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Each bus can carry at most 24 passengers from a train station to a certain company. All passengers boarding the buses are traveling to the company. This morning, there were x passengers, and 4 buses were needed to take all of the passengers to the company. How many buses will be needed next Monday, when there will be 2x + 90 passengers?
(1) Last Monday, when there were 2x passengers, 8 buses were needed.
(2) On another day, when there were 10x passengers, 40 buses were needed.
(1) Last Monday, when there were 2x passengers, 8 buses were needed.
(2) On another day, when there were 10x passengers, 40 buses were needed.
02 Mar 2026, 23:58
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kevincan
The max pax in a bus is 24.
So, as per question stem, for 4 buses, we need x passengers.
So, we can say for sure there was (3*24) + a pax in 4 buses.
The number of pax in 4 buses = 72 + a = x
Where a can hold values from 1 to 24.
The number of pax x lies between 73 and 96.
We need to find :
Quote:
Statement 1:
Last Monday, when there were 2x passengers, 8 buses were needed.
X = (3*24)+a
2x = 2*(3*24)+2a = 6*24 + 2a
6 buses plus the remaining 2a pax in 2 buses.
If a is between 1 to 12, we need 1 more buses.
If a is between 13 and 24, we need 2 more buses.
Hence, value of a cannot be found for certain. Insufficient
Statement 2:
On another day, when there were 10x passengers, 40 buses were needed.
x = (3*24)+a
10x = 10*(3*24)+ 10a = 30 *24 + 10 a = 30 buses + 10 a pax accommodated in 10 buses.
For 10 buses, the pax count is max 240, minimum 217 ( slightly greater than 9*24).
So, the difference between 240-217 = 23 which holds a single bus only.
If 10a =240, then a =24
If 10a = 217, then a = 21.7
We need to find : 2x +90
2*(3*24+a)+90 = 6*24 + 2a + 90 = 6*24 + 2a + (3*24)+18 = (9*24)+2a +18
So, we have 9 full buses, plus 2a+18
If a = 24, then 9 full buses + 2*24 + 18 = 11 full buses + 18 = 12 buses over all.
If a = 21.7 , then 9 full buses + (2*21.7)+ 18 = 9 full bus + (2*24) + 13.4 = 11 full buses + 13.4 = 12 buses over all.
Hence, we need 12 buses.
Sufficient
Option B
04 Mar 2026, 23:53
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i think the question should mention that each bus has to be filled for it to travel to the company
