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If a and b are integers such that 5 ≥ a > 1 and b ≥ – 2, x then which of the following cannot be the value of a – b?
- a)–5
- b)–3
- c)2
- d)7
- e)8
Correct answer is option 'E'. Can you explain this answer?
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Most Upvoted Answer
If a and b are integers such that 5 ≥ a > 1 and b ≥ – 2...
Given:
1. 5 ≥ a > 1
2. b ≥ –2
To find the maximum value of a – b, we should choose the largest possible value for a and the smallest possible value for b.
1. 5 ≥ a > 1
2. b ≥ –2
To find the maximum value of a – b, we should choose the largest possible value for a and the smallest possible value for b.
Max value of a: Since 5 ≥ a > 1, the largest possible value for a is 5.
Min value of b: Since b ≥ –2, the smallest possible value for b is –2.
Therefore, the maximum value of a – b is 5 - (-2) = 7.
To find the minimum value of a – b, we should choose the smallest possible value for a and the largest possible value for b.
Min value of a: Since 5 ≥ a > 1, the smallest possible value for a is 2.
Max value of b: Since b ≥ –2, there is no restriction on the maximum value of b.
Therefore, the minimum value of a – b is 2 - (-2) = 4.
So, the range of possible values for a – b is 4 ≤ a – b ≤ 7.
Now let's analyze the given answer choices:
A. –5: This value is within the range of possible values (4 ≤ a – b ≤ 7).
B. –3: This value is within the range of possible values (4 ≤ a – b ≤ 7).
C. 2: This value is within the range of possible values (4 ≤ a – b ≤ 7).
D. 7: This value is within the range of possible values (4 ≤ a – b ≤ 7).
E. 8: This value is NOT within the range of possible values (4 ≤ a – b ≤ 7).
B. –3: This value is within the range of possible values (4 ≤ a – b ≤ 7).
C. 2: This value is within the range of possible values (4 ≤ a – b ≤ 7).
D. 7: This value is within the range of possible values (4 ≤ a – b ≤ 7).
E. 8: This value is NOT within the range of possible values (4 ≤ a – b ≤ 7).
Therefore, the answer is E. The value 8 cannot be the result of a – b based on the given conditions.
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If a and b are integers such that 5 ≥ a > 1 and b ≥ – 2, x then which of the following cannot be the value of a – b?a)–5b)–3c)2d)7e)8Correct answer is option 'E'. Can you explain this answer?
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