For these statements, the following is true : x is divisible by 28 and by 15. For each statement, say whether it must be true, could be true, or cannot be true.
x is divisible by 20.

Answer

To determine whether the statement "x is divisible by 20" must be true, could be true, or cannot be true given that "x is divisible by 28 and by 15", we can follow these steps:

### Step 1: Understand the divisibility of x
We know that:
- x is divisible by 28
- x is divisible by 15

### Step 2: Factor the numbers
Next, we can factor these numbers to understand their divisibility:
- 28 can be factored as \(4 \times 7\)
- 15 can be factored as \(5 \times 3\)

### Step 3: Determine divisibility by 4 and 5
Since x is divisible by 28, it must also be divisible by 4 (as \(28 = 4 \times 7\)).
Similarly, since x is divisible by 15, it must also be divisible by 5 (as \(15 = 5 \times 3\)).

### Step 4: Combine the results
Now that we have established that:
- x is divisible by 4
- x is divisible by 5

We can conclude that if x is divisible by both 4 and 5, then it must also be divisible by their product:
\[ 4 \times 5 = 20 \]

### Step 5: Conclusion
Therefore, since x is divisible by both 4 and 5, we conclude that x must be divisible by 20.

### Final Answer
The statement "x is divisible by 20" must be true.

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