Q. A solution contains 20% sugar. If 5 liters of the solution is taken, how much sugar is in that solution?
A.
1 liter
B.
0.5 liters
C.
2 liters
D.
1.5 liters
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Solution
Sugar in 5 liters = 20% of 5 = 0.2 * 5 = 1 liter.
Correct Answer: A — 1 liter
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Q. A solution contains 25% alcohol. If 200 ml of the solution is taken, how much alcohol is present in it?
A.
50 ml
B.
25 ml
C.
75 ml
D.
100 ml
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Solution
25% of 200 ml = 0.25 * 200 = 50 ml of alcohol.
Correct Answer: A — 50 ml
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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?
A.
15%
B.
16%
C.
17%
D.
18%
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Solution
Total salt = (3 * 0.2) + (5 * 0.1) = 0.6 + 0.5 = 1.1. Total mixture = 3 + 5 = 8. Percentage = (1.1/8) * 100 = 13.75%.
Correct Answer: A — 15%
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Q. A square has a perimeter of 40 cm. What is the area of the square?
A.
100 cm²
B.
200 cm²
C.
150 cm²
D.
250 cm²
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Solution
Perimeter of a square = 4 × side. Thus, 40 = 4 × side, giving side = 10 cm. Area = side² = 10² = 100 cm².
Correct Answer: A — 100 cm²
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Q. A store offers a 30% discount on a jacket originally priced at $200. If the store then increases the price by 10% after the discount, what is the final price?
A.
$140
B.
$150
C.
$160
D.
$170
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Solution
Discounted Price = $200 - ($200 * 0.30) = $200 - $60 = $140. After a 10% increase, Final Price = $140 + ($140 * 0.10) = $140 + $14 = $154.
Correct Answer: C — $160
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Q. A store offers a 30% discount on a jacket that is originally priced at $200. If the store then applies an additional 10% discount on the already discounted price, what is the final selling price? (2023)
A.
$140
B.
$150
C.
$160
D.
$170
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Solution
First discount: $200 - (30% of $200) = $200 - $60 = $140. Second discount: $140 - (10% of $140) = $140 - $14 = $126.
Correct Answer: A — $140
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Q. A store offers a discount of 25% on a product. If the selling price is $75, what was the original price?
A.
$100
B.
$90
C.
$80
D.
$70
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Solution
Let the original price be x. After a 25% discount, the selling price is 0.75x. Setting this equal to $75 gives 0.75x = $75, so x = $75 / 0.75 = $100.
Correct Answer: A — $100
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Q. A student scored 60, 70, and 80 in three subjects. If he wants to achieve an average of 75, what score does he need in the fourth subject? (2023)
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Solution
Let the score in the fourth subject be x. The average is (60 + 70 + 80 + x) / 4 = 75. Solving gives x = 85.
Correct Answer: D — 85
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Q. A sum of money invested at compound interest becomes $1500 in 2 years and $1800 in 3 years. What is the rate of interest?
A.
10%
B.
12%
C.
15%
D.
20%
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Solution
The interest for the third year is $300 (1800 - 1500). The principal for the second year is $1500, so the rate is (300/1500) * 100 = 20%.
Correct Answer: B — 12%
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Q. A sum of money invested at compound interest becomes $1600 in 2 years and $1764 in 3 years. What is the rate of interest?
A.
10%
B.
12%
C.
15%
D.
20%
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Solution
The amount increases from $1600 to $1764 in one year, which is an increase of $164. The rate can be calculated as (164/1600) * 100 = 10.25%, which rounds to approximately 12%.
Correct Answer: B — 12%
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Q. A sum of money invested at compound interest grows to $1500 in 2 years and to $1800 in 3 years. What is the rate of interest?
A.
10%
B.
15%
C.
20%
D.
25%
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Solution
Using the formula for compound interest, we find the growth factor from $1500 to $1800 over 1 year, which gives a rate of approximately 15%.
Correct Answer: B — 15%
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Q. A sum of money is invested at a certain rate of compound interest. If the amount becomes three times in 10 years, what is the rate of interest?
A.
10%
B.
15%
C.
20%
D.
25%
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Solution
Using the formula A = P(1 + r)^t, where A = 3P, t = 10. Solving for r gives r = (3^(1/10)) - 1, which approximates to 15%.
Correct Answer: B — 15%
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Q. A sum of money is invested at a compound interest rate of 12% per annum. How long will it take for the investment to double?
A.
5 years
B.
6 years
C.
7 years
D.
8 years
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Solution
Using the rule of 72, 72/12 = 6 years to double the investment.
Correct Answer: B — 6 years
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Q. A teacher has 48 pencils and 60 erasers. She wants to distribute them equally among students. What is the maximum number of students she can distribute to? (2023)
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Solution
The HCF of 48 and 60 is 12, which is the maximum number of students she can distribute to equally.
Correct Answer: A — 12
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Q. A teacher has an average of 85% in her class. If she has 20 students, what is the total percentage score of the class? (2023)
A.
