Q. The area of a rhombus is 60 square cm and one diagonal is 10 cm. What is the length of the other diagonal?
A.
12 cm
B.
15 cm
C.
10 cm
D.
8 cm
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Solution
Area = (1/2) × d1 × d2. Thus, 60 = (1/2) × 10 × d2, giving d2 = 12 cm.
Correct Answer:
B
— 15 cm
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Q. The area of a rhombus is 60 square cm. If one diagonal is 10 cm, what is the length of the other diagonal?
A.
12 cm
B.
15 cm
C.
10 cm
D.
8 cm
Show solution
Solution
Area = (1/2) × d1 × d2. Thus, 60 = (1/2) × 10 × d2, giving d2 = 60/(5) = 12 cm.
Correct Answer:
B
— 15 cm
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Q. The area of a sector of a circle is 30 cm² and the radius is 5 cm. What is the angle of the sector in degrees?
A.
60 degrees
B.
72 degrees
C.
90 degrees
D.
120 degrees
Show solution
Solution
Area of sector = (θ/360) × πr². Thus, 30 = (θ/360) × 3.14 × 25. Solving gives θ = (30 × 360) / (3.14 × 25) ≈ 72 degrees.
Correct Answer:
B
— 72 degrees
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Q. The author implies that addressing inequalities requires:
A.
A collective effort from all sectors of society.
B.
A focus solely on economic factors.
C.
Ignoring historical contexts.
D.
A reduction in government involvement.
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Solution
The author implies that a collective effort is necessary to effectively address the complex issue of inequalities.
Correct Answer:
A
— A collective effort from all sectors of society.
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Q. The author uses the phrase 'the cycle of poverty' to illustrate:
A.
The inevitability of poverty.
B.
The interconnectedness of various forms of inequality.
C.
The temporary nature of poverty.
D.
The lack of government intervention in poverty.
Show solution
Solution
The phrase 'the cycle of poverty' highlights how different forms of inequality are interconnected and perpetuate each other.
Correct Answer:
B
— The interconnectedness of various forms of inequality.
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Q. The average of a set of numbers is 50. If one number is removed, the average becomes 48. What was the number that was removed?
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Solution
Let the number of items be n. Total sum = 50n. After removing one number, the new sum = 48(n - 1). Setting up the equation gives the removed number as 52.
Correct Answer:
B
— 52
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Q. The average of three consecutive integers is 20. What is the smallest of these integers? (2023)
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Solution
Let the integers be x, x+1, x+2. The average is (x + (x + 1) + (x + 2)) / 3 = 20. Solving gives x = 18.
Correct Answer:
A
— 18
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Q. The average score of a student in five subjects is 72. If the student scores 80 in the sixth subject, what will be the new average?
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Solution
New average = (72 * 5 + 80) / 6 = (360 + 80) / 6 = 440 / 6 = 73.33, which rounds to 74.
Correct Answer:
C
— 76
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Q. The HCF of two numbers is 1 and their LCM is 60. Which of the following pairs could represent these numbers? (2023)
A.
5 and 12
B.
3 and 20
C.
4 and 15
D.
6 and 10
Show solution
Solution
The pair 5 and 12 has an HCF of 1 and an LCM of 60.
Correct Answer:
A
— 5 and 12
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Q. The HCF of two numbers is 7 and their LCM is 84. If one of the numbers is 21, what is the other number? (2023)
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Solution
Using the relation HCF * LCM = Product of the numbers, we have 7 * 84 = 21 * x, which gives x = 42.
Correct Answer:
B
— 42
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Q. The LCM of two numbers is 120 and their HCF is 8. If one number is 32, what is the other number? (2023)
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Solution
Using the relation HCF * LCM = Product of the numbers, we have 8 * 120 = 32 * x, which gives x = 40.
