x and y are two different positive numbers. For the statement "x + y is positive", tick the correct box.
Answer options:
A.
Always true
B.
Sometimes true
C.
Never true
How to approach this question
Consider the properties of positive numbers. A positive number is any number greater than zero.
If you take any positive number (x) and add it to any other positive number (y), will the result always be positive?
Try some examples:
- If x=2 and y=3, x+y = 5 (positive).
- If x=0.1 and y=0.5, x+y = 0.6 (positive).
Since adding two numbers greater than zero will always result in a number greater than zero, the statement is always true.
Full Answer
A.Always true✓ Correct
Always true
The question states that x and y are both positive numbers. This means x > 0 and y > 0.
When you add two numbers that are both greater than zero, the sum must also be greater than zero.
For example, let x = 5 and y = 10. Both are positive. x + y = 5 + 10 = 15, which is positive.
Let x = 0.1 and y = 100. Both are positive. x + y = 100.1, which is positive.
There is no case where adding two positive numbers can result in a negative or zero answer. Therefore, the statement "x + y is positive" is always true.
Common mistakes
✗ Thinking of cases with negative numbers, which are excluded by the question.
Expert