Logical Reasoning

Logical Reasoning

WHAT IS IT?

Logical reasoning is universal and it is used just about every time a person makes a logical decision. It comes up in school, at work, and even in normal life. Once you master the art of solving logical reasoning questions, then you can apply logical reasoning to your arguments and sway people to agree with you.

Logical reasoning is the process of using a rational series of steps based on mathematical procedures, and given statements to arrive at a conclusion. It is generally a crucial section in aptitude and IQ tests. Having better developed logical reasoning skills make you able to understand, analyze, and question arguments based on statements or questions. These skills can be used to make an argument stronger or weaker.

Logical reasoning questions come in various formats including number series, verbal reasoning, analogies, and logical problems. I will offer a general approach to each problem type, which might be a step by step analysis, or a drawing. Some techniques may be more helpful to some than others. Test different approaches to see what works best for you.

Basic logical reasoning questions involving number series:

General Approach: First look at the numbers, do they increase or decrease? Then, if they do change, then by how much? For example, if the question asks what the next number in the series is and begins “2, 4, 6, 8, 10…,” then I would see that the numbers are increasing by 2 each time. So, I would add 2 to the last number and the correct answer would be 12.

1. 4, 2, 1, ½, ¼…what should be the next number in the series?

• ⅓
• ⅛
• 1/14
• 1/12

The pattern is being cut in half, so the next number in the series after ¼ should be ⅛.

2. 7, 10, 8, 11, 9, 12…what should be the next number in the series?

• 6
• 8
• 10
• 13

The pattern is increasing by 3, then decreasing by 2, so the next number in the series after 12 should be 10.

3. 8, 16, 12, 24, 20, 40, 36… what should be the next number in the series?

• 8
• 54
• 60
• 72

The pattern is doubling and then decreasing by 4, so the next number in the series after 36 should be 72.

Basic logical reasoning questions involving verbal reasoning:

General Approach: You must assume each statement to be true and reason through the problem, step by step. Do not infer anything that is not supported factually. Sometimes the answer may be obvious because it is logic that you naturally go through.

4. Evan is 11 years old. For 2 years, he has been asking his parents for a puppy. His parents have told him that the believe a dog would not be happy in an apartment, but they have given him permission to have a bird. Evan has not yet decided what kind of bird he would like to have.

• Evan’s parents like birds better than they like dogs
• Evan does not like birds
• Evan and his parents live in an apartment
• Evan and his parents would like to move

Since Evan’s parents believe that a dog would not be happy in an apartment, we can reasonably conclude that the family lives in an apartment. We do not know how Evan’s parents feel about birds or how Evan feels about birds.

5. Jennifer is older than her cousin Maria. Maria’s brother Ben is older than Jennifer. When Maria and Ben are visiting with Jennifer, all three like to play Monopoly. Maria wins more often than Jennifer does.

• When Bart plays Monopoly with Maria and Jennifer, he often loses.
• Of the three, Jennifer is the oldest.
• Jennifer hates to lose at Monopoly.
• Of the three, Maria is the youngest.

Since we know that Ben is older than Jennifer and Jennifer is older than Maria, Maria must be the youngest of the three. We know nothing about how often Ben wins or loses and we do not know whether Jennifer hates losing or not.

Analogies:

General Approach: If you can create a statement that explains the relationship between the first two objects, you can apply the same general idea to the third object and the answer. For example, “if it says apple is to fruit as broccoli is to,” then your statement might be that an apple is a type of fruit and broccoli is a type of vegetable. The correct answer would be vegetable.

6. Odometer is to mileage as compass is to

• direction
• speed
• needle
• sailing

The correct answer is direction. Odometer is an instrument that measures mileage. A compass is an instrument that determines direction.

7. Marathon is to race as hibernation is to

• nap
• winter
• sleep
• bear

The correct answer is sleep. A marathon is a long type of race. Hibernation is a long period of sleep.

8. Window is to pane as book is to

• glass
• cover
• novel
• page

The correct answer is page. A window is made up of one or more panes. A book is made up of one or more pages.

9. Optimist is to cheerful as pessimist is to

• gloomy
• petty
• mean
• helpful

The correct answer is gloomy. Optimistic people tend to be cheerful and see the positive side to things, whereas pessimistic people tend to be gloomy and see the negative side. While pessimists might be mean, that word does not have the same relation to pessimists as cheerful does to optimists.

10. Embarrassed is to humiliated as frightened is to

• courageous
• terrified
• agitated
• angry

The correct answer is terrified. A person is humiliated when he or she has been extremely embarrassed. A person is terrified when he or she has been extremely frightened.

Logical problems:

General Approach: Each problem consists of 3 statements. Based on the first two statements, you must determine if the third statement is true, false, or uncertain. These problems can generally be drawn out in one way or another to show how the items in each statement are interrelated. For example, if it says that “1. Abe is faster than Bill. 2.Cate is faster than Abe. 3. Cate is faster than Bill.” The correct answer would be that #3 is true. If you use X > Y to represent who is faster, then A > B and C > A, so C > A > B.

11. Tim is older than Elena.

Curtis is older than Tim.

Elena is older than Curtis.

If the first two statements are true, the third statement is

• True
• False
• Uncertain

The correct answer is that the third statement is false. If T > E and C > T, then C > T > E. Elena is the youngest of the three, so the statement is false.

12. Apartments in the Runnyvale Manor cost less than apartments in The Grapevine Commons.

Apartments in the Livingwell Gate cost more than apartments in the The Grapevine Commons.

Of the three apartment buildings, the Livingwell Gate costs the most.

If the first two statements are true, the third statement is

• True
• False
• Uncertain

The correct answer is that the third statement is true. If GC > RM and LG > GC, then           LG > GC > RM. Livingwell Gate is the most expensive apartment complex.

13. During the past year, Josh saw more movies than Stephen.

Stephen saw fewer movies than Darren.

Darren saw more movies than Josh.

If the first two statements are true, the third statement is

• True
• False
• Uncertain

The correct answer is that the third statement is uncertain. If J > S and D > S, then both J and D saw more movies than S and there are no facts to say who saw the most.

Independent Task:

WALT - Solve a problem by using logical reasoning.

GOT it Resource - Problem Sheet 8