MockQuestions

Logic Reasoning Test I

20 Questions Created By

Many companies, including Apple, Volkswagen, and Pfizer, apply Aptitude Tests to help identify interview candidates with the strongest numerical, verbal, perceptual, and spatial abilities.

How to Prepare For a Logic-Based Aptitude Test

What is logic?

Logic is a system of evaluation (not truth) that assesses relationships and connections between categories.

Why is logic valuable?

Logic allows us to test arguments to determine if they logically follow or not. Arguments can be very convincing but logically flawed.

Example 1

  1. All banks are financial institutions
  2. Wells Fargo is a bank
  3. Therefore, Wells Fargo is a financial institution

This argument has a proper logic form, so the conclusion necessarily follows.

Here is the form:

  1. All A are B
  2. Wells Fargo is an A
  3. Therefore, Wells Fargo is a B

Here is a diagram to help show the relationship between statements 1 and 2.

Example 2

  1. All banks are financial institutions
  2. Wells Fargo is a financial institution
  3. Therefore, Wells Fargo is a bank

This argument looks correct, but it has an invalid logical form, so the conclusion does not necessarily follow.

Here is the form:

  1. All A are B
  2. Wells Fargo is an A
  3. Therefore, Wells Fargo is a B

Here is a diagram to help show the relationship between statements 1 and 2.

This form will always produce a logically unsound conclusion, no matter what you plug in for A, B, and Wells Fargo. It can be true or false, this doesn’t matter.

This form will always produce a logically unsound conclusion, no matter what you plug in for A, B, and Wells Fargo. It can be true or false, this doesn’t matter.

Example 2

  1. All banks are financial institutions
  2. Wells Fargo is a financial institution
  3. Therefore, Wells Fargo is a bank

This argument looks correct, but it has an invalid logical form, so the conclusion does not necessarily follow.

Here is the form:

  1. All A are B
  2. Wells Fargo is an A
  3. Therefore, Wells Fargo is a B

Here is a diagram to help show the relationship between statements 1 and 2.

This form will always produce a logically unsound conclusion, no matter what you plug in for A, B, and Wells Fargo. It can be true or false, this doesn’t matter.

Does it have to be true to be logical?

For example, let’s substitute false sentences and see if conclusion still necessarily follows

  1. All Aliens are from Mars
  2. Bethany is an alien
  3. Therefore, Bethany is from Mars

That conclusion still follows from Statement 1 and Statement 2! The argument is ‘valid’, which means it passes the structure test. We don’t need to worry if each statement is factually true!

How does this relate to Aptitude Tests?

Aptitude exams are not testing your factual knowledge or truth-claims. Aptitude tests are designed to test your logical thinking, spatial knowledge, verbal comprehension and categorizing, and numerical skills.

Preparing for Aptitude Test requires learning specific skills and practicing them a lot.

Logical Statements

There are two types of Logical Reasoning Methods:

  1. Deductive Reasoning
    • Step-by-step proof with no room for error. Conclusion always follows
      • E.g., 5x +2 = 12 (we can determine that x=2 always)
      • E.g., Adam is taller than Bethany. Bethany is taller than Chris. Therefore, Adam is taller than Chris
  2. Inductive Reasoning
    • Probability based reasoning with some room for error. Conclusion most likely follows.
      • E.g., Adam always shows up to work on time, so he will show up tomorrow on time.
      • It has rained every Halloween, so it will likely rain this year too.

The Main Difference?

  1. Deductive arguments are stronger because they are air-tight (i.e., the conclusion always follows)
  2. Inductive arguments are at best 99.9% true (i.e., the conclusion most likely follows).

How does this relate to Aptitude Tests?

Aptitude tests target your numerical skills requiring deductive logic skills.

E.g., Find the next number in the sequence.

25 15 21 11 17 ____?

Deduction requires finding the relation between each number sequence! Logical deduction between first three number sequence should reveal the logical pattern. (Did you say 7?)

‘All’, ‘No’, and ‘Some’ Statements

All Deductive Arguments are made up of one of FOUR STATEMENTS

  1. All A are B (All Banks are Financial Institutions)
  2. No A are B (No Cats are Dogs)
  3. Some A are B (Some Americans are Dentists)
  4. Some A are not B (Some Americans are not Dentists)

Those are the only 4 kinds of statements we can ever make. Imagine you invite 10 people to your housewarming party. Here are all the options for saying who showed up!

