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 poly1Polygon poly1: Polygon [A, B, 4] Polygon poly1Polygon poly1: Polygon [A, B, 4] Polygon poly1_1Polygon poly1_1: Polygon [A_1, B_1,4] Polygon poly1_1Polygon poly1_1: Polygon [A_1, B_1,4] Polygon poly1_2Polygon poly1_2: Polygon [A_2, B_2,4] Polygon poly1_2Polygon poly1_2: Polygon [A_2, B_2,4] Polygon poly1_4Polygon poly1_4: Polygon [A_4, B_4,4] Polygon poly1_4Polygon poly1_4: Polygon [A_4, B_4,4] Segment fSegment f: Segment [A, B] of Polygon poly1Segment gSegment g: Segment [B, C] of Polygon poly1Segment hSegment h: Segment [C, D] of Polygon poly1Segment iSegment i: Segment [D, A] of Polygon poly1Segment f_1Segment f_1: Segment [A_1, B_1] of Polygon poly1_1Segment g_1Segment g_1: Segment [B_1, C_1] of Polygon poly1_1Segment h_1Segment h_1: Segment [C_1, D_1] of Polygon poly1_1Segment i_1Segment i_1: Segment [D_1, A_1] of Polygon poly1_1Segment f_2Segment f_2: Segment [A_2, B_2] of Polygon poly1_2Segment g_2Segment g_2: Segment [B_2, C_2] of Polygon poly1_2Segment h_2Segment h_2: Segment [C_2, D_2] of Polygon poly1_2Segment i_2Segment i_2: Segment [D_2, A_2] of Polygon poly1_2Segment f_4Segment f_4: Segment [A_4, B_4] of Polygon poly1_4Segment g_4Segment g_4: Segment [B_4, C_4] of Polygon poly1_4Segment h_4Segment h_4: Segment [C_4, D_4] of Polygon poly1_4Segment i_4Segment i_4: Segment [D_4, A_4] of Polygon poly1_4Segment jSegment j: Segment [E, F] Segment j_1Segment j_1: Segment [E_1, F_1] Segment j_2Segment j_2: Segment [E_2, F_2] Segment kSegment k: Segment [K, L] Segment k_1Segment k_1: Segment [K_1, L_1] Segment lSegment l: Segment [M, N] Segment k_2Segment k_2: Segment [K_2, L_2] Segment k_3Segment k_3: Segment [K_3, L_3] Segment k_4Segment k_4: Segment [K_4, L_4] Vector uVector u: Vector [G, H] Vector uVector u: Vector [G, H] Vector vVector v: Vector [I, J] Vector vVector v: Vector [I, J] Vector wVector w: Vector [O, P] Vector wVector w: Vector [O, P] xtext1 = “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

Choices

Choice (4)Response

a.

Polygon poly1Polygon poly1: Polygon [A, B, 4] Polygon poly1Polygon poly1: Polygon [A, B, 4] Segment fSegment f: Segment [A, B] of Polygon poly1Segment gSegment g: Segment [B, C] of Polygon poly1Segment hSegment h: Segment [C, D] of Polygon poly1Segment iSegment i: Segment [D, A] of Polygon poly1Segment jSegment j: Segment [E, F] Segment j_1Segment j_1: Segment [E_1, F_1] Segment j_2Segment j_2: Segment [E_2, F_2] Vector uVector u: Vector [G, H] Vector uVector u: Vector [G, H] text1 = ” “

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

b.

Polygon poly1Polygon poly1: Polygon [A, B, 4] Polygon poly1Polygon poly1: Polygon [A, B, 4] Segment fSegment f: Segment [A, B] of Polygon poly1Segment gSegment g: Segment [B, C] of Polygon poly1Segment hSegment h: Segment [C, D] of Polygon poly1Segment iSegment i: Segment [D, A] of Polygon poly1Segment jSegment j: Segment [E, F] Segment j_1Segment j_1: Segment [E_1, F_1] Segment j_2Segment j_2: Segment [E_2, F_2] Vector uVector u: Vector [I, J] Vector uVector u: Vector [I, J] ×text1 = “×”

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

c.

Polygon poly1Polygon poly1: Polygon [A, B, 4] Polygon poly1Polygon poly1: Polygon [A, B, 4] Segment fSegment f: Segment [A, B] of Polygon poly1Segment gSegment g: Segment [B, C] of Polygon poly1Segment hSegment h: Segment [C, D] of Polygon poly1Segment iSegment i: Segment [D, A] of Polygon poly1Segment jSegment j: Segment [E, F] Segment j_1Segment j_1: Segment [E_1, F_1] Segment j_2Segment j_2: Segment [E_2, F_2] Vector uVector u: Vector [G, H] Vector uVector u: Vector [G, H] ×text1 = “×”

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

d.

Polygon poly1Polygon poly1: Polygon [A, B, 4] Polygon poly1Polygon poly1: Polygon [A, B, 4] Segment fSegment f: Segment [A, B] of Polygon poly1Segment gSegment g: Segment [B, C] of Polygon poly1Segment hSegment h: Segment [C, D] of Polygon poly1Segment iSegment i: Segment [D, A] of Polygon poly1Segment jSegment j: Segment [E, F] Segment j_1Segment j_1: Segment [E_1, F_1] Segment j_2Segment j_2: Segment [E_2, F_2] Vector uVector u: Vector [I, J] Vector uVector u: Vector [I, J] ×text1 = “×”

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

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