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Difficulty:
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20%
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A shipment of 70 items is to be divided into three lots. How many pieces are in the largest of the three lots?
(1) The number of items in the largest lot is equal to the sum of the number of items of the other two lots.
(2) The smallest lot contains 10 items.
_________________
(1) The number of items in the largest lot is equal to the sum of the number of items of the other two lots.
(2) The smallest lot contains 10 items.
_________________
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Aks111
Joined: 13 Mar 2017
Last visit: 08 Jul 2026
Posts: 144
Location: India
Schools: ISB '23 Rotman '24 Ross '24
WE:Information Technology (Consulting)
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Schools: ISB '23 Rotman '24 Ross '24
Posts: 144
A shipment of 70 items is to be divided into three lots. How many pieces are in the largest of the three lots?
Let the 3 lots contain be a, b, and 70-(a+b) pieces and assume largest lot has 70-(a+b) pieces.
(1) The number of items in the largest lot is equal to the sum of the number of items of the other two lots.
=> 70-(a+b) = a+b
=> 70 = 2(a+b) => a+b = 35
Therefore, the largest lot has 35 pieces.
Statement 1 alone is sufficient.
(2) The smallest lot contains 10 items.
=> This implies that the remaining two lots contain a total of 60 pieces. So, the largest lot can contain anywhere between 49 and 31 pieces.
Statement 2 alone is not sufficient.
Answer: A
Let the 3 lots contain be a, b, and 70-(a+b) pieces and assume largest lot has 70-(a+b) pieces.
(1) The number of items in the largest lot is equal to the sum of the number of items of the other two lots.
=> 70-(a+b) = a+b
=> 70 = 2(a+b) => a+b = 35
Therefore, the largest lot has 35 pieces.
Statement 1 alone is sufficient.
(2) The smallest lot contains 10 items.
=> This implies that the remaining two lots contain a total of 60 pieces. So, the largest lot can contain anywhere between 49 and 31 pieces.
Statement 2 alone is not sufficient.
Answer: A
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