Quantitative Aptitude & Reasoning for Competitive Exams

Quantitative Aptitude & Reasoning

Algebra & Number Theory Arithmetic Aptitude Data Interpretation Geometry & Mensuration Logical Reasoning

Q. If logx(16) = 4, what is the value of x?

A. 2
B. 4
C. 8
D. 16

Solution

x = 16^(1/4) = 2.

Correct Answer: B — 4

Q. If n is an even integer, which of the following is always odd?

A. n + 1
B. n + 2
C. n - 2
D. n - 1

Solution

n - 1 is odd since subtracting 1 from an even number results in an odd number.

Correct Answer: D — n - 1

Q. If n is an odd integer, which of the following is always even?

A. n + 1
B. n - 1
C. 2n
D. All of the above

Solution

Both n + 1 and n - 1 are even, and 2n is always even.

Correct Answer: D — All of the above

Q. If the HCF of two numbers is 1, what can be said about the numbers?

A. They are even
B. They are odd
C. They are coprime
D. They are multiples of each other

Solution

If the HCF is 1, the numbers are coprime, meaning they have no common factors other than 1.

Correct Answer: C — They are coprime

Q. If the HCF of two numbers is 15 and their LCM is 150, what is the product of the two numbers?

A. 225
B. 1500
C. 300
D. 75

Solution

The product of the two numbers is equal to the product of their HCF and LCM, which is 15 * 150 = 2250.

Correct Answer: B — 1500

Q. If the HCF of two numbers is equal to one of the numbers, what can be inferred?

A. The numbers are equal
B. One number is a multiple of the other
C. The numbers are coprime
D. The numbers are both prime

Solution

If the HCF is equal to one of the numbers, it means that one number is a multiple of the other.

Correct Answer: B — One number is a multiple of the other

Q. If the LCM of two numbers is 120 and one of the numbers is 30, what is the other number?

A. 40
B. 60
C. 20
D. 10

Solution

The other number can be found using the formula: LCM = (a * b) / HCF. Here, 120 = (30 * b) / HCF. Assuming HCF is 30, b = 120 / 30 = 40.

Correct Answer: A — 40

Q. If the LCM of two numbers is 36 and their HCF is 6, what is the product of the two numbers?

A. 72
B. 108
C. 216
D. 144

Solution

The product of the two numbers is LCM * HCF = 36 * 6 = 216.

Correct Answer: C — 216

Q. If the LCM of two numbers is 72 and one of the numbers is 8, what is the other number?

A. 9
B. 18
C. 36
D. 72

Solution

The other number can be found using the formula LCM(a, b) = (a * b) / HCF(a, b). Here, 72 = (8 * x) / HCF(8, x). The other number is 18.

Correct Answer: B — 18

Q. If the LCM of two numbers is 84 and one of the numbers is 12, what is the other number?

A. 7
B. 21
C. 28
D. 14

Solution

The other number can be found using the formula: LCM = (a * b) / HCF. Here, 84 = (12 * b) / HCF. The other number is 28.

Correct Answer: C — 28

Q. If the roots of the equation x^2 + px + q = 0 are 3 and -2, what is the value of p?

A. 1
B. 5
C. -1
D. -5

Solution

Using the sum of roots: p = -(3 + (-2)) = -1.

Correct Answer: B — 5

Q. If the roots of the equation x^2 - px + q = 0 are 3 and 4, what is the value of p?

A. 7
B. 12
C. 9
D. 10

Solution

The sum of the roots is p = 3 + 4 = 7.

Correct Answer: A — 7

Q. If the sequence is defined by a_n = 3n + 1, what is a_4?

A. 10
B. 11
C. 12
D. 13

Solution

a_4 = 3(4) + 1 = 12 + 1 = 13.

Correct Answer: A — 10

Q. If x + 3 = 10, what is the value of x?

A. 5
B. 6
C. 7
D. 8

Solution

x = 10 - 3 = 7.

Correct Answer: B — 6

Q. If x + 5 = 12, what is the value of x?

A. 5
B. 7
C. 12
D. 17

Solution

Subtracting 5 from both sides gives x = 7.

Correct Answer: B — 7

Q. If x = 2^(3) and y = 2^(4), what is the value of x/y?

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

Solution

x/y = 2^(3)/2^(4) = 2^(3-4) = 2^(-1) = 1/2.

Correct Answer: C — 2

Q. If x = 2^(3/4), what is x^4?

A. 2
B. 4
C. 8
D. 16

Solution

x^4 = (2^(3/4))^4 = 2^3 = 8.

Correct Answer: C — 8

Q. If x = 3, what is the value of 2x^2 - 5?

A. 1
B. 7
C. 10
D. 11

Solution

Substituting x = 3 gives 2(3^2) - 5 = 18 - 5 = 13.

Correct Answer: B — 7

Q. If x = √(25), what is the value of x^2?

A. 5
B. 10
C. 25
D. 0

Solution

x = √(25) = 5, thus x^2 = 5^2 = 25.

Correct Answer: C — 25

Q. If x is an integer such that 3x + 5 is even, what can be said about x?

A. x is even
B. x is odd
C. x can be any integer
D. x is a prime number

Solution

For 3x + 5 to be even, x must be odd.

Correct Answer: A — x is even

Q. If x ≡ 3 (mod 5), what is the value of x when x is the smallest positive integer?

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

Solution

The smallest positive integer satisfying x ≡ 3 (mod 5) is 3.

Correct Answer: C — 3

Q. If x^2 + 4x + 4 = 0, what is the value of x?

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

Solution

This is a perfect square: (x + 2)^2 = 0, so x = -2.

Correct Answer: A — -2

Q. If x^2 - 5x + 6 = 0, what are the roots of the equation?

A. x = 1, 6
B. x = 2, 3
C. x = -2, -3
D. x = 0, 6

Solution

Factoring gives (x - 2)(x - 3) = 0, so x = 2 and x = 3.

Correct Answer: B — x = 2, 3

Q. If x^2 - 9 = 0, what are the values of x?

A. -3, 3
B. 0
C. 3
D. 9

Solution

Factoring gives (x - 3)(x + 3) = 0, so x = -3 or x = 3.

Correct Answer: A — -3, 3

Q. Solve for x: 2x + 3 = 11

A. 2
B. 3
C. 4
D. 5

Solution

Subtract 3 from both sides: 2x = 8. Then divide by 2: x = 4.

Correct Answer: B — 3

Q. Solve for x: 3x + 5 = 20.

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

Solution

3x = 15, so x = 5.

Correct Answer: A — 5

Q. Solve for x: 3x^2 - 12 = 0.

A. x = 2
B. x = -2
C. x = 4
D. x = -4

Solution

Add 12 to both sides: 3x^2 = 12. Divide by 3: x^2 = 4. Thus, x = ±2.

Correct Answer: A — x = 2

Q. Solve for x: 4x^2 - 12x + 9 = 0.

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

Solution

This factors to (2x - 3)(2x - 3) = 0, giving the double root x = 3.

Correct Answer: B — x = 3

Q. Solve for x: 4x^2 - 16 = 0.

A. x = 2
B. x = -2
C. x = 4
D. x = -4

Solution

Add 16 to both sides: 4x^2 = 16. Divide by 4: x^2 = 4. Thus, x = ±2.

Correct Answer: A — x = 2

Q. Solve for x: 5x^2 + 10x = 0.

A. x = 0, -2
B. x = 2, 0
C. x = -2, 2
D. x = 5, 0

Solution

Factoring gives 5x(x + 2) = 0, so x = 0 or x = -2.

Correct Answer: A — x = 0, -2

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