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15 May 2025, 00:30
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
79% (01:29) correct
21%
(02:07)
wrong
based on 90
sessions
History
Date
Time
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Not Attempted Yet
If 0 > a > b, which of the following must be true?
A. a^2 > a * b
B. b^2 > a * b
C. b > a + 1
D. b > a - 1
E. b > a^2 * b
Gentle note to all experts and tutors: Please refrain from replying to this question until the Official Answer (OA) is revealed. Let students attempt to solve it first. You are all welcome to contribute posts after the OA is posted. Thank you all for your cooperation!
A. a^2 > a * b
B. b^2 > a * b
C. b > a + 1
D. b > a - 1
E. b > a^2 * b
Gentle note to all experts and tutors: Please refrain from replying to this question until the Official Answer (OA) is revealed. Let students attempt to solve it first. You are all welcome to contribute posts after the OA is posted. Thank you all for your cooperation!
15 May 2025, 01:12
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which inequality must be true given \(0 > a > b\).
Since \(a\) and \(b\) are negative with \(a\) less negative than \(b\), we test each option with \(a = -1\), \(b = -2\) to find counterexamples.
Option A: \(a^2 > a \cdot b\)
\((-1)^2 = 1\), \((-1) \cdot (-2) = 2\). Since \(1 < 2\), \(a^2 \not> a \cdot b\). False.
Option B: \(b^2 > a \cdot b\)
\((-2)^2 = 4\), \((-1) \cdot (-2) = 2\). Since \(4 > 2\), try another pair, \(a = -1\), \(b = -3\): \((-3)^2 = 9\), \((-1) \cdot (-3) = 3\), \(9 > 3\). Holds here, but we need it to always be true. Let's keep checking the other options if they too pass or fail the test.
Option C: \(b > a + 1\)
\(-2 \not> -1 + 1 = 0\). False.
Option D: \(b > a - 1\)
\(-2 > -1 - 1 = -2\), false (equality, not greater).
Option E: \(b > a^2 \cdot b\)
\(-2 \not> (-1)^2 \cdot (-2) = -2\) ( False, equality)
Answer: B
Since \(a\) and \(b\) are negative with \(a\) less negative than \(b\), we test each option with \(a = -1\), \(b = -2\) to find counterexamples.
Option A: \(a^2 > a \cdot b\)
\((-1)^2 = 1\), \((-1) \cdot (-2) = 2\). Since \(1 < 2\), \(a^2 \not> a \cdot b\). False.
Option B: \(b^2 > a \cdot b\)
\((-2)^2 = 4\), \((-1) \cdot (-2) = 2\). Since \(4 > 2\), try another pair, \(a = -1\), \(b = -3\): \((-3)^2 = 9\), \((-1) \cdot (-3) = 3\), \(9 > 3\). Holds here, but we need it to always be true. Let's keep checking the other options if they too pass or fail the test.
Option C: \(b > a + 1\)
\(-2 \not> -1 + 1 = 0\). False.
Option D: \(b > a - 1\)
\(-2 > -1 - 1 = -2\), false (equality, not greater).
Option E: \(b > a^2 \cdot b\)
\(-2 \not> (-1)^2 \cdot (-2) = -2\) ( False, equality)
Answer: B
15 May 2025, 01:51
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Both a and b are negative
A. a^2 > a * b
a(a-b)>0
a<b
False
B. b^2 > a * b
b(b-a)>0
b<a
True
C. b > a + 1
If a is already greater than b then adding 1 to a will still do not change the relation. This will be always false
D. b > a - 1
Imagine on number line, b<a and then b>a-1 only if |b-a|<1
This cannot be true always
E. b > a^2 * b
b(a^2 -1)<0
a^2 -1>0
a^2>1
This cannot be true always
Answer B
A. a^2 > a * b
a(a-b)>0
a<b
False
B. b^2 > a * b
b(b-a)>0
b<a
True
C. b > a + 1
If a is already greater than b then adding 1 to a will still do not change the relation. This will be always false
D. b > a - 1
Imagine on number line, b<a and then b>a-1 only if |b-a|<1
This cannot be true always
E. b > a^2 * b
b(a^2 -1)<0
a^2 -1>0
a^2>1
This cannot be true always
Answer B
Bunuel
If 0 > a > b, which of the following must be true?
A. a^2 > a * b
B. b^2 > a * b
C. b > a + 1
D. b > a - 1
E. b > a^2 * b
Gentle note to all experts and tutors: Please refrain from replying to this question until the Official Answer (OA) is revealed. Let students attempt to solve it first. You are all welcome to contribute posts after the OA is posted. Thank you all for your cooperation!
A. a^2 > a * b
B. b^2 > a * b
C. b > a + 1
D. b > a - 1
E. b > a^2 * b
Gentle note to all experts and tutors: Please refrain from replying to this question until the Official Answer (OA) is revealed. Let students attempt to solve it first. You are all welcome to contribute posts after the OA is posted. Thank you all for your cooperation!