Correct Answer:
B
— 40
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Q. The LCM of two numbers is 84 and their HCF is 12. If one of the numbers is 36, what is the other number? (2023)
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Solution
Using the relation: LCM * HCF = Product of the numbers, we have 84 * 12 = 36 * x, solving gives x = 28.
Correct Answer:
A
— 28
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Q. The LCM of two numbers is 84 and their HCF is 12. What are the two numbers? (2023)
A.
24 and 42
B.
12 and 84
C.
28 and 36
D.
21 and 48
Show solution
Solution
Let the two numbers be 12x and 12y. Then, LCM(12x, 12y) = 12 * LCM(x, y) = 84, which gives LCM(x, y) = 7. The pairs (x, y) that satisfy this are (3, 4) or (4, 3), leading to 24 and 42.
Correct Answer:
A
— 24 and 42
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Q. The LCM of two numbers is 84 and their HCF is 12. What is the sum of the two numbers if they are both less than 100? (2023)
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Solution
Let the two numbers be 12a and 12b. Then, 12ab = 84, so ab = 7. The pairs (1, 7) and (7, 1) give us 12 and 84, which sum to 96.
Correct Answer:
B
— 72
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Q. The ratio of the lengths of two sides of a triangle is 4:5. If the shorter side is 16 cm, what is the length of the longer side?
A.
20 cm
B.
25 cm
C.
30 cm
D.
15 cm
Show solution
Solution
If the shorter side is 16 cm and the ratio is 4:5, then the longer side can be calculated as (5/4) * 16 cm = 20 cm.
Correct Answer:
A
— 20 cm
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Q. The ratio of the number of cats to dogs in a shelter is 4:3. If there are 28 cats, how many dogs are there?
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Solution
The ratio of cats to dogs is 4:3. If there are 28 cats, we can set up the proportion: 4/3 = 28/x. Solving for x gives us x = 21. Therefore, there are 21 dogs.
Correct Answer:
A
— 21
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Q. The sum of the first n terms of a harmonic progression is given by which of the following formulas?
A.
n/(a+b)
B.
2n/(a+b)
C.
n/(ab)
D.
2n/(ab)
Show solution
Solution
The sum of the first n terms of a harmonic progression can be expressed as 2n/(a+b) where a and b are the first two terms.
Correct Answer:
B
— 2n/(a+b)
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Q. Two bells toll at intervals of 15 seconds and 20 seconds. If they toll together at 12:00 PM, when will they toll together again? (2023)
A.
12:05 PM
B.
12:10 PM
C.
12:15 PM
D.
12:20 PM
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Solution
The LCM of 15 and 20 is 60 seconds. Therefore, they will toll together again at 12:01 PM.
Correct Answer:
B
— 12:10 PM
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Q. Two numbers have an HCF of 7 and an LCM of 84. If one of the numbers is 21, what is the other number? (2023)
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Solution
Using the relationship between HCF, LCM, and the numbers: (21 * x) / 7 = 84. Solving gives x = 42.
Correct Answer:
B
— 42
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Q. Two numbers have an HCF of 8 and an LCM of 72. If one of the numbers is 16, what is the other number? (2023)
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Solution
Using the relationship LCM = (Product of the numbers) / HCF, we can find the other number: 72 = (16 * x) / 8, leading to x = 24.
Correct Answer:
B
— 24
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Q. What can be concluded about the applications of digital sum based on the passage? (2023)
A.
They are limited to theoretical mathematics.
B.
They are diverse and widespread in technology.
C.
They are primarily used in educational contexts.
D.
They are mostly outdated and rarely used.
Show solution
Solution
The passage indicates that the applications of digital sum are diverse and widespread in technology, showcasing its versatility.
Correct Answer:
B
— They are diverse and widespread in technology.
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Q. What can be concluded about the author's perspective on individual responsibility in addressing inequalities? (2023)
A.
Individual responsibility is the sole factor in reducing inequalities.
B.
The author believes individual actions are insignificant.
C.
The author advocates for a balance between individual and systemic solutions.
D.
