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If a and b are integers, ab = −5, and a − b > 0
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25 Oct 2016, 13:15
25 Oct 2016, 13:15
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If a and b are integers, ab = −5, and a − b > 0, which of the following must be true?
I. \(a > -1\)
II. b is odd
III. \(|a|=5\)
A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III
I. \(a > -1\)
II. b is odd
III. \(|a|=5\)
A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III
Drill 2
Question: 9
Page: 287
Question: 9
Page: 287
Re: If a and b are integers, ab = −5, and a − b > 0
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25 Oct 2016, 13:17
25 Oct 2016, 13:17
2
Expert Reply
Explanation
If a and b are integers with a product of −5, then there are only 4 options: a = 5 and b = −1; a = −5 and b = 1; a = 1 and b = −5; and a = −1 and b = 5. The requirement that a − b > 0 eliminates the second and fourth options, leaving only a = 5 and b = −1 and a = 1 and b = −5. (I) and (II) are both true for these two cases and (III) is not true if a = 1, making choice C the answer.
If a and b are integers with a product of −5, then there are only 4 options: a = 5 and b = −1; a = −5 and b = 1; a = 1 and b = −5; and a = −1 and b = 5. The requirement that a − b > 0 eliminates the second and fourth options, leaving only a = 5 and b = −1 and a = 1 and b = −5. (I) and (II) are both true for these two cases and (III) is not true if a = 1, making choice C the answer.
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Re: If a and b are integers, ab = −5, and a − b > 0
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17 Nov 2016, 11:39
17 Nov 2016, 11:39
2
sandy wrote:
If a and b are integers, ab = −5, and a − b > 0, which of the following must be true?
I. a > -1
II. b is odd
III. |a| = 5
A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III
I. a > -1
II. b is odd
III. |a| = 5
A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III
GIVEN: a and b are integers, and ab = -5
Using integers, there are only four ways to get a product of -5:
case a: a = 1 and b = -5
case b: a = -1 and b = 5
case c: a = 5 and b = -1
case d: a = -5 and b = 1
HOWEVER, we're also told that a − b > 0
If we add b to both sides of that inequality, we see that a > b
If a must be greater than b, then we can rule out case b and case d.
This leaves us with only two possible cases:
case a: a = 1 and b = -5
case c: a = 5 and b = -1
Now check the statements:
I. a > -1
Since cases a and c BOTH confirm that a > -1, statement I MUST be true
II. b is odd
Since cases a and c BOTH confirm that b is odd, statement II MUST be true
III. |a| = 5
In case a, |a| = |1| = 1. So, statement III NEED NOT be true
Answer:
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