Logical Reasoning: Practice Questions & Worked Solutions

Which one of the five makes the best comparison? LIVE is to EVIL as 5232 is to:

Eddie received both the 15th highest and the 15th lowest mark in the class. How many students are in the class?

Three messages were intercepted at communications headquarters. The code was broken and it was found that "Berok tenlis krux" means "secret attack Wednesday" and "Baroom zax tenlis" means "secret plans included" and "Gradnor berok plil elan" means "Wednesday victory is ours". What does "krux" mean?

Some postcards are polar bears, and some washing machines sneeze a lot; also hedgehogs speak Chinese, and all that speak Chinese sneeze a lot. But no polar bears sneeze a lot. Some washing machines speak Chinese and all postcards are washing machines. Therefore some postcards speak Chinese.

Suppose you have 40 blue socks and 40 white socks in a drawer. If you reach into the drawer without looking at the socks, what is the smallest amount of socks you must take out to make sure that you have a pair of socks of the same colour?

You are in a prison, you like to smoke. You have 10 used pieces of cigarettes. From 3 used pieces, you can make one cigarette and smoke it. (after smoking you get a used cigarette again). How many cigarettes can you smoke?

Three suspects: A, B, and C are questioned about a theft.
A says, 'I didn't do it.'
B says, 'A is lying.'
C says, 'B is lying.'
If only one of them is telling the truth, who committed the theft?

A box contains three coins: one with two heads, one with two tails, and one fair coin (one head and one tail). You randomly select a coin and flip it. The result is heads. What is the probability that the coin you selected is the one with two heads?

In a room of 100 people, 90% are truthful and 10% always lie. You ask a random person, 'Is the person next to you truthful?' What is the probability that the person next to them is truthful if the answer is 'Yes'?

You are given four cards. Each card has a number on one side and a letter on the other. The cards show:
A, 7, D, and 4.
Which cards must you flip to verify the rule 'If a card has a vowel on one side, it has an even number on the other side'?

A politician claims: 'If I am elected, taxes will not increase.' Taxes increased after the election. What can you conclude?

If all cats are mammals and some mammals are not carnivores, which of the following must be true?

If it rains, the ground will be wet. The ground is not wet. What can you conclude?

All squares are rectangles. Some rectangles are not parallelograms. Which of the following must be true?

If no humans are immortal and some mortals are humans, what follows logically?

A train always arrives on time if the weather is clear. The weather is not clear. What can you infer?

A scientist states:
'If a certain chemical is added to water, the solution will turn blue only if the water is acidic.'
The solution did not turn blue. What can you conclude?

In a town, 70% of people own cars, 40% own bicycles, and 20% own both. What percentage of people own either a car or a bicycle but not both?

A detective investigates three suspects: A, B, and C.
The detective knows that exactly one of them is guilty and that the guilty person always lies.
A says, 'I am not guilty.'
B says, 'A is guilty.'
C says, 'B is lying.'
Who is guilty?

You have four switches, each controlling one of four lightbulbs. Exactly one switch is faulty, and it always flips the opposite state of the lightbulb it controls. How many switches must you test to guarantee finding the faulty one?

In a sequence of numbers, each term is the sum of the previous two terms. The 6th term is 13, and the 7th term is 21. What is the 9th term?

You are given three jars labeled incorrectly:
1. Apples
2. Oranges
3.Apples & Oranges.

You can pick one fruit from one jar to determine all correct labels. Which jar should you pick from?

A company has 100 employees. 60% of them work in engineering, and 40% of them work remotely. If 20% of all employees work remotely in engineering, how many employees work on-site in non-engineering roles?

You have a scale and 8 identical-looking coins. One coin is counterfeit and weighs less. How many weighings are needed to guarantee finding the counterfeit?

A detective is investigating a murder. There are three suspects: Alice, Bob, and Carol. The following statements are made
Alice says, 'Bob did it.'
Bob says, 'Carol did it.'
Carol says, 'Bob is lying.'
If only one of them is telling the truth, who committed the murder?

