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13 Jun 2025, 06:34
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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:
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61% (02:30) correct
39%
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If A and B are non-zero numbers such that AB > 0, 2A + B < 0, and 1/A < 1/B , which of the following must be true?
(A) |A - B| < |A| - |B|
(B) |A - B| = |A| - |B|
(C) |A - B| > |A| - |B|
(D) |A - B| ≥ |A| - |B|
(E) |A - B| ≤ |A| - |B|
(A) |A - B| < |A| - |B|
(B) |A - B| = |A| - |B|
(C) |A - B| > |A| - |B|
(D) |A - B| ≥ |A| - |B|
(E) |A - B| ≤ |A| - |B|
13 Jun 2025, 14:18
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siddhantvarma
If A and B are non-zero numbers such that AB > 0, 2A + B < 0, and 1/A < 1/B , which of the following must be true?
(A) |A - B| < |A| - |B|
(B) |A - B| = |A| - |B|
(C) |A - B| > |A| - |B|
(D) |A - B| ≥ |A| - |B|
(E) |A - B| ≤ |A| - |B|
AB > 0, and 2A + B < 0 => from here we can infer that A, and B both have to be negative.(A) |A - B| < |A| - |B|
(B) |A - B| = |A| - |B|
(C) |A - B| > |A| - |B|
(D) |A - B| ≥ |A| - |B|
(E) |A - B| ≤ |A| - |B|
1/A < 1/B => this is true when A = -0.1 and B = -0.5; so let's test the options with these values.
(A) LHS = 0.6, RHS = -0.4, we proved LHS is not less than RHS, so |A - B| < |A| - |B| can be false.
(B) Same as above, it does not have to be equal.
(D) and (E) have an equality sign too, but we proved that it doesn't have to be equal.
So, the only correct option remains is (C)
Answer C.
15 Jun 2025, 21:37
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AB>0 and 2A+B<0, so A,B<0.
1/A < 1/B, so B<A<0.
Replace A=-a; B=-b with b>a.
|A|-|B| = a-b
|A-B| = |-a-(-b)| = |b-a| = b-a > a-b
So: |A-B| > |A|-|B|
Can also pick example values:
A=-0.25, B=-0.5
|A|-|B|= 0.25 - 0.5
|A-B|=|-0.25 -(-0.5)|= 0.5 - 0.25 > 0.25 - 0.5 > |A|-|B|
Answer: C
1/A < 1/B, so B<A<0.
Replace A=-a; B=-b with b>a.
|A|-|B| = a-b
|A-B| = |-a-(-b)| = |b-a| = b-a > a-b
So: |A-B| > |A|-|B|
Can also pick example values:
A=-0.25, B=-0.5
|A|-|B|= 0.25 - 0.5
|A-B|=|-0.25 -(-0.5)|= 0.5 - 0.25 > 0.25 - 0.5 > |A|-|B|
Answer: C
