From Statement 1, A is currently 33. Statement 2 confirms A is older than 25, thus sufficient.

Using the distance formula, the distance between P and Q is √((3-1)² + (3-1)²) = √8, which is less than 5.

Statement 1 indicates z is even since adding 1 to an even number results in an odd number.

From Statement 1, x > 10. From Statement 2, x < 15. Both statements together confirm x is greater than 10.

Statement 1 alone is not sufficient as m is negative. Statement 2 alone is not sufficient as n is positive. Together, they cannot confirm the product is positive.

From Statement 1, x/y = 4y/y = 4, which is greater than 2. Statement 2 confirms y = 2, thus sufficient.

From Statement 1, z < 10 implies z² < 100. Statement 2 does not contradict this, thus both statements confirm z² < 100.

From Statement 1 and Statement 2, a + b > 20 + 30 = 50, thus sufficient.

Statement 1 indicates k > 1. Statement 2 confirms k is prime. Together, they confirm k is a prime number.

From Statement 1, y < 20. From Statement 2, y > 16. Both statements confirm y is less than 20.

The conclusion is not valid because while no birds are fish, it does not imply that no birds are animals since birds can belong to a different category of animals.

The conclusion is valid because if no mammals lay eggs and all birds lay eggs, it follows that no birds can be mammals.

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

3x = 15, so x = 5.

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

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

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

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

This factors to (x + 3)(x + 3) = 0, so x = -3.

Subtract 4 from both sides: 3y = 15. Divide by 3: y = 5.

The conclusion is valid because if some cars are electric and all electric vehicles are eco-friendly, it follows that those cars that are electric must also be eco-friendly.

The conclusion is valid because if some fruits are apples and all apples are sweet, it follows that those fruits that are apples must also be sweet.

The conclusion is not valid because just because some teachers are not professors does not imply that those teachers are not educated.

Distance = (Speed of A + Speed of B) * Time = (60 km/h + 90 km/h) * 2 h = 150 km.

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

Factoring gives (x + 4)(x - 2) = 0, so x = -4 and x = 2.

This factors to (x + 2)(x + 2) = 0, so the double root is x = -2.

The pattern skips one letter each time: A (skip B) C (skip D) E (skip F) G, so next is I.

12 divided by 7 is 1 with a remainder of 5, so 12 mod 7 = 5.

15 divided by 4 equals 3.75.