Q. If the HCF of two numbers is 5 and their LCM is 100, what is the sum of the two numbers? (2023)
A.
30
B.
25
C.
50
D.
45
Solution
Let the two numbers be 5x and 5y. Then, HCF(5x, 5y) = 5 and LCM(5x, 5y) = 100. This gives xy = 20. The pairs (x, y) that satisfy this are (4, 5) or (5, 4), leading to the sum 5(4 + 5) = 45.
Q. If the LCM of two numbers is 60 and their HCF is 5, what is the sum of the two numbers if they are both less than 30? (2023)
A.
25
B.
35
C.
40
D.
30
Solution
Let the two numbers be 5a and 5b. Then, LCM(5a, 5b) = 5 * LCM(a, b) = 60, which gives LCM(a, b) = 12. The pairs (3, 4) work, giving numbers 15 and 20, which sum to 35.
Q. If the least common multiple (LCM) of two numbers is 36 and their greatest common divisor (GCD) is 6, what can be inferred about the product of the two numbers?
A.
It is 216.
B.
It is 72.
C.
It is 36.
D.
It is 6.
Solution
The product of two numbers is equal to the product of their LCM and GCD: 36 * 6 = 216.
Q. If the least common multiple (LCM) of two numbers is 60 and their greatest common divisor (GCD) is 5, which of the following pairs could represent these two numbers?
A.
(5, 12)
B.
(10, 30)
C.
(15, 20)
D.
(5, 15)
Solution
The product of the two numbers is equal to the LCM multiplied by the GCD. Thus, 60 * 5 = 300. The pair (15, 20) satisfies this condition since 15 * 20 = 300.
Q. If the least common multiple (LCM) of two numbers is 60 and their greatest common divisor (GCD) is 12, what can be inferred about the product of the two numbers?
A.
It is 720.
B.
It is 60.
C.
It is 12.
D.
It is 5.
Solution
The product of two numbers is equal to the product of their LCM and GCD. Therefore, 60 * 12 = 720.
Q. If the length of a rectangle is increased by 20% and the width is decreased by 10%, what is the percentage change in the area?
A.
8% increase
B.
10% decrease
C.
12% increase
D.
2% decrease
Solution
Let the original length be L and width be W. The new length is 1.2L and the new width is 0.9W. The original area is LW and the new area is (1.2L)(0.9W) = 1.08LW. The percentage change in area is ((1.08LW - LW) / LW) * 100 = 8% increase.
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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