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Deductive Reasoning I

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Deductive reasoning is the process of making specific conclusions from contextualized information. This can be with numbers, patterns, scientific data, human behavior, or just everyday information. It is a common form of reasoning and is hence used in many jobs that require some form of problem-solving.

Introduction



Deductive reasoning is the process of making specific conclusions from contextualized information. This can be with numbers, patterns, scientific data, human behavior, or just everyday information. It is a common form of reasoning and is hence used in many jobs that require some form of problem-solving. To list a handful of jobs where deductive reasoning is important:





Not all of these jobs will require a dedicated deductive reasoning test to get hired, but you’ll more than likely encounter one during the program--or as a requirement for enrolling in the program. For instance, the TEAS-test for nursing programs has a scientific reasoning portion, as does the MCAT for medical school. The ACT for general college admission has a scientific reasoning portion as well, so you’ll likely encounter this no matter your field of study if you are enrolling in a University.

General deductive reasoning is your ability to make conclusions from generalized information that doesn’t require any content knowledge. Scientific reasoning is deductive reasoning in a specific area of science. This guide will orient you with general deductive reasoning strategies and will serve as an excellent beginner’s guide if you are pursuing further in this direction.



Number Patterns



These display a series of numbers and require you to deduce the pattern and then repeat it. Let’s jump right in: what is the next number in this series?

4, 5, 9, 14, 23, _______

Solution (spoiler): This pattern starts by adding 1 to the first number, then adding the previous number to result in the next number. 4 + 1 = 5, 5 + 4 = 9, 9+5 = 14 so on and so forth. This can be a tricky pattern to pick up on.

Let’s look at another example. What is the next number in this series?

32, 16, 28, 14, 26, _______

Solution (spoiler): This pattern starts decreases by 16, then increases by 12, decreases by 14, then increases by another 12. The clues here are that the increase by 12 is consistent, while the decreasing number varies. But the decreasing pattern varies.

Let’s isolate the points we want to deduce.

32 - 16 = 16 is the first decrease

28 - 14 = 14 is the second decrease

The number decreases by half! This will make the next step the series decrease by 13.

If ever you get stuck on a number pattern, write out the increase/decrease between each step of the pattern. This will give you an additional angle on the pattern and often leads you to the solution.



Spatial Patterns



These are the same type of questions as number patterns except they use shapes instead of numbers. This utilizes a different part of the brain. Some people are more inclined towards numbers and others towards shapes. It’s useful to know which areas you are strong or weak in.

What will the next object look like in this pattern?

Solution (spoiler):

1st Step: This pattern begins with both blocks moving in opposite directions. One block moves clockwise while the other moves counterclockwise.

2nd Step: This follows the same pattern as the first step. Both blocks end at the top-right corner.

3rd Step: With both blocks in the top-right corner, one block will move clockwise while the other block moves counterclockwise. We’ll end with one block in the middle column of the top row, with the other block being in the middle row of the right column.

What object will come next in this pattern?

Solution (spoiler):The pattern starts with two circles: 1 red and 1 blue. In each step, there is a shape added and the colors of the circles change. Since there are two components that change, that means there will be two patterns we must identify:

1st Step: Instead of a full circle being added to the top, a half-circle was added. We now have enough information to deduce the patterns. In each step, the amount of circle that is added is half of the previous step, and it is the color red. Additionally, each step involves a color rotation of each existing circle: Blue circles become green, green circles become red and red circles become blue.

2nd Step: Following the pattern, green circles will become red, red circles will become blue, and blue circles will become green. Additionally, there will be a quarter circle added to the top of the object.

Note: the orientation of the quarter circle is not specified in the pattern. Drawing it with a different orientation is not incorrect.



Logic statements



Logic statements present you with several sentences that you must piece together to make a logical conclusion.



  1. All squares are rectangles
  2. Some 4-sided shapes are squares
  3. Some 4-sided shapes are rectangles



What do we have enough information to deduce?

A) All rectangles are squares

B) Some rectangles are squares

C) All 4-sided shapes are rectangles or squares

D) A rectangle can have more than four sides.

Solution (spoiler): B

We can’t deduce choice A. Just because a square is a rectangle does not mean that a rectangle is a square.

We also can’t deduce choice C. Some 4-sided shapes are neither a rectangle nor a square, such as trapezoids, diamonds, and parallelograms. Finally, option D is also incorrect. It is an untrue statement and there is no information in the passage to suggest that D is correct.

Therefore, choice B “some rectangles are squares” is true. We can deduce this from statement 1.

This is an example of narrow categories fitting into broad categories. Another example is “all basketball players are athletes, but not all athletes are basketball players. You’ll generally encounter this at least once in a deductive reasoning test. Logic statements depend on your verbal reasoning. They may be a struggle if you don’t normally practice them, but you’ll rapidly build comfort and familiarity with them the more you practice.



Evaluation



The previous types of questions we’ve covered have pretty specific formats. Very often you will have general reasoning questions. These require analysis of the question (quantitative or qualitative) and then an evaluation of the most logical answer.

Every year, the money in a bank account doubles. Which of the following statements will be true?

a) There will be 10x as much money in five years from now as there will be two years from now

b) There will be 16x as much money in eight years from now as there will be four years from now

c) There will be 8x as much money in five years from now as there will be three years from now

d) There will be 32x as much money in ten years from now as there will be six years from now.

Solution (spoiler): B

A good strategy is to eliminate the choices one at a time until you’ve found the correct answer.

Choic​​e A: In year 5, there will be 8x as much money as there was in year 2. Choice A is incorrect.

Choice B: In year 8, there will be 16x as much money as there was in year 4. Choice B is correct!



Conclusion



There are many types of deductive reasoning questions that you can practice. Practicing these types of questions will cause you to improve your deductive reasoning over time. In addition to practicing these questions, one of the best ways to improve your deductive reasoning in general is to perform inquiries in real life. Whether it’s at your job, at school or at home, asking questions and looking for the answer (and not just googling it) will make you a better problem solver and deductive thinker.

Practice Multiple Tests

Logical Reasoning Deductive Reasoning