**Analytical Reasoning – Introduction with Examples – Question with Answers and Explanations.**

# Introduction to Analytical Reasoning

Analytical reasoning refers to the ability to break down complex problems or situations into smaller components, identify patterns and relationships between them, and draw logical conclusions. It involves thinking critically, using deductive and inductive reasoning, and analyzing information to solve problems. Analytical reasoning is an essential skill in various domains, such as mathematics, science, business, and everyday life.

Here are a few examples to illustrate how analytical reasoning is used in daily life:

- Planning a trip: When planning a trip, you need to consider various factors such as transportation options, accommodation, budget, and activities. Analytical reasoning helps you break down these components, evaluate different options, and make logical decisions. For instance, you might analyze flight prices, compare hotel reviews, and consider the proximity of attractions to determine the best itinerary within your budget.
- Solving puzzles: Engaging in puzzles, riddles, or brain teasers requires analytical reasoning. For example, when solving a Sudoku puzzle, you analyze the existing numbers, identify missing numbers, consider the possibilities based on the rules of the game, and logically deduce the correct placements to complete the puzzle.
- Decision-making: Analytical reasoning is crucial when making important decisions. For instance, imagine you’re considering two job offers. You would analyze factors such as salary, benefits, work-life balance, career growth opportunities, and company culture. By weighing these factors and evaluating their relative importance, you can make a reasoned decision.
- Problem-solving: Analytical reasoning plays a significant role in problem-solving. Let’s say your computer is malfunctioning. You would analyze the symptoms, research potential causes, and systematically test different solutions to identify and resolve the issue. This process involves breaking down the problem, considering possible solutions, and using logical reasoning to arrive at the best course of action.
- Data analysis: In various fields, such as marketing, finance, or research, analytical reasoning is essential for interpreting and analyzing data. For instance, when analyzing sales data, you might identify patterns, correlations, or trends that can inform business strategies or decision-making.

Overall, analytical reasoning is a cognitive skill that allows individuals to deconstruct complex problems, evaluate information, and arrive at well-reasoned conclusions. It is a valuable tool for decision-making, problem-solving, and critical thinking in various aspects of daily life.

#### Basic analytical reasoning questions along with their answers and explanations:

- Question: There are five friends – Ahmad, Abu Bakar, Nauman, Daud, and Hussain. They have different ages. Ahmad is older than Abu Bakar but younger than Daud. Nauman is older than Hussain, but younger than Abu Bakar. Who is the youngest?

Answer: Nauman is the youngest. The age order from youngest to oldest is Nauman, Hussain, Abu Bakar, Ahmad, and Daud.

Explanation: We can deduce the age order by comparing the given information. Based on the clues, we know that Nauman is older than Hussain, but younger than Abu Bakar. Therefore, Nauman must be the youngest among the five friends.

- Question: In a group of students, 40% like math, 30% like science, and 20% like both subjects. What percentage of students do not like math or science?

Answer: 10% of students do not like math or science.

Explanation: To find the percentage of students who do not like math or science, we need to subtract the percentage of students who like both subjects (20%) from the total (100%). Thus, 100% – 20% = 80%. However, this includes students who like either math or science. Since the given percentages are overlapping, we subtract the sum of percentages who like math (40%) and science (30%) from 80%: 80% – 40% – 30% = 10%.

- Question: A company produced 500 products in the first month, and the production increased by 20% each subsequent month. How many products did they produce in the third month?

Answer: The company produced 660 products in the third month.

Explanation: To find the number of products produced in the third month, we need to calculate 20% of the production in the second month and add it to the second month’s production. In the first month, they produced 500 products. In the second month, the production increased by 20%, which is 500 * 0.20 = 100 products. Therefore, the production in the second month is 500 + 100 = 600 products. In the third month, the production increases by 20% again, which is 600 * 0.20 = 120 products. Thus, the production in the third month is 600 + 120 = 660 products.

- Question: A bookshop offers a 20% discount on all books. If a book initially costs Rs-50, what is the discounted price?

Answer: The discounted price of the book is Rs-40.

