If x is greater than or equal to 25 and y is less than or equal to 40, then which one of the following is alwa

Question

If x is greater than or equal to 25 and y is less than or equal to 40, then which one of the following is always correct?

Accepted Answer

The given conditions are: 1. x is greater than or equal to 25 (x >= 25) 2. y is less than or equal to 40 (y <= 40) Let's analyze each option: A) x is greater than y This is not always correct. For example, if x = 25 and y = 40, then x is not greater than y. B) (y - x) is greater than 15 To find the maximum possible value of (y - x), we take the maximum possible y and the minimum possible x. Maximum y = 40 Minimum x = 25 So, the maximum value of (y - x) = 40 - 25 = 15. Since (y - x) can be 15, it is not always greater than 15. Hence, this is not always correct. C) (y - x) is less than or equal to 15 From the given conditions: y <= 40 x >= 25 which implies -x <= -25 (multiplying an inequality by -1 reverses the sign) Adding these two inequalities: y + (-x) <= 40 + (-25) y - x <= 15 This inequality is derived directly from the given conditions and is always true. Hence, this option is always correct. D) (x - y) is greater than or equal to 65 To find the minimum possible value of (x - y), we take the minimum possible x and the maximum possible y. Minimum x = 25 Maximum y = 40 So, the minimum value of (x - y) = 25 - 40 = -15. Since (x - y) can be -15, it is not always greater than or equal to 65. Hence, this is not always correct. Therefore, the only statement that is always correct is C.

Answer

x is greater than y

Answer

(y - x) is greater than 15

Answer

(y - x) is less than or equal to 15

Answer

(x - y) is greater than or equal to 65

If x is greater than or equal to 25 and y is less than or equal to 40, then which one of the following is always correct?

Explanation

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