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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 of the jacket?

A. $140
B. $150
C. $160
D. $170

Solution

Discounted Price = $200 - ($200 * 0.30) = $140. New Price = $140 + ($140 * 0.10) = $140 + $14 = $154.

Correct Answer: B — $150

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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

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

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 store offers a discount of 25% on a shirt that costs $40. What is the final price after the discount? (2023)

A. $30
B. $35
C. $25
D. $20

Solution

Discount = 25% of $40 = $10. Final price = $40 - $10 = $30.

Correct Answer: A — $30

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Q. A store offers a discount of 30% on a jacket that is originally priced at $150. What is the amount of discount?

A. $30
B. $40
C. $50
D. $60

Solution

Discount = 30% of $150 = 0.30 * $150 = $45.

Correct Answer: A — $30

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Q. A store sells a laptop for $800 after applying a discount of 20%. What was the original price of the laptop?

A. $1000
B. $960
C. $800
D. $840

Solution

Let the original price be x. Selling Price = x - 20% of x = 0.8x. Thus, 0.8x = 800, so x = 1000.

Correct Answer: A — $1000

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Q. A student calculates the density of a substance as 8.0 g/cm³ with an uncertainty of ±0.1 g/cm³. What is the density range?

A. 7.9 g/cm³ to 8.1 g/cm³
B. 8.0 g/cm³ to 8.2 g/cm³
C. 8.0 g/cm³ to 8.1 g/cm³
D. 7.5 g/cm³ to 8.5 g/cm³

Solution

Density range = 8.0 ± 0.1 = 7.9 g/cm³ to 8.1 g/cm³.

Correct Answer: A — 7.9 g/cm³ to 8.1 g/cm³

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Q. A student divides a number by 6 and gets a remainder of 4. If he divides the same number by 3, what will be the remainder? (2023)

A. 0
B. 1
C. 2
D. 4

Solution

If the number is of the form 6k + 4, when divided by 3, it gives a remainder of 1 (4 % 3 = 1).

Correct Answer: D — 4

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Q. A student has a 70% chance of passing an exam. If he takes the exam twice, what is the probability that he passes at least once?

A. 0.49
B. 0.91
C. 0.51
D. 0.70

Solution

The probability of passing at least once is 1 - (0.3^2) = 1 - 0.09 = 0.91.

Correct Answer: B — 0.91

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Q. A student has a 70% chance of passing an exam. What is the probability of failing the exam?

A. 0.3
B. 0.7
C. 0.5
D. 0.2

Solution

Probability of failing = 1 - Probability of passing = 1 - 0.7 = 0.3.

Correct Answer: A — 0.3

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Q. A student has a 70% chance of passing an exam. What is the probability that the student fails the exam?

A. 0.3
B. 0.7
C. 0.5
D. 0.2

Solution

The probability of failing the exam is 1 - 0.7 = 0.3.

Correct Answer: A — 0.3

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Q. A student has scores of 60, 70, and 80 in three tests. If he wants an average of 75 after the fourth test, what score does he need?

A. 90
B. 85
C. 80
D. 75

Solution

Let the fourth score be x. (60 + 70 + 80 + x) / 4 = 75 => 210 + x = 300 => x = 90.

Correct Answer: A — 90

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Q. A student is selected at random from a class of 40 students, where 25 are boys and 15 are girls. What is the probability that the student is a girl given that the student is not a boy?

A. 1/3
B. 1/2
C. 2/3
D. 3/4

Solution

The total number of students that are not boys is 15 (girls). The probability of selecting a girl given that the student is not a boy is 15/15 = 1.

Correct Answer: C — 2/3

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Q. A student is selected at random from a class of 40 students, where 25 are boys and 15 are girls. What is the probability that the student is a boy given that the student is not a girl?

A. 1/2
B. 3/4
C. 5/8
D. 2/5

Solution

If the student is not a girl, they must be a boy. Therefore, P(Boy | Not Girl) = 1.

Correct Answer: B — 3/4

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Q. A student is selected at random from a group of 40 students, where 25 are studying Mathematics and 15 are studying Physics. What is the probability that the student is studying Mathematics given that they are not studying Physics?

A. 5/8
B. 3/8
C. 1/2
D. 1/3

Solution

If the student is not studying Physics, they must be studying Mathematics. Therefore, P(Math | Not Physics) = 1.

Correct Answer: A — 5/8

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Q. A student is selected at random from a group of 40 students, where 25 are studying Mathematics and 15 are studying Physics. What is the probability that the student is studying Physics given that the student is not studying Mathematics?

A. 0
B. 1/3
C. 3/8
D. 1/2

Solution

If the student is not studying Mathematics, they must be studying Physics. Therefore, the probability is 1.

Correct Answer: B — 1/3

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Q. A student is selected at random from a group of students who study Mathematics and Physics. If 70% study Mathematics and 40% study both subjects, what is the probability that a student studies Physics given that they study Mathematics?

