Practice Questions for Algebra - Number Theory

1. Even Odd | Algebra - Number Theory

If x and y are both odd numbers, which of the following is an odd number?

(a)
x + y
(b)
x + y + 1
(c)
xy - 1
(d)
xy + 1
(e)
None of these

2. Even Odd | Algebra - Number Theory

If x is an even number and y is an odd number then which of the following is even.

A. (y – x) × (x – y)
B. (x – y) × (x + y)
C. (x × y) × (y + x)

(a)
Only A and B
(b)
Only C
(c)
Only A and C
(d)
Only B and C
(e)
All A, B and C

3. Even Odd | Algebra - Number Theory

If x is an even number and y is an odd number then which of the following is even.

A. x^y + y^y
B. y^x − x^x
C. y × x^y

(a)
Only A
(b)
Only B
(c)
Only C
(d)
Only A and B
(e)
Only B and C

4. Even Odd | Algebra - Number Theory

If x is an even number and y is an odd number then which of the following is even.

A. y × (x + y) – y^y
B. x × (x – y) – x^y
C. x^y × (y^y – y) – x^x

(a)
Only A
(b)
Only A and B
(c)
Only A and C
(d)
Only B and C
(e)
All A, B and C

5. Even Odd | Algebra - Number Theory

If x is an even number and y is an odd number then which of the following is even.

A. (x – y) + (x^y + y) – x^y
B. (x – y) – (x^y – x) + x^y
C. (x + y) × (x^y + y) × x^y

(a)
Only B
(b)
Only A and B
(c)
Only B and C
(d)
Only A and C
(e)
Only A

6. Even Odd | Algebra - Number Theory

If x is an even number and y is an odd number then which of the following is even.

A. x^x + x^y + (y – x)
B. y^x + x^y – (y + x)
C. x^x + y^y + (x – y)

(a)
Only A and B
(b)
Only A and C
(c)
Only B and C
(d)
Only C

7. Even Odd | Algebra - Number Theory

Given positive odd integers x, y and z, which of the following is not necessarily true?

(a)
x²y²z² is odd
(b)
2(x² + x³)z² is even
(c)
5x + y + z⁴ is odd
(d)
$\frac{z^{2} (x^{4} + y^{4})}{2}$ is even

8. Even Odd | Algebra - Number Theory

Let x, y and z be distinct integers, that are odd and positive. Which one of the following statements cannot be true?

(a)
xyz² is odd
(b)
(x − y)²z is even
(c)
(x + y − z)²(x + y) is even
(d)
(x − y) (y + z) (x + y − z) is odd

9. Even Odd | Algebra - Number Theory

Let x and y be positive integers such that x is prime and y is composite. Then,

(a)
(y – x) cannot be an even integer
(b)
xy cannot be an even integer
(c)
(x + y)/x cannot be an even integer
(d)
None of these

10. Even Odd | Algebra - Number Theory

If a, b and c are positive integers, then (a + b)(b + c)(c + a) is even or odd?

Mark your answer as:
1, if even
2, if odd
3, if the answer can’t be determined

Backspace

7 8 9 4 5 6 1 2 3 0 . -

Clear All Submit

11. Even Odd | Algebra - Number Theory

The sum of 100 natural numbers will be:

Type in your answer as
1 for even
2 for odd
3 for cannot be determined

Backspace

7 8 9 4 5 6 1 2 3 0 . -

Clear All Submit

12. Even Odd | Algebra - Number Theory

The sum of 100 odd natural numbers will be:

Type in your answer as
1 for even
2 for odd
3 for cannot be determined

Backspace

7 8 9 4 5 6 1 2 3 0 . -

Clear All Submit

13. Even Odd | Algebra - Number Theory

The sum of 77 even natural numbers will be:

Type in your answer as
1 for even
2 for odd
3 for cannot be determined

Backspace

7 8 9 4 5 6 1 2 3 0 . -

Clear All Submit

14. Even Odd | Algebra - Number Theory

Two different prime numbers X and Y, both are greater than 10, then which of the following must be true?

(a)
X + Y > 30
(b)
X - Y ≠ 25
(c)
Either (a) or (b)
(d)
None of these

15. Even Odd | Algebra - Number Theory

x, y and z are distinct prime numbers in ascending orders such that x + y + z is even. Which of the following is true?

(a)
(x - y) × z is even
(b)
(y - z) × x is odd
(c)
(z - x) × y is even
(d)
(x + y) × z is odd
(e)
None of these

Even Odd | Algebra - Number Theory

Feedback