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?
a) x is greater than y
b) (y-x) is greater than 15
c) (y-x) is less than or equal to 15
d) (x+y) is greater than or equal to 65​

Answer 1

Given :  x is greater than or equal to 25 and y is less than or equal to 40

To Find : which one of the following is always correct?

a) x is greater than y

b) (y-x) is greater than 15

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

d) (x+y) is greater than or equal to 65​

Step-by-step explanation:

x is greater than or equal to 25

=> x ≥ 25

=> x = 25 + a   a ≥ 0

y is less than or equal to 40

=> y ≤ 40

=> y = 40 - b     b  ≥ 0

x is greater than y  - Not always true

as  25 < 40

y - x   =  40 - b  -  (25 + a)

= 15 - (b + a)  

b + a   ≥ 0   as a ≥ 0 ,  b  ≥ 0

Hence  15 - (b + a)    ≤ 15

so

y - x   ≤ 15

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

option C is correct

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