  1. All invitees showed up (10/10)
  2. No invitees showed Up (0/10)
  3. Some invitees showed up (at least 1/10)
  4. Some invitees did not show up (at least 1/10)

There is no 5th or 6th option!

How does this relate to Aptitude Tests?

E.g., What necessarily follows from the following reported statements

All workers are required to sign new contracts. Some workers are getting ready to retire.

Answer

If all the workers (A) are required to sign a new contract (B) AND If some workers (A) are getting ready to retire (C), THEN Some who are getting ready to retire are not signing a new contract (the answer is D)

If-Then Statements

The most common statements are ‘conditional’ statements (If-Then).

If ________, then __________.

The term after ‘if’ is the antecedent.

The term after ‘then’ is the consequent.

We use conditional statements everyday, multiple times a day. We live in a world of conditional statements!

How does this relate to the Aptitude Test?

Conditionals are important because they lead to logical implications that are rarely stated.

Conditional: If Adam arrives first, then Bethany arrives seventh.

Fact: Bethany arrives sixth.

Conclusion: ??????????



Answer: Adam does not arrive first. But why?!?

Because it doesn’t logically follow? But still, WHY?!?

Let’s look at the form next!

Logical Implications: Most Common Error of Reasoning!

The most common tool used on Aptitude Tests is logical implications (i.e., what follows)

Most common logical error?

  1. If they liked me in the interview, then they will call me back.
  2. They called me back!
  3. Therefore, they liked me in the interview.

This is logically unsound

Why? It has a logically bad form.

  1. If A, then B
  2. B
  3. Therefore, A

Try plugging in a basic example and see if it follows.

If I have a dog, then I have an animal.

I have an animal.

Therefore, I have a dog.

If all you knew was that I had an animal at home, can you conclusively determine that I must have a dog at home? NO!

But if you knew I had a dog at home, can you conclusively determine that I have an animal at home? YES!

That is because it matters which of my conditions I satisfy!

I have an animal.

The same logic applies to the interview-call example! If all you knew was that they called me back, can you conclusively determine that they liked you in the interview? NO! Maybe they called to tell you that you forgot your thermus in the interview room or they called you by accident!

Logic matters! Aptitude tests want to make sure you can REASON PROPERLY.

Three Important Implication Rules

There are three central rules of implication we use all the time.

  1. Modus Ponens (Latin for ‘affirming’)

    If A, then B

    A

    Therefore, B


  2. Modus Tolens (Latin for ‘rejecting’)

    If A, then B

    Not-B

    Therefore, Not-A


  3. Disjunctive Implication

    A or B

    Not-A

    Therefore, B


Notice: The second premise is “I will not apply”, therefore “I will wait”. Some make the common following error:

That is always incorrect. It is possible to do both. However, if you don’t do one, then you MUST do the other!

Think about it. Imagine you are at a Starbucks and order a coffee. The Barista asks “would you like sugar OR cream?” and you say ‘Either/Or is fine”. If the Barista served you a coffee with just sugar, you can’t complain. If the barista served you a coffee with just cream, you can’t complain. If the barista served you a coffee with sugar AND cream, you can’t complain. Only if the barista serves you a coffee with neither sugar nor cream, can you complain!

How does this relate to Aptitude Tests?

Aptitude Tests target skills in drawing proper inferences/implications from given statements. Can I Convert the FOUR STATEMENTS into Conditionals-Statements?

All statements can be transformed into a conditional (If you are a statement, then you can be transformed into a conditional!)

Here are some examples:

  1. Humans are vulnerable creatures = If you are a human, then you are vulnerable
  2. No interviewees are ever late = If you are an interview, then you are never late.
  3. Whatever you do, I support you = If you do whatever, then I will support you
  4. Last person leaving turns lights off = If you are last person leaving, then you must turn off the lights
  5. Either you love me, or I am leaving = If you don’t love me, then I am leaving
  6. No ticket, no entry = If you do not have a ticket, then you may not Enter
  7. The government is responsible = If you are the government, then you are responsible
  8. Whenever I am happy, I laugh = If I am happy, then I am laughing
  9. Whoever says that is a liar = If you say that, then you are a liar
  10. We either leave today or tomorrow = If I leave today, then I do not leave tomorrow (or: If I leave tomorrow, then I do not leave today)

How does this relate to Aptitude Tests?

The better you can turn statements into conditions, the easier you will be able to work through the logic! (If you can turn statements into conditions, then the easier it will get!)