Individual responsibility is irrelevant to the discussion of inequalities.
Show solution
Solution
The author suggests that both individual actions and systemic changes are necessary to effectively address inequalities.
Correct Answer:
C
— The author advocates for a balance between individual and systemic solutions.
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Q. What can be concluded about the domain of a function based on the passage?
A.
It includes all real numbers.
B.
It is the set of all possible output values.
C.
It is the set of all possible input values.
D.
It is always finite.
Show solution
Solution
The domain of a function refers to the set of all possible input values (x-values) for which the function is defined.
Correct Answer:
C
— It is the set of all possible input values.
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Q. What can be concluded about the relationship between digital sum and traditional methods?
A.
Digital sum is less effective than traditional methods.
B.
Digital sum complements traditional methods in certain applications.
C.
Digital sum is a replacement for all traditional methods.
D.
There is no relationship between digital sum and traditional methods.
Show solution
Solution
The passage indicates that digital sum can complement traditional methods in specific contexts.
Correct Answer:
B
— Digital sum complements traditional methods in certain applications.
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Q. What can be concluded about the relationship between digital sum and traditional arithmetic from the passage? (2023)
A.
Digital sum is a replacement for traditional arithmetic.
B.
Digital sum complements traditional arithmetic in certain contexts.
C.
There is no relationship between the two.
D.
Traditional arithmetic is more efficient than digital sum.
Show solution
Solution
The passage indicates that digital sum complements traditional arithmetic, particularly in specific applications.
Correct Answer:
B
— Digital sum complements traditional arithmetic in certain contexts.
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Q. What can be concluded about the relationship between digital sum and traditional arithmetic methods?
A.
Digital sum is a direct replacement for traditional methods.
B.
Digital sum complements traditional methods in certain areas.
C.
Traditional methods are more reliable than digital sum.
D.
There is no relationship between the two.
Show solution
Solution
The passage indicates that digital sum complements traditional arithmetic methods in specific applications.
Correct Answer:
B
— Digital sum complements traditional methods in certain areas.
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Q. What can be concluded about the relationship between digital sum and traditional arithmetic? (2023)
A.
Digital sum is a replacement for traditional arithmetic.
B.
Digital sum complements traditional arithmetic in specific applications.
C.
There is no relationship between the two.
D.
Traditional arithmetic is more efficient than digital sum.
Show solution
Solution
The passage indicates that digital sum complements traditional arithmetic, particularly in digital contexts.
Correct Answer:
B
— Digital sum complements traditional arithmetic in specific applications.
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Q. What can be concluded about the relationship between wealth and access to opportunities from the passage?
A.
Wealth has no impact on access to opportunities.
B.
Wealth directly correlates with access to better opportunities.
C.
Access to opportunities is solely based on merit.
D.
Wealth is irrelevant in discussions of inequality.
Show solution
Solution
The passage indicates that wealth significantly influences access to opportunities, reinforcing existing inequalities.
Correct Answer:
B
— Wealth directly correlates with access to better opportunities.
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Q. What can be inferred about the author's perspective on cultural beliefs and their impact on inequalities?
A.
Cultural beliefs have no impact on inequalities.
B.
Cultural beliefs can exacerbate inequalities.
C.
Cultural beliefs are the primary cause of inequalities.
D.
Cultural beliefs are easily changed.
Show solution
Solution
The author suggests that cultural beliefs can exacerbate existing inequalities, indicating their significant impact.
Correct Answer:
B
— Cultural beliefs can exacerbate inequalities.
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Q. What can be inferred about the author's perspective on the role of education in addressing inequalities?
A.
Education alone can solve all inequalities.
B.
Education is a crucial but insufficient factor.
C.
Education exacerbates existing inequalities.
D.
Education is irrelevant to the discussion of inequalities.
Show solution
Solution
The author suggests that while education is important, it must be accompanied by other measures to effectively address inequalities.
Correct Answer:
B
— Education is a crucial but insufficient factor.
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