Final Answer:
The two fractions that satisfy the given conditions are 3/5 and 4/7.
So, option B is correct.
Step-by-step explanation:
Let's analyze the options one by one with the given conditions:
Condition 1:
Each fraction must be greater than 2/5.
Condition 2:
The product of the fractions should be less than 2/5.
Condition 3:
Each fraction must also be greater than 1/2.
Condition 4:
The product of the fractions must be greater than 1/2.
Now let's check the options against these conditions:
A) 3/4 and 3/8
3/4 is greater than 2/5 and greater than 1/2, so it passes Conditions 1 and 3.
3/8 is greater than 2/5 but not greater than 1/2, so it fails Condition 3.
For their product: (3/4) * (3/8) = 9/32, which is less than 2/5. This part passes Condition 2, but since one of the fractions did not pass all the conditions, this set does not satisfy the overall requirements.
B) 3/5 and 4/7
3/5 is greater than 2/5 and greater than 1/2, so it passes Conditions 1 and 3.
4/7 is greater than 2/5 and greater than 1/2, so it passes Conditions 1 and 3.
For their product: (3/5) * (4/7) = 12/35, which is less than 2/5 and greater than 1/2, passing Conditions 2 and 4.
Thus, option B satisfies all conditions.
C) 2/3 and 5/6
Both fractions are greater than 2/5 and greater than 1/2, passing Conditions 1 and 3.
For their product: (2/3) * (5/6) = 5/9, which is greater than 2/5 but also greater than 1/2, it fails Condition 2.
D) 1/2 and 1/3
1/2 is greater than 2/5 but not greater than 1/2, so it fails Condition 3.
1/3 is not greater than 2/5 and not greater than 1/2, so it fails both Conditions 1 and 3.
Their product, (1/2) * (1/3) = 1/6, which is less than 2/5, passing Condition 2, but since the fractions fail multiple conditions, this set does not satisfy the overall requirements.
Therefore, the answer to find two fractions that satisfy all given conditions is B) 3/5 and 4/7.