Quantitative Aptitude for Competitive Exam Success

Quantitative Aptitude

Algebra Arithmetic Geometry & Mensuration Modern Math Number Systems

Q. If 15 is congruent to x modulo 6, what is the value of x?

A. 3
B. 9
C. 15
D. 21

Solution

15 mod 6 = 3, so x = 3.

Correct Answer: A — 3

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Q. If 15 students like both History and Geography, 25 like History, and 20 like Geography, how many students like only Geography?

A. 5
B. 10
C. 15
D. 20

Solution

The number of students who like only Geography is: 20 - 15 = 5.

Correct Answer: A — 5

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Q. If 25% of a group like tea, 15% like coffee, and 5% like both, what percentage like either tea or coffee?

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

Solution

Using inclusion-exclusion, the percentage who like either is 25% + 15% - 5% = 35%.

Correct Answer: A — 35%

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Q. If 25% of a group like tea, 35% like coffee, and 10% like both, what percentage like only tea?

A. 15%
B. 25%
C. 10%
D. 20%

Solution

The percentage who like only tea is 25% - 10% = 15%.

Correct Answer: A — 15%

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Q. If 25% of a group of 200 people like sports, 15% like music, and 5% like both, what percentage of people like only sports?

A. 20%
B. 15%
C. 10%
D. 5%

Solution

The percentage of people who like only sports is 25% - 5% = 20%.

Correct Answer: A — 20%

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Q. If 25% of a group of 200 people like tea, 15% like coffee, and 5% like both, what percentage like only tea?

A. 20%
B. 15%
C. 10%
D. 5%

Solution

The number of people who like only tea is 25% of 200 - 5% of 200 = 20%.

Correct Answer: A — 20%

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Q. If 25% of a population likes apples, 15% likes oranges, and 5% likes both, what percentage likes either fruit?

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

Solution

Using inclusion-exclusion, the percentage that likes either fruit is 25% + 15% - 5% = 35%.

Correct Answer: A — 35%

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Q. If 25% of a population likes apples, 35% likes oranges, and 10% likes both, what percentage likes only apples?

A. 15%
B. 25%
C. 10%
D. 5%

Solution

The percentage of people who like only apples is 25% - 10% = 15%.

Correct Answer: A — 15%

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Q. If 25% of a population likes reading, 15% likes writing, and 5% likes both, what percentage likes either reading or writing?

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

Solution

Using inclusion-exclusion, the percentage of people who like either activity is: 25% + 15% - 5% = 35%.

Correct Answer: A — 35%

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Q. If 2x ≡ 4 (mod 6), what is the smallest non-negative integer solution for x?

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

Solution

Dividing both sides by 2 gives x ≡ 2 (mod 3), hence the smallest non-negative solution is 2.

Correct Answer: C — 2

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Q. If 2^(x+3) = 32, what is the value of x?

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

Solution

Since 32 can be expressed as 2^5, we have 2^(x+3) = 2^5, thus x + 3 = 5, leading to x = 2.

Correct Answer: C — 3

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Q. If 3x ≡ 9 (mod 12), what is the value of x?

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

Solution

Dividing both sides by 3 gives x ≡ 3 (mod 12), which means x can be 3.

Correct Answer: B — 2

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Q. If 3x ≡ 9 (mod 6), what is the value of x?

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

Solution

3x = 9 mod 6 simplifies to x = 3 mod 2, so x = 2.

Correct Answer: C — 2

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Q. If 4 different books are to be arranged on a shelf, how many arrangements are possible?

A. 16
B. 24
C. 32
D. 48

Solution

The number of arrangements of 4 distinct books is 4! = 24.

Correct Answer: B — 24

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Q. If 4 different books are to be arranged on a shelf, how many different arrangements are possible?

A. 16
B. 24
C. 32
D. 48

Solution

The number of arrangements of 4 distinct books is 4! = 24.

Correct Answer: B — 24

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Q. If 40 students like Mathematics, 30 like Science, and 10 like both subjects, how many students like only Mathematics?

A. 30
B. 20
C. 10
D. 40

Solution

The number of students who like only Mathematics is 40 - 10 = 30.