Explanation: To find the discounted price, we need to subtract 20% of the original price from the original price. 20% of Rs-50 is Rs-50 * 0.20 = Rs-10. Subtracting Rs-10 from Rs-50 gives us the discounted price of Rs-50 – Rs-10 = Rs-40.

- Question: There are three boxes labeled “Apples,” “Oranges,” and “Mixed.” Each box is labeled incorrectly. If you can only pick one fruit from one box to correct the labels, which box would you choose?

Answer: You would choose the box labeled “Mixed.”

Explanation: Since each box is labeled incorrectly, we can deduce that the box labeled “Mixed” cannot contain mixed fruits. If the box labeled “Mixed” contained mixed fruits, then the labels on all boxes would be incorrect. Therefore, by selecting fruit from the box labeled “Mixed” and finding the fruit type inside, we can correctly label all three boxes.

- Question: A car travels 240 miles in 4 hours. At the same speed, how far will it travel in 7 hours?

Answer: The car will travel 420 miles in 7 hours.

Explanation: To find the distance the car will travel in 7 hours, we can use the concept of speed. The car travels 240 miles in 4 hours, which means its speed is 240 miles / 4 hours = 60 miles per hour. If the car maintains the same speed for 7 hours, it will travel 60 miles/hour * 7 hours = 420 miles.

- Question: A square has an area of 49 square units. What is its perimeter?

Answer: The perimeter of the square is 28 units.

Explanation: The area of a square is calculated by squaring the length of one side. In this case, the area is given as 49 square units, so the length of one side is √49 = 7 units. Since all sides of a square are equal, the perimeter is 4 times the length of one side. Therefore, the perimeter is 4 * 7 = 28 units.

- Question: If 3 workers can complete a task in 10 days, how many days will it take for 5 workers to complete the same task?

Answer: It will take 6 days for 5 workers to complete the task.

Explanation: We can use the concept of worker-time equivalence to solve this problem. If 3 workers can complete the task in 10 days, then the total worker-days required is 3 workers * 10 days = 30 worker-days. Since the total worker days required remains the same, if we increase the number of workers to 5, the number of days needed to complete the task will decrease. Therefore, 30 worker-days / 5 workers = 6 days.

- Question: A train travels at a speed of 60 mph from point A to point B. It returns from point B to point A at a speed of 40 mph. What is the average speed for the round trip?

Answer: The average speed for the round trip is 48 mph.

Explanation: To find the average speed for the round trip, we can use the concept of harmonic mean. The harmonic mean of two speeds is calculated as the reciprocal of the arithmetic mean of the reciprocals of the speeds. In this case, the reciprocals of the speeds are 1/60 and 1/40. The arithmetic mean of these reciprocals is (1/60 + 1/40) / 2 = 1/48. Taking the reciprocal of 1/48 gives us an average speed of 48 mph.

- Question: In a class of 30 students, 20% are girls. How many boys are there in the class?

Answer: There are 24 boys in the class.

Explanation: If 20% of the students are girls, then the remaining 80% must be boys. To find the number of boys, we calculate 80% of the total number of students: 80% of 30 students = 0.80 * 30 = 24 students.

- Question: A bag contains 4 red marbles and 6 blue marbles. If you randomly select two marbles without replacement, what is the probability that both marbles are red?

Answer: The probability of selecting two red marbles is 2/15.

Explanation: The total number of marbles in the bag is 4 + 6 = 10. When the first marble is selected, there are 4 red marbles out of 10. After the first red marble is selected, there are 3 red marbles left out of 9. Therefore, the probability of selecting two red marbles is (4/10) * (3/9) = 2/15.

- Question: A store sells a shirt for Rs-20, which is a 25% profit on the cost price. What is the cost price of the shirt?

Answer: The cost price of the shirt is Rs-16.

Explanation: If the selling price is Rs-20 and it represents a 25% profit on the cost price, then the cost price can be calculated by dividing the selling price by 1 + the profit percentage. The profit percentage is 25%, so 1 + 0.25 = 1.25. Therefore, the cost price is Rs-20 / 1.25 = Rs-16.