1600%
B.
1700%
C.
1800%
D.
1900%
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Solution
Total percentage score = Average percentage × Number of students = 85% × 20 = 1700%.
Correct Answer: A — 1600%
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Q. A teacher has an average score of 85 for her class of 20 students. If one student scores 95, what will be the new average if the class size increases to 21? (2023)
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Solution
Total score = 85 × 20 + 95 = 1700 + 95 = 1795. New average = 1795 / 21 = 85.95, which rounds to 86.
Correct Answer: C — 86
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Q. A train leaves a station and travels at a speed of 90 km/h. How long will it take to travel 270 km?
A.
2 hours
B.
3 hours
C.
4 hours
D.
5 hours
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Solution
Time = Distance / Speed. Here, time = 270 km / 90 km/h = 3 hours.
Correct Answer: B — 3 hours
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Q. A train travels 120 km at a speed of 60 km/h. How long does it take to complete the journey?
A.
1 hour
B.
1.5 hours
C.
2 hours
D.
2.5 hours
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Solution
Time = Distance / Speed = 120 km / 60 km/h = 2 hours.
Correct Answer: C — 2 hours
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Q. A trapezium has bases of lengths 10 cm and 6 cm, and a height of 4 cm. What is its area? (2023)
A.
32 cm²
B.
36 cm²
C.
40 cm²
D.
44 cm²
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Solution
Area = (1/2) * (base1 + base2) * height = (1/2) * (10 + 6) * 4 = 32 cm².
Correct Answer: A — 32 cm²
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Q. A trapezium has bases of lengths 10 cm and 6 cm, and a height of 4 cm. What is the area of the trapezium?
A.
32 cm²
B.
40 cm²
C.
36 cm²
D.
28 cm²
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Solution
Area of a trapezium = (1/2) × (base1 + base2) × height = (1/2) × (10 + 6) × 4 = 32 cm².
Correct Answer: A — 32 cm²
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Q. A triangle has sides of lengths 7 cm, 24 cm, and 25 cm. What is the area of the triangle? (2021)
A.
84 cm²
B.
96 cm²
C.
120 cm²
D.
168 cm²
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Solution
The triangle is a right triangle (7² + 24² = 25²). The area is (1/2) * base * height = (1/2) * 7 * 24 = 84 cm².
Correct Answer: A — 84 cm²
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Q. According to the passage, which of the following is a common misconception about inequality?
A.
It is only an economic issue.
B.
It affects everyone equally.
C.
It can be easily solved.
D.
It is a global issue.
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Solution
The passage clarifies that inequality is multifaceted and not limited to economic factors.
Correct Answer: A — It is only an economic issue.
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Q. Based on the passage, which of the following is NOT a reason given for the persistence of inequalities?
A.
Historical injustices
B.
Lack of education
C.
Government negligence
D.
Cultural beliefs
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Solution
The passage does not mention government negligence as a reason for the persistence of inequalities.
Correct Answer: C — Government negligence
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Q. Based on the passage, which of the following is NOT a suggested method for addressing inequalities?
A.
Implementing progressive taxation.
B.
Increasing access to quality education.
C.
Promoting economic growth without regulation.
D.
Enhancing social welfare programs.
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Solution
The passage does not support the idea of promoting unregulated economic growth as a method to address inequalities.
Correct Answer: C — Promoting economic growth without regulation.
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Q. For a number to be divisible by 10, which of the following must be true?
A.
It must end in 0
B.
It must be a two-digit number
C.
It must be a prime number
D.
It must be even
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Solution
A number is divisible by 10 if it ends in 0.
Correct Answer: A — It must end in 0
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Q. From a group of 8 people, how many ways can a team of 4 be selected?
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Solution
The number of ways to choose 4 people from 8 is given by 8C4 = 70.
Correct Answer: B — 56
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Q. How does the author support the claims made about digital sum? (2023)
A.
By providing historical examples.
B.
By citing recent technological advancements.
C.
By referencing mathematical theories.
D.
By discussing personal experiences.
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Solution
The author supports the claims about digital sum by citing recent technological advancements that utilize this concept.
Correct Answer: B — By citing recent technological advancements.
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Q. How many ways can 5 different colored balls be placed in 3 different boxes if each box can hold any number of balls?
A.
243
B.
125
C.
256
D.
3125
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Solution
Each ball has 3 choices (boxes), so for 5 balls, the total arrangements = 3^5 = 243.
Correct Answer: A — 243
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Q. How many ways can 5 students be seated in a row of 5 chairs?
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Solution
The number of ways to arrange 5 students in 5 chairs is 5! = 120.
Correct Answer: A — 120
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Q. If 'A' is a number in base-5 and is represented as '43', what is its decimal equivalent?
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Solution
'43' in base 5 is calculated as 4*5^1 + 3*5^0 = 20 + 3 = 23.
Correct Answer: B — 23
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