Bunuel wrote:
If a < b and c < b, is abc < a ?
(1) ab < 0
(2) ac > 0
a < b and c < b or b < c
--> a < b < c
Question: Is abc < a ?
--> Is abc - a < 0
--> Is a(bc - 1) < 0
(1) ab < 0
For product to be negative, both should have opposite signs
--> Since a < b
a < 0 & b > 0. Also, c > 0 (Since c > b)
To Find: If a(bc - 1) < 0 or not
Since a < 0, bc - 1 should be greater than 1
We do not know anything about the values of b & c. Eg: b = 1/2 & c = 1, bc = 1/2 (<1); or if b = 2 & c = 3, bc = 6 (>1) -->
Insufficient(2) ac > 0
--> a > 0 & c > 0 or a < 0 & c < 0
Case 1: a > 0 & c > 0: --> b > 0
To Find: If a(bc - 1) < 0 or not
If a > 0, bc - 1 should be less than 0
We do not know anything about the values of b & c. Eg: b = 1/2 & c = 1, bc = 1/2 (<1); or if b = 2 & c = 3, bc = 6 (>1) -->
InsufficientCase 2: a < 0 & c < 0: --> b < 0
To Find: If a(bc - 1) < 0 or not
If a < 0, bc - 1 should be greater than 0
We do not know anything about the values of b & c. Eg: b = -1 & c = -1/2, bc = 1/2 (<1); or if b = -3 & c = -2, bc = 6 (>1) -->
InsufficientCombining (1) & (2),
a < 0 & b > 0; --> c > 0Since a < 0, bc - 1 should be greater than 0
We do not know anything about the values of b & c. Eg: b = 1/2 & c = 1, bc = 1/2 (<1); or if b = 2 & c = 3, bc = 6 (>1) -->
InsufficientOption E
Highlighted part doesn't satisfy the Second statement (ac >0) hence it is incorrect
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