment h Segment h: Segment [G, H] of Polygon poly2 Segment i Segment i: Segment [H, I] of Polygon poly2 Segment j Segment j: Segment [I, J] of Polygon poly2 Segment k Segment k: Segment [J, E] of Polygon poly2 Point S_4 S_4 = (3.24,3.22) Point W W = (3.64,3.22)

Figure Shows the Shapes in Rectangle Choice A

Find the right answer

b.

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 k_1 Segment k_1: Segment [K, L] of Quadrilateral poly3 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, K] of Quadrilateral poly3 Point P P = (-0.62,3.28) Point P P = (-0.62,3.28) Point S S = (-1.22,3.28) Point S_1 S_1 = (-0.22,3.26)

Figure Shows the Shapes in Rectangle Choice B

Find the right answer

c.

Segment a_3 Segment a_3: Segment [A_3, B_3] of Quadrilateral poly1_3 Segment b_3 Segment b_3: Segment [B_3, C_3] of Quadrilateral poly1_3 Segment c_3 Segment c_3: Segment [C_3, D_3] of Quadrilateral poly1_3 Segment d_3 Segment d_3: Segment [D_3, A_3] of Quadrilateral poly1_3 Segment z_1 Segment z_1: Segment [Z, E_1] of Pentagon poly4 Segment e_1 Segment e_1: Segment [E_1, F_1] of Pentagon poly4 Segment f_1 Segment f_1: Segment [F_1, G_1] of Pentagon poly4 Segment g_1 Segment g_1: Segment [G_1, H_1] of Pentagon poly4 Segment h_1 Segment h_1: Segment [H_1, Z] of Pentagon poly4 Point P_1 P_1 = (5.14,3.18) Point P_1 P_1 = (5.14,3.18) Point S_9 S_9 = (4.74,3.5) Point S_ {10} S_ {10} = (5.54,3.52)

Figure Shows the Shapes in Rectangle Choice C

Find the right answer

d.

Segment a_3 Segment a_3: Segment [A_3, B_3] of Quadrilateral poly1_3 Segment b_3 Segment b_3: Segment [B_3, C_3] of Quadrilateral poly1_3 Segment c_3 Segment c_3: Segment [C_3, D_3] of Quadrilateral poly1_3 Segment d_3 Segment d_3: Segment [D_3, A_3] of Quadrilateral poly1_3 Segment i Segment i: Segment [G, H] of Triangle poly1 Segment g Segment g: Segment [H, I] of Triangle poly1 Segment h Segment h: Segment [I, G] of Triangle poly1 Point P_1 P_1 = (5.54,3.38) Point P_1 P_1 = (5.54,3.38) Point S_9 S_9 = (4.64,3.4) Point S_ {10} S_ {10} = (5.12,3.2)

Figure Shows the Shapes in Rectangle Choice D

Find the right answer