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07 Aug 2025, 05:37
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A department store received a shipment of two types of boxes on Monday: fragile and non-fragile. Did more than half of the fragile boxes contain electronics?
(1) Two-thirds of the boxes in the shipment are fragile.
(2) Four-fifths of the boxes in the shipment contain electronics.
(1) Two-thirds of the boxes in the shipment are fragile.
(2) Four-fifths of the boxes in the shipment contain electronics.
07 Aug 2025, 05:37
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Official Solution:
A department store received a shipment of two types of boxes on Monday: fragile and non-fragile. Did more than half of the fragile boxes contain electronics?
(1) Two-thirds of the boxes in the shipment are fragile.
This is insufficient, as we are given no information about how many boxes contain electronics.
(2) Four-fifths of the boxes in the shipment contain electronics.
If 80% (4/5) of the boxes were non-fragile and all of those contained electronics, then none of the fragile boxes would contain electronics (answer: NO). On the other hand, if 80% of the boxes were fragile and all of those contained electronics, then all fragile boxes would contain electronics (answer: YES). Not sufficient.
(1)+(2) Assume there are 15 boxes in total (LCM of 3 and 5).
From (1), we get that 10 fragile boxes and 5 non-fragile.
From (2), we get that 12 boxes contain electronics.
Even in the worst case where all 5 non-fragile boxes contain electronics, the remaining 7 electronics boxes must be among the 10 fragile boxes. So at least 7 out of 10 fragile boxes contain electronics, which is more than half.
Sufficient.
Answer: C
A department store received a shipment of two types of boxes on Monday: fragile and non-fragile. Did more than half of the fragile boxes contain electronics?
(1) Two-thirds of the boxes in the shipment are fragile.
This is insufficient, as we are given no information about how many boxes contain electronics.
(2) Four-fifths of the boxes in the shipment contain electronics.
If 80% (4/5) of the boxes were non-fragile and all of those contained electronics, then none of the fragile boxes would contain electronics (answer: NO). On the other hand, if 80% of the boxes were fragile and all of those contained electronics, then all fragile boxes would contain electronics (answer: YES). Not sufficient.
(1)+(2) Assume there are 15 boxes in total (LCM of 3 and 5).
From (1), we get that 10 fragile boxes and 5 non-fragile.
From (2), we get that 12 boxes contain electronics.
Even in the worst case where all 5 non-fragile boxes contain electronics, the remaining 7 electronics boxes must be among the 10 fragile boxes. So at least 7 out of 10 fragile boxes contain electronics, which is more than half.
Sufficient.
Answer: C
