Here are 100 multiple choice questions on analytical thinking, with answers and rationales: In the classic "brain teaser" about a farmer crossing a river with a fox, a goose, and a bag of grain, why can't the farmer leave the fox alone with the goose? A. The fox will attack the goose B. The goose will attack the fox C. The fox will eat the grain D. The goose will eat the grain The correct answer is: A Rationale: In the classic logic puzzle, the fox is a predator that would eat the goose if left unattended with it. If a single truth-teller always tells the truth, and a single liar always lies, what happens when a truth-teller says "I am a liar"? A. It is a paradox with no resolution B. The speaker must be a liar C. The speaker must be a truth-teller D. There is not enough information to determine The correct answer is: A Rationale: This is the famous "liar paradox" where a truth-teller claiming to be a liar results in a statement that is neither fully true nor fully false - an unresolvable paradox. You have a barrel of water with 59 apples floating in it. How can you divide the apples into two equal groups? A. Remove 29 apples and divide the rest B. Pour out some water so the apples are no longer floating C. It cannot be done D. Chop 1 apple into 2 pieces The correct answer is: B Rationale: When the apples are floating, they cannot be divided into groups. By removing some water, the apples will no longer float freely and can be separated into two piles. Which of the following sequences of shaped holes will allow the passing through of only a circular hole and nothing else? A. Circle, square, triangle B. Square, triangle, circle C. Triangle, circle, square D. Triangle, square, circle The correct answer is: B Rationale: If a hole is shaped like a square, a circle can pass through it. But if the circle hole comes before the square, no other shape can pass through after the circle. You are given two ropes and a lightsource. You know one rope burns for exactly 30 minutes while the other burns for 45 minutes, but you don't know which is which. How can you use the ropes to measure exactly 15 minutes of time? A. Impossible with only those ropes B. Light one rope, when half remains light the other end C. Light both ends of both ropes simultaneously D. Light one rope, when half remains light the other rope The correct answer is: D Rationale: By lighting one full rope and then the other when half of the first has burned, the remaining ropes will all be burned out after 15 additional minutes. You are given an 8 gallon and a 5 gallon jug. Using only those containers, how can you measure out precisely 4 gallons of water? A. Fill the 8 gallon, then pour into the 5 gallon leaving 3 gallons B. Fill the 5 gallon twice C. Fill the 8 gallon, pour into 5 leaving 3, refill 8, then pour 4 from 8 into 5 D. Impossible with only those containers The correct answer is: C Rationale: By using the alternating fill and pour method, the 3 gallons remaining from the first transfer can be combined with 4 more from the 8 gallon jug into the 5 gallon, measuring exactly 4 gallons. I am the beginning of sorrow and the end of sickness. You cannot have one without me, though I may sometimes prove costly. What am I? A. Money B. The letter S C. Pain D. Debt The correct answer is: B Rationale: The letter S fits the riddle, as it begins "sorrow" and ends "sickness", and words cannot be spelled without it, though having too many S's is "costly". A horse is tied to a 20 foot rope and there is a bale of hay 26 feet from the hitching post. How can the horse can reach the bale of hay with the rope remaining tied? A. Stand closer to the hitching post B. The rope must be longer C. The rope is tied to something in the middle allowing it to swing out further D. This is impossible with that length rope The correct answer is: C Rationale: With just the rope tied at one end, the semi-circle radius is limited to 20 feet. But if the rope runs through a ring attached to something else, it can swing out further. A man is trapped in a room with no windows and only one door which is locked from the outside. The room initially has no lights but has a woodfire furnace and a ton of dry wood. In the middle of the room is a wooden table, two chairs, and a bookshelf filled with books. How could he get himself out? A. Use the fire to burn through the door B. Use the fire for smoke signals until rescued C. Use the fire for warmth until rescued D. Set the table and books on fire so smoke triggers sprinklers and opens the door The correct answer is: D Rationale: Burning the door would take too long. Using smoke for warmth or signals wouldn't free him. But creating enough smoke could potentially trigger a fire alarm or sprinklers and have the door opened from outside. Jim is negotiating with Tom and Harry about splitting $1500 three ways. Tom says he must get $800. Harry says he must get $500. Jim says this is impossible, how much does he want? A. $200 B. $500 C. $800 D. $1000 The correct answer is: A Rationale: If Tom gets $800 and Harry gets $500, that leaves only $200 remaining out of the original $1500 for Jim. A woman had two large pails, one holding twice as much as the other. In the larger pail, there were some gold rocks. When she transferred a third of the gold rocks from the larger pail to the smaller pail, the smaller pail became full. Originally, what fraction of the larger pail was filled by the gold rocks? A. 1/2 B. 1/3 C. 2/3 D. 3/4 The correct answer is: C Rationale: If 1/3 of the rocks filled the smaller pail which was 1/2 the size of the larger, that means the original rocks filled 2/3 of the larger pail. If 6 workers can build 6 buildings in 6 days, how many days would it take 8 workers to build 4 buildings? A. 2 days B. 3 days C. 4 days D. 6 days The correct answer is: B Rationale: With 6 workers building 1 building per day, 8 workers would build 4/3 as many per day. So 4 buildings at that rate would take 3 days. What single English word is represented by this pattern of letters: m////\rd? A. Upward B. Inward C. Onward D. Skyward The correct answer is: A Rationale: The slashes represent the letter V, so the word spelled out is m////\rd = upward. A person standing ankle-deep in a lake throws a rock into the center of the lake. The waves rippling outward from where the rock landed are confined to a circular area. How does the circumference of this circular area change as the waves get larger? A. It gets larger B. It stays the same C. It gets smaller D. It cannot be determined The correct answer is: B Rationale: While the radius increases, the circumference of any circle is simply 2πr, which remains constant as r grows. There are three houses in a row with three utilities - electricity, gas, and water. One utility goes under the yard to the middle house, and the other two go over the yards to the outside houses. If the three utility connections cannot cross each other above or below ground, what is the maximum number of utility connections that can be made? A. 2 B. 3 C. 4 D. 6 The correct answer is: C Rationale: One utility must go underground to the middle, leaving 2 to go overground to the outer houses without crossing paths.