ExpertEasy1 markMultiple Choice
AQA GCSE · Question 13.2 · Number
x and y are two different positive numbers. For the statement "x - y is negative", tick the correct box.
x and y are two different positive numbers. For the statement "x - y is negative", tick the correct box.
Answer options:
A.
Always true
B.
Sometimes true
C.
Never true
How to approach this question
Consider the statement "x - y is negative". This is equivalent to asking if x - y < 0, or x < y.
Since x and y are just two different positive numbers, it is possible for x to be smaller than y, or for y to be smaller than x.
- Case 1 (statement is true): Let x = 3 and y = 5. Both are positive. x - y = 3 - 5 = -2, which is negative.
- Case 2 (statement is false): Let x = 5 and y = 3. Both are positive. x - y = 5 - 3 = 2, which is positive.
Since the statement is true for some values and false for others, it is "Sometimes true".
Full Answer
B.Sometimes true✓ Correct
Sometimes true
The question states that x and y are two different positive numbers. We need to determine if the statement "x - y is negative" is always true, sometimes true, or never true.
The expression x - y will be negative if y is larger than x.
The expression x - y will be positive if x is larger than y.
Let's test two scenarios:
1. **Let x = 2 and y = 10.** Both are positive and different.
x - y = 2 - 10 = -8. The result is negative. So the statement can be true.
2. **Let x = 10 and y = 2.** Both are positive and different.
x - y = 10 - 2 = 8. The result is positive. So the statement can be false.
Because we have found a case where the statement is true and a case where it is false, the correct answer is "Sometimes true".
Common mistakes
✗ Assuming x is always bigger than y, or vice versa.\n✗ Forgetting that the numbers can be any positive values.
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