A. 0.4
B. 0.3
C. 0.5
D. 0.6

Solution

Using the formula P(Physics|Mathematics) = P(Physics and Mathematics) / P(Mathematics) = 0.4 / 0.7 = 0.571.

Correct Answer: A — 0.4

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Q. A student is selected from a class of 40 students, where 25 are girls and 15 are boys. What is the probability that the student is a girl given that the student is not a boy?

A. 1
B. 0
C. 1/2
D. 3/4

Solution

If the student is not a boy, they must be a girl. Therefore, the probability is 1.

Correct Answer: A — 1

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Q. A student measures a length as 30.2 m, but the actual length is 30 m. What is the error in measurement?

A. 0.2 m
B. 0.1 m
C. 0.3 m
D. 0.5 m

Solution

Error = Measured value - True value = 30.2 m - 30 m = 0.2 m.

Correct Answer: A — 0.2 m

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Q. A student measures the length of a rod as 15.3 cm. If the true length is 15 cm, what is the error in measurement?

A. 0.3 cm
B. 0.2 cm
C. 0.1 cm
D. 0.5 cm

Solution

Error in measurement = Measured value - True value = 15.3 - 15 = 0.3 cm.

Correct Answer: A — 0.3 cm

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Q. A student measures the length of a rod as 150 cm with a possible error of 2 cm. What is the range of the true length?

A. 148 cm to 152 cm
B. 149 cm to 151 cm
C. 150 cm to 152 cm
D. 150 cm to 154 cm

Solution

True length can vary from 150 - 2 to 150 + 2, which is 148 cm to 152 cm.

Correct Answer: A — 148 cm to 152 cm

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Q. A student measures the length of a rod multiple times and records the values: 10.1 cm, 10.2 cm, 10.0 cm, 10.3 cm. What is the average length of the rod?

A. 10.0 cm
B. 10.1 cm
C. 10.2 cm
D. 10.3 cm

Solution

Average length = (10.1 + 10.2 + 10.0 + 10.3) / 4 = 10.15 cm.

Correct Answer: B — 10.1 cm

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Q. A student measures the length of a rod multiple times and records values of 10.1 cm, 10.2 cm, and 10.0 cm. What is the average length of the rod?

A. 10.0 cm
B. 10.1 cm
C. 10.2 cm
D. 10.3 cm

Solution

Average length = (10.1 + 10.2 + 10.0) / 3 = 10.1 cm.

Correct Answer: B — 10.1 cm

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Q. A student measures the length of a table as 1.20 m with an uncertainty of 0.02 m. What is the total length if he measures 3 tables?

A. 3.60 m
B. 3.58 m
C. 3.62 m
D. 3.64 m

Solution

Total length = 3 * 1.20 m = 3.60 m. The uncertainty for 3 tables = 3 * 0.02 m = 0.06 m.

Correct Answer: A — 3.60 m

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Q. A student measures the mass of an object as 200 g with an uncertainty of ±2 g. What is the relative uncertainty?

A. 1%
B. 0.5%
C. 2%
D. 0.1%

Solution

Relative uncertainty = (Uncertainty / Measured value) * 100 = (2 / 200) * 100 = 1%.

Correct Answer: B — 0.5%

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Q. A student measures the speed of a car as 60 km/h with an uncertainty of ±2 km/h. What is the percentage error in the speed measurement?

A. 3.33%
B. 2.0%
C. 1.5%
D. 4.0%

Solution

Percentage error = (Uncertainty / Measured value) * 100 = (2 / 60) * 100 = 3.33%.

Correct Answer: A — 3.33%

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Q. A student measures the speed of a car as 60 km/h with an uncertainty of ±2 km/h. What is the percentage uncertainty?

A. 3.33%
B. 2.5%
C. 4.0%
D. 5.0%

Solution

Percentage uncertainty = (Uncertainty / Measured value) * 100 = (2 / 60) * 100 = 3.33%.

Correct Answer: A — 3.33%

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Q. A student measures the speed of a car as 60.0 km/h with an uncertainty of ±2.0 km/h. What is the percentage uncertainty in the speed measurement?

A. 3.33%
B. 2.0%
C. 1.67%
D. 5.0%

Solution

Percentage uncertainty = (absolute uncertainty / measured value) * 100 = (2.0 / 60.0) * 100 = 3.33%.

Correct Answer: A — 3.33%

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Q. A student measures the temperature of water as 25°C with an uncertainty of ±0.5°C. What is the minimum temperature?

A. 24.5°C
B. 25.0°C
C. 25.5°C
D. 26.0°C

Solution

Minimum temperature = Measured value - Uncertainty = 25.0 - 0.5 = 24.5°C.

Correct Answer: A — 24.5°C

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Q. A student measures the time period of a pendulum as 2.0 s with an uncertainty of ±0.1 s. What is the absolute error in the time period?

A. 0.1 s
B. 0.05 s
C. 0.2 s
D. 0.01 s

Solution

The absolute error is given directly as ±0.1 s.

Correct Answer: A — 0.1 s

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Major Competitive Exams

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