Correct Answer: B — 20

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Q. If 4x ≡ 1 (mod 9), what is the smallest positive integer solution for x?

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

Solution

The multiplicative inverse of 4 mod 9 is 7, since 4 * 7 = 28 ≡ 1 (mod 9).

Correct Answer: A — 1

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Q. If 4x ≡ 8 (mod 12), what is the smallest non-negative integer solution for x?

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

Solution

Dividing both sides by 4 gives x ≡ 2 (mod 3), so the smallest non-negative solution is 2.

Correct Answer: C — 2

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Q. If 4x ≡ 8 (mod 12), what is the smallest non-negative solution for x?

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

Solution

Dividing the equation by 4 gives x ≡ 2 (mod 3). The smallest non-negative solution is x = 2.

Correct Answer: C — 2

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Q. If 4^(x-1) = 1/16, what is the value of x? (2023)

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

Solution

Since 1/16 can be expressed as 4^(-2), we have 4^(x-1) = 4^(-2), thus x - 1 = -2, leading to x = -1.

Correct Answer: C — 2

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Q. If 4^(x-1) = 64, what is the value of x?

A. 3
B. 4
C. 5
D. 6

Solution

Since 64 can be expressed as 4^3, we have 4^(x-1) = 4^3, thus x - 1 = 3, leading to x = 4.

Correct Answer: B — 4

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Q. If 5 liters of a 20% solution is mixed with 15 liters of a 30% solution, what is the percentage concentration of the resulting mixture?

A. 24%
B. 26%
C. 28%
D. 30%

Solution

Total salt = (0.2*5) + (0.3*15) = 1 + 4.5 = 5.5 liters. Total volume = 5 + 15 = 20 liters. Concentration = (5.5/20)*100 = 27.5%.

Correct Answer: A — 24%

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Q. If 5 workers can complete a task in 10 days, how many days will it take for 10 workers to complete the same task?

A. 5 days
B. 10 days
C. 15 days
D. 20 days

Solution

Work done = Workers * Days. Total work = 5 * 10 = 50 worker-days. For 10 workers, Days = Total work / Workers = 50 / 10 = 5 days.

Correct Answer: A — 5 days

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Q. If 5x ≡ 10 (mod 15), what is the value of x?

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

Solution

Dividing both sides by 5 gives x ≡ 2 (mod 3), which means x can be 2.

Correct Answer: C — 2

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Q. If 6 different colored balls are to be arranged in a row, how many arrangements are possible?

A. 720
B. 600
C. 360
D. 480

Solution

The number of arrangements of 6 different colored balls is 6! = 720.

Correct Answer: A — 720

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Q. If 60% of a mixture is liquid X and the rest is liquid Y, what is the ratio of liquid Y to liquid X?

A. 1:2
B. 2:3
C. 3:2
D. 1:3

Solution

If 60% is X, then 40% is Y. The ratio of Y to X = 40:60 = 2:3.

Correct Answer: A — 1:2

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Q. If 60% of students like reading fiction, 40% like reading non-fiction, and 10% like both, what percentage of students like at least one genre?

A. 90%
B. 100%
C. 80%
D. 70%

Solution

Using inclusion-exclusion, the percentage is 60% + 40% - 10% = 90%.

Correct Answer: A — 90%

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Q. If 60% of students like reading, 40% like writing, and 10% like both, what percentage of students like only reading?

A. 50%
B. 40%
C. 30%
D. 20%

Solution

The percentage of students who like only reading is 60% - 10% = 50%.

Correct Answer: A — 50%

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Q. If 60% of students like reading, 40% like writing, and 10% like both, what percentage of students like only writing?

A. 30%
B. 40%
C. 10%
D. 50%

Solution

The percentage of students who like only writing is 40% - 10% = 30%.

Correct Answer: A — 30%

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Q. If 60% of students play cricket, 40% play football, and 10% play both, what percentage of students play either cricket or football?

A. 90%
B. 80%
C. 70%
D. 60%

Solution

Using inclusion-exclusion, the percentage of students who play either cricket or football is: 60% + 40% - 10% = 90%.

Correct Answer: B — 80%

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Quantitative Aptitude

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