In a town, everyone either always tells the truth or always lies. You meet three people: A, B, and C. A says, 'I am truthful.' B says, 'A is lying.' C says, 'B is lying.' Who is truthful?

You have three switches in one room that control three light bulbs in another room. You cannot see the light bulbs from the switch room. How can you determine which switch controls which bulb if you can only enter the bulb room once?

A family of five needs to cross a river. They have one boat that can hold up to two people. The father cannot be left with any of the daughters unless the mother is present. The mother cannot be left with any of the sons unless the father is present. How can they all cross?

A clock shows 3:15. What is the angle between the hour hand and the minute hand?

A prisoner must choose between three doors. Behind one door is freedom, and behind the other two are tigers. After the prisoner chooses a door, the warden opens one of the other two doors to reveal a tiger. The prisoner is then given the option to switch doors. What should the prisoner do?

A researcher claims:
'If a plant receives sunlight, it will grow.'
In an experiment, some plants that received sunlight did not grow. What can be concluded?

A group of students takes a logic test. If a student answers Question 1 correctly, they will also answer Question 2 correctly. If Student A answered Question 2 incorrectly, what can be concluded?

You are told that
'All software engineers know Python.'
You meet a person who does not know Python. What can you conclude?

A company policy states:
'If an employee works overtime, they will receive extra pay.'
An employee received extra pay but did not work overtime. What can you conclude?

In a tournament, every player either wins or loses each match. If Player A wins against Player B and Player B wins against Player C, what can be concluded about Player A and Player C?

You are told,
'Either Alice or Bob (but not both) will attend the meeting.'
Later, you see both Alice and Bob at the meeting. What can you conclude?

You have two ropes. Each rope has the property that if you light one end, it takes exactly 60 minutes to burn completely. However, the ropes do not burn at a uniform rate. For example, half the rope may burn in 1 minute and the rest in 59 minutes. How can you measure exactly 45 minutes using these two ropes?

In a town, there are 100 people. 60 people are left-handed, 50 people are right-handed, and 40 people are ambidextrous. What is the minimum number of people who must be both left-handed and ambidextrous?

A person is asked to choose one of five doors numbered 1 through 5. If the person picks the first door, they must then choose the second door. If they choose the second, they must choose the third, and so on. If the person chooses the fifth door, they go back to the first door. If the person is told that they will not be choosing the fifth door, what is the probability that they will choose door 3?

You are on a bridge with a torch and 3 other people. The torch can only light the way for 1 person at a time. The 4 people have different walking speeds: 1 minute, 2 minutes, 5 minutes, and 10 minutes. If two people cross together, they must go at the slower person's pace. What is the fastest time in which all 4 people can cross the bridge?

A prisoner is locked in a room with two doors. One door leads to certain death, the other leads to freedom. There are two guards, one who always tells the truth and one who always lies. The prisoner can ask one question to determine which door leads to freedom. What is the question they should ask?

A box contains 10 red balls, 10 blue balls, and 10 green balls. You are blindfolded and randomly select 3 balls. What is the probability that at least 2 of the balls are the same color?

You have a 10x10 grid of squares, some of which are black and some are white. You are told that every white square is adjacent to exactly 2 black squares. What is the maximum number of white squares that can be in this grid?

You are given a 5x5 grid. Some squares are marked with 'X' and some are empty. You are told that no two 'X's are adjacent to each other, either horizontally, vertically, or diagonally. What is the maximum number of 'X's that can be placed in the grid?

This sequence of four words, "triangle, glove, clock, bicycle," corresponds to this sequence of numbers "3, 5, 12, 2."

Sixteen hours are to one day as twenty days are to June's length

If the word, "TAN," is written under the word, "SLY," and the word, "TOT," is written under "TAN," then the word, "SAT," is formed diagonally.

If Monday is the first day of the month, the very next Saturday is the fifth day of the month.

Frank is taller than John. Ralph is taller than Frank. Therefore, John is the shortest boy.

If a doughnut shaped house has two doors to the outside and three doors to the inner courtyard, then it's possible to end up back at your starting place by walking through all five doors of the house without ever walking through the same door twice.