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We are to find if Fe > 1/2;
Statement 1,
Two-thirds of the boxes in the shipment are fragile.
F = 2/3; This alone is not sufficient as it does not mention anything about the boxes having electronics
F - Fragile Boxes
Statement 2,
(2) Four-fifths of the boxes in the shipment contain electronics.
E = 4/5; This alone is not sufficient as it does not mention anything whether the boxes are fragile or non fragile.
E - Boxes with electronics
Taking Statements 1 & 2 together,
F = 2/3, E = 4/5
Taking LCM, we get F = 10/15 & NF = 5/15; NF is not fragile.
E = 4/5 = 12/15
Now out of 12 boxes with E, if 5 was in NF boxes, there still would be 7 boxes with E that are marked F;
Now to answer the question "Did more than half of the fragile boxes contain electronics?", since number of F boxes is 10, 7/10 > 1/2 and therefore, together the statements are sufficient
Correct option is Option C
Statement 1,
Two-thirds of the boxes in the shipment are fragile.
F = 2/3; This alone is not sufficient as it does not mention anything about the boxes having electronics
F - Fragile Boxes
Statement 2,
(2) Four-fifths of the boxes in the shipment contain electronics.
E = 4/5; This alone is not sufficient as it does not mention anything whether the boxes are fragile or non fragile.
E - Boxes with electronics
Taking Statements 1 & 2 together,
F = 2/3, E = 4/5
Taking LCM, we get F = 10/15 & NF = 5/15; NF is not fragile.
E = 4/5 = 12/15
Now out of 12 boxes with E, if 5 was in NF boxes, there still would be 7 boxes with E that are marked F;
Now to answer the question "Did more than half of the fragile boxes contain electronics?", since number of F boxes is 10, 7/10 > 1/2 and therefore, together the statements are sufficient
Correct option is Option C
