Q. A sequence of numbers is in arithmetic progression. If the first term is 8 and the last term is 32, and there are 6 terms, what is the common difference?
A.
4
B.
5
C.
6
D.
3
Solution
Using the formula for the last term: a + (n-1)d = last term, we have 8 + 5d = 32. Solving gives d = 4.
Q. A shopkeeper sells a shirt for $30 after giving a discount of 20%. What was the original price of the shirt?
A.
$36
B.
$40
C.
$42
D.
$45
Solution
Let the original price be x. After a 20% discount, the selling price is 80% of x. Thus, 0.8x = 30. Solving for x gives x = 30/0.8 = 37.5. Therefore, the original price is $36.
Q. A shopkeeper sells a shirt for $30 after giving a discount of 25%. What was the original price of the shirt?
A.
$40
B.
$35
C.
$45
D.
$50
Solution
Let the original price be x. After a 25% discount, the selling price is x - 0.25x = 0.75x. Setting this equal to $30 gives 0.75x = 30, so x = 30/0.75 = $40.
Q. A shopkeeper sells a shirt for $30, making a profit of 20%. What was the cost price of the shirt?
A.
$25
B.
$20
C.
$24
D.
$22
Solution
Let the cost price be x. The selling price is given by x + 0.2x = 1.2x. Setting this equal to $30 gives us 1.2x = 30, so x = 30/1.2 = 25. Thus, the cost price of the shirt is $25.
Q. A shopkeeper sells a shirt for $30, which is a 20% profit on the cost price. What is the cost price of the shirt?
A.
$24
B.
$25
C.
$26
D.
$27
Solution
Let the cost price be x. The selling price is 30, which is 120% of the cost price. Therefore, 1.2x = 30. Solving for x gives x = 30/1.2 = 25. Thus, the cost price is $25.
Q. A solution contains 20% sugar. If 5 liters of this solution is diluted with 10 liters of water, what is the new percentage of sugar in the solution?
A.
10%
B.
15%
C.
20%
D.
25%
Solution
Initial sugar = 20% of 5 liters = 1 liter. Total volume after dilution = 5 + 10 = 15 liters. New percentage = (1/15) * 100 = 6.67%.
Q. A solution contains 25% sugar. If 10 liters of water is added to 30 liters of this solution, what is the new concentration of sugar in the solution?
A.
15%
B.
20%
C.
25%
D.
30%
Solution
Initial sugar = 0.25 * 30 = 7.5 liters. New total volume = 30 + 10 = 40 liters. New concentration = (7.5/40) * 100 = 18.75%.
Q. A solution contains 25% sugar. If 8 liters of this solution is diluted with 4 liters of water, what is the new concentration of sugar in the solution?
Q. A solution is made by mixing 3 parts of solution A and 5 parts of solution B. If solution A contains 20% salt and solution B contains 10% salt, what is the percentage of salt in the final mixture?
Q. A solution is made by mixing 4 liters of a 20% acid solution with 6 liters of a 30% acid solution. What is the concentration of acid in the final mixture?
Q. A solution is made by mixing 5 liters of a 10% acid solution with 15 liters of a 20% acid solution. What is the concentration of acid in the final mixture?
Q. A store increases the price of an item by 25% and then offers a discount of 20% on the new price. What is the final price if the original price was $80?
A.
$70
B.
$75
C.
$80
D.
$85
Solution
New price after increase = 80 * 1.25 = $100. Discount = 20% of 100 = $20. Final price = 100 - 20 = $80.
Q. A store offers a 10% discount on a product that costs $200. If the store then applies an additional 5% discount on the already discounted price, what is the final selling price?
A.
$180
B.
$190
C.
$185
D.
$175
Solution
First discount: 200 - 10% of 200 = 200 - 20 = 180. Second discount: 180 - 5% of 180 = 180 - 9 = 171.
Quantitative Aptitude is a crucial component of various competitive exams, including the CAT. Mastering this subject not only enhances your mathematical skills but also boosts your confidence during exams. Practicing MCQs and objective questions is essential for effective exam preparation, as it helps identify important questions and strengthens your grasp of key concepts.
What You Will Practise Here
Number Systems and Properties
Percentage, Profit and Loss
Ratio and Proportion
Time, Speed, and Distance
Averages and Mixtures
Algebraic Expressions and Equations
Data Interpretation and Analysis
Exam Relevance
Quantitative Aptitude is a significant topic in various examinations, including CBSE, State Boards, NEET, and JEE. In these exams, you can expect questions that test your understanding of basic concepts, application of formulas, and problem-solving skills. Common question patterns include multiple-choice questions that require quick calculations and logical reasoning.
Common Mistakes Students Make
Misunderstanding the question requirements, leading to incorrect answers.
Overlooking units of measurement in word problems.
Not applying the correct formulas for different types of problems.
Rushing through calculations, resulting in simple arithmetic errors.
Failing to interpret data correctly in graphs and tables.
FAQs
Question: What are the best ways to prepare for Quantitative Aptitude in exams? Answer: Regular practice with MCQs, understanding key concepts, and reviewing mistakes can significantly improve your performance.
Question: How can I improve my speed in solving Quantitative Aptitude questions? Answer: Practice timed quizzes and focus on shortcuts and tricks to solve problems quickly.
Start solving practice MCQs today to test your understanding of Quantitative Aptitude and enhance your exam readiness. Remember, consistent practice is the key to success!
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