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D
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Difficulty:
95%
(hard)
Question Stats:
40% (02:08) correct
60%
(02:01)
wrong
based on 80
sessions
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Over the course of a certain month, Olga, a saleswoman, sold 20 cars, and each of her 7 colleagues sold at least 1 car. Did Olga sell as many or more cars than at least 4 of her colleagues?
(1) The average (arithmetic mean) of the number of cars sold by Olga’s 7 colleagues is 12.
(2) The median of the number of cars sold by Olga’s 7 colleagues is 18.
(1) The average (arithmetic mean) of the number of cars sold by Olga’s 7 colleagues is 12.
(2) The median of the number of cars sold by Olga’s 7 colleagues is 18.
23 Jan 2026, 06:00
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ExpertsGlobal5
Given constraint Olga =20 , and the rest of the seven colleague sold ATLEAST 1 each.
We need to find.: Did Olga sell as many or more cars than at least 4 of her colleagues?
Statement 1:
The average (arithmetic mean) of the number of cars sold by Olga’s 7 colleagues is 12.
If arithmetic mean =12 for 7 colleagues. Then the total 🟰 12*7 = 84.
case 1: let’s allocate 21 for 4 persons, this amounts to 84. Leaving three colleagues with value 0 ( violating constraint at least 1).
Did Olga sell more than or equal to at least 4 of her colleagues? No
Case 2: Lets put 21 to three colleagues, amounting to 63. And we are left with 21 to be split among the rest of the 4 persons.
With worst case scenario of 1 each, we can get a combination of 18,1,1,1. So four persons are less than Olga. Hence, Yes.
Case 3: Lets allocate 20 to 4 persons and we are left with 4 to be allotted to three persons.
All are either equal to or lesser than Olga. Hence Yes.
Thus, Sufficient
Statement 2:
The median of the number of cars sold by Olga’s 7 colleagues is 18.
Median is 18, which means the 4th value is 18.
Considering the scenario of the first three values equal to 18, then we can be sure that 4 values are lesser than Olga.
Hence, Sufficient
Option D
25 Jan 2026, 10:15
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Explanation:
Hint: Statement (1): In worst case scenarios, the 7 colleagues sold {21, 21, 21, 18, 1, 1, 1} or {20, 20, 20, 20, 2, 1, 1} cars respectively; still, Olga’s sale exceeds or matches the sale by 4 of her colleagues.
Detailed explanation:
The number of cars sold by Olga = 20.
The number of cars sold by each of Olga’s 7 colleagues is at least 1.
We need to find whether the number of cars sold by Olga is greater than at least 4 of her colleagues.
Statement (1)
The average number of cars sold by Olga’s 7 colleagues is 12, which implies that the total number of cars sold = 7 x 12 = 84.
Since Olga sold 20 cars, for at least four of her colleagues to outsell her, each would need to sell a minimum of 21 cars. This would mean that these four colleagues collectively would have to sell 4 x 21 = 84 cars.
However, this scenario implies that the remaining three colleagues sold zero cars, which contradicts the given information that each colleague sold at least one car.
Therefore, it is not possible for at least four of her colleagues to sell more cars than she did.
It is possible to determine with certainty that Olga sold as many or more cars than at least 4 of her colleagues. Hence, Statement (1) is sufficient.
Statement (2)
Since the median number of cars sold by Olga's 7 colleagues is 18, it implies that when the number of cars sold by each colleague is arranged in ascending order, the first four colleagues will each have sold 18 or fewer cars.
It is possible to determine with certainty that Olga sold as many or more cars than at least 4 of her colleagues. Hence, Statement (2) is sufficient.
D is the correct answer choice.
