Analytical

Analytical

Puzzle Hard 2

⏱ 10:00

600%
  • Questions 1-6 In a telecommunications-cable assembly plant, cables are assembled by twisting plastic-coated wires together. There are wires of exactly six different solid colors – red, yellow, violet, green, white, and black. Wires must be assembled into single cables according to the following rules: Each cable must contain at least three wires and wires of at least three different colors. At most two wires in a single cable can be black. At most two wires in a single cable can be white. There can be at most one wire of each of the other colors in a single cable. If one wire is red, then one wire must be yellow. If one wire is violet, then no wire can be green. Which of the following could be the complete set of wires in an acceptable cable?
  • The maximum number of wires that can be used in an acceptable cable is
  • If exactly one black wire and exactly one white wire are used in an assembled cable, which of the following must be true?
  • If a white wire and a violet wire must be among the wires chosen for a particular cable, any of the following pairs of wires could complete the cable EXCEPT a
  • If an assembled cable consists of exactly five wires, each a different color, it could be true that color NOT used is
  • If there is an additional requirement that violet must be used if yellow is used, which of the following must be true?
  • Question 7-10 Shoummo Rubaiyat, a volunteer, uses a truck to pick up donations of unsold food and clothing from stores and to deliver them to locations where they can be distributed. He drives only along a certain network of roads. In the network there are two-way roads connecting each of the following pairs of points: 1 with 2, 1 with 3, 1 with 5, 2 with 6, 3 with 7, 5 with 6, and 6 with 7. There are also one-way roads going from 2 to 4, from 3 to 2, and from 4, to 3. There are no other roads in the network, and the roads in the network do not intersect. To make a trip involving pickups and deliveries, the volunteer always takes a route that for the whole trip passes through the fewest of the points 1 through 7, counting a point twice if the volunteer passes through it twice. His home is at point 3. Donations can be picked up at a supermarket at point 1, a clothing store at point 5, and bakery point at point 4. Deliveries can be made as needed to a tutoring center at point 2, a distribution center at point 6, and a shelter at point 7. If Shoummo starts at the supermarket and next is to go to the shelter, the first intermediate point his route passes through must be
  • If, starting from home, Shoummo next to is to make pickups for the shelter at the supermarket and the bakery (in either order), the first two intermediate points on his route, beginning with the first, must be
  • If, starting from the clothing store, Shoummo next is to pick up break at either the supermarket or the bakery (whichever stop makes his route go through the fewest of the points) and then is to go to the shelter, the first two points he reaches after the clothing store, beginning with the first, must be
  • If Shoummo is to make a trip starting at the shelter, next going to the bakery for a pickup, and then ending at the distribution center, the first two intermediate points on his route, beginning with the first, can be
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