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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?

AB > 0; (A>0 & B>0) or (A<0 & B<0)

Case 1: A>0 & B>0
2A + B < 0 ; Not feasible

Case 2: A<0 & B<0
2A + B<0; feasible
1/A - 1/B < 0
(B-A)/AB < 0
B - A < 0
A - B > 0; A>B
|A-B| = A-B = -|A|+|B| = - (|A|-|B|)

IMO C
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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 : This tells us that either both A & B are + ve or both are -ve.
2A + B < 0 : This tells us both A & B are - ve.
1/A < 1/B : This means A > B

Notice that LHS and RHS of all options is same, only sign differs.
Keeping in mind the above constraints lets assume A = -2 and B = -3.

LHS: |A-B| = |-2-(-3)| = |-2+3| = |1| = 1
RHS: |A| - |B| = |-2| - |-3| = 2-3 = -1

Thus, LHS > RHS... Option C.
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