- Question: John saves 20% of his monthly income. If he saves Rs-300, what is his monthly income?

Answer: His monthly income is Rs-1500.

Explanation: If John saves 20% of his monthly income, then the amount he saves represents 20% of his income. Let’s assume his monthly income is x. Therefore, 20% of x is equal to Rs-300. Mathematically, this can be expressed as 0.20 * x = Rs-300. Solving for x gives us x = Rs-1500.

- Question: A recipe requires 2 cups of flour to make 12 cookies. How many cups of flour are needed to make 30 cookies?

Answer: 5 cups of flour are needed to make 30 cookies.

Explanation: We can use the concept of proportionality to solve this problem. If 12 cookies require 2 cups of flour, then the ratio of cookies to flour is 12/2 = 6/1. This means that for every 6 cookies, we need 1 cup of flour. To find out how many cups of flour are needed for 30 cookies, we can set up a proportion: 6/1 = 30/x. Solving for x gives us x = 5. Therefore, 5 cups of flour are needed to make 30 cookies.

- Question: A swimming pool can be filled with three pipes in 6 hours. If all three pipes are opened simultaneously, how long will it take to fill the pool?

Answer: It will take 2 hours to fill the pool.

Explanation: If three pipes can fill the pool in 6 hours, then the combined rate at which they fill the pool is 1/6 of the pool per hour. This means that in one hour, the three pipes together can fill 1/6 of the pool. Therefore, to fill the entire pool, it will take 1 hour / (1/6) = 6/1 = 2 hours.

- Question: A recipe calls for 1/4 teaspoon of salt. If you want to make four times the amount of the recipe, how much salt will you need?

Answer: You will need 1 teaspoon of salt.

Explanation: If the original recipe calls for 1/4 teaspoon of salt and you want to make four times the amount, you need to multiply 1/4 by 4. Multiplying 1/4 by 4 gives us 1 teaspoon. Therefore, you will need 1 teaspoon of salt.

- Question: In a group of 50 people, 25 people speak English, 20 people speak French, and 10 people speak both languages. How many people speak at least one of these two languages?

Answer: 35 people speak at least one of the two languages.

Explanation: To find the number of people who speak at least one of the two languages, we need to add the number of people who speak English (25) and the number of people who speak French (20), and then subtract the number of people who speak both languages (10) to avoid double-counting. Therefore, 25 + 20 – 10 = 35 people speak at least one of the two languages.

- Question: A football team won 60% of their matches. If they played 25 matches, how many matches did they win?

Answer: They won 15 matches.

Explanation: If the team won 60% of their matches, then the number of matches they won is equal to 60% of the total number of matches played. Mathematically, this can be expressed as 60% of 25 matches = 0.60 * 25 = 15 matches.

- Question: A box contains 5 red balls, 3 blue balls, and 2 green balls. If one ball is randomly drawn from the box, what is the probability that it is blue or green?

Answer: The probability of drawing a blue or green ball is 50%.

Explanation: The total number of balls in the box is 5 + 3 + 2 = 10. The number of blue or green balls is 3 + 2 = 5. Therefore, the probability of drawing a blue or green ball is 5/10 = 50%.

- Question: A car rental agency charges Rs-30 per day for renting a car and an additional Rs-0.20 per mile driven. If a customer rents a car for 5 days and drives 100 miles, how much will the customer be charged?

Answer: The customer will be charged Rs-130.

Explanation: The daily rental cost is Rs-30, and the mileage cost is Rs-0.20 per mile. For 5 days, the rental cost is Rs-30 * 5 = Rs-150. The mileage cost for 100 miles is Rs-0.20 * 100 = Rs-20. Adding the rental cost and mileage cost together gives us a total charge of Rs-150 + Rs-20 = Rs-170. Therefore, the customer will be charged Rs-170.

Analytical Reasoning – Introduction with Examples.Analytical Reasoning – Introduction with Examples.Analytical Reasoning – Introduction with Examples.Analytical Reasoning – Introduction with Examples.Analytical Reasoning – Introduction with Examples

By: NOTESPK