Maths Olympiad Prep

Track / Stage 4 / 69 of 340 #329 of 1964

Problem 329

AMC 12 late, AIME early
Geometry Difficulty 4.6 Find the answer

2. Which of the following statements is correct?
(1) Two faces are parallel, and the rest of the faces are trapezoids; the geometric solid formed by these faces is a frustum.
(2) A frustum is the remaining solid after a smaller pyramid is cut off from a larger pyramid by a plane parallel to the base.
(3) Two edges of a frustum without a common vertex are skew lines.
(4) In a regular quadrilateral frustum, the lateral edges and the diagonals of the non-intersecting upper and lower bases are mutually perpendicular skew lines.
(A)(1) and (2) (B)(2) and (4) (C)(2) and (3) (D) (1) and (3)

The source for this one didn't record the answer, so there is nothing to check what you type against. Work it on paper and mark yourself against the solution below.

Official solution

B

Translate the text above into English, please retain the original text's line breaks and format, and output the translation result directly.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.