IMO Level 1- Mathematics Olympiad (SOF) Class 7: Questions 982 - 982 of 1022

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Question number: 982

» Logical and Analytical Reasoning

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Appeared in Year: 2012

MCQ▾

Question

The given question figures (I), (II), (III) and (IV). There is a definite relationship between figures (I) and (II). Establish a similar relationship between figures (III) and (IV) by selecting a suitable figure from the options that would replace (? ) in 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_2, B_2,4] Polygon poly1_2 Polygon poly1_2: Polygon [A_2, B_2,4] Polygon poly1_4 Polygon poly1_4: Polygon [A_4, B_4,4] Polygon poly1_4 Polygon poly1_4: Polygon [A_4, B_4,4] 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_2, B_2] of Polygon poly1_2 Segment g_2 Segment g_2: Segment [B_2, C_2] of Polygon poly1_2 Segment h_2 Segment h_2: Segment [C_2, D_2] of Polygon poly1_2 Segment i_2 Segment i_2: Segment [D_2, A_2] of Polygon poly1_2 Segment f_4 Segment f_4: Segment [A_4, B_4] of Polygon poly1_4 Segment g_4 Segment g_4: Segment [B_4, C_4] of Polygon poly1_4 Segment h_4 Segment h_4: Segment [C_4, D_4] of Polygon poly1_4 Segment i_4 Segment i_4: Segment [D_4, A_4] of Polygon poly1_4 Segment j Segment j: Segment [E, F] Segment j_1 Segment j_1: Segment [E_1, F_1] Segment j_2 Segment j_2: Segment [E_2, F_2] Segment k Segment k: Segment [K, L] Segment k_1 Segment k_1: Segment [K_1, L_1] Segment l Segment l: Segment [M, N] Segment k_2 Segment k_2: Segment [K_2, L_2] Segment k_3 Segment k_3: Segment [K_3, L_3] Segment k_4 Segment k_4: Segment [K_4, L_4] Vector u Vector u: Vector [G, H] Vector u Vector u: Vector [G, H] Vector v Vector v: Vector [I, J] Vector v Vector v: Vector [I, J] Vector w Vector w: Vector [O, P] Vector w Vector w: Vector [O, P] x text1 = “x” text1_1 = ” “ text1_2 = ” “ ? text1_3 = “? “ (I) text1_4 = ” (I) “ (II) text1_5 = ” (II) “ (III) text1_6 = ” (III) “ (IV) text1_7 = ” (IV) “

Image of Relationships of Two Figures with Each Other

Showing the image of relationships of two figures with each other, so find (IV) figure that is related to (III)

Choices

Choice (4) Response

a.

Polygon poly1 Polygon poly1: Polygon [A, B, 4] Polygon poly1 Polygon poly1: Polygon [A, B, 4] 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 j Segment j: Segment [E, F] Segment j_1 Segment j_1: Segment [E_1, F_1] Segment j_2 Segment j_2: Segment [E_2, F_2] Vector u Vector u: Vector [G, H] Vector u Vector u: Vector [G, H] text1 = ” “

Image of (IV) Figure That is Related to (III): Choice A

Showing the image of (IV) figure that is related to (III)

b.

Polygon poly1 Polygon poly1: Polygon [A, B, 4] Polygon poly1 Polygon poly1: Polygon [A, B, 4] 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 j Segment j: Segment [E, F] Segment j_1 Segment j_1: Segment [E_1, F_1] Segment j_2 Segment j_2: Segment [E_2, F_2] Vector u Vector u: Vector [I, J] Vector u Vector u: Vector [I, J] × text1 = “×”

Image of (IV) Figure That is Related to (III): Choice B

Showing the image of (IV) figure that is related to (III)

c.

Polygon poly1 Polygon poly1: Polygon [A, B, 4] Polygon poly1 Polygon poly1: Polygon [A, B, 4] 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 j Segment j: Segment [E, F] Segment j_1 Segment j_1: Segment [E_1, F_1] Segment j_2 Segment j_2: Segment [E_2, F_2] Vector u Vector u: Vector [G, H] Vector u Vector u: Vector [G, H] × text1 = “×”

Image of (IV) Figure That is Related to (III): Choice C

Showing the image of (IV) figure that is related to (III)

d.

Polygon poly1 Polygon poly1: Polygon [A, B, 4] Polygon poly1 Polygon poly1: Polygon [A, B, 4] 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 j Segment j: Segment [E, F] Segment j_1 Segment j_1: Segment [E_1, F_1] Segment j_2 Segment j_2: Segment [E_2, F_2] Vector u Vector u: Vector [I, J] Vector u Vector u: Vector [I, J] × text1 = “×”

Image of (IV) Figure That is Related to (III): Choice D

Showing the image of (IV) figure that is related to (III)