Half the people

[BTGmoderatorDC]

Half the people on a bus get off at each stop after the first, and no one gets on after the first stop. If only one person gets off at stop number 7, how many people got on at the first stop?

A. 128
B. 64
C. 32
D. 16
E. 8

Can some experts set up the best formulas in this?

OA B

[GMATGuruNY]

Half the people on a bus get off at each stop after the first, and no one gets on after the first stop. If only one person gets off at stop number 7, how many people got on at the first stop?

A. 128
B. 64
C. 32
D. 16
E. 8

The prompt should indicate that the bus contains no passengers when it leaves the station.
We can PLUG IN THE ANSWERS, which represent the number of passengers picked up at the first stop.
At each subsequent stop, the number of passengers decreases by 1/2.
When the correct answer is plugged in, one person will disembark at the 7th stop.

B: 64
2nd stop --> 32 passengers
3rd stop --> 16 passengers
4th stop --> 8 passengers
5th stop --> 4 passengers
6th stop --> 2 passengers
7th stop --> 1 passenger
Success!
At the 7th stop, the number of passengers decreases from 2 to 1, implying that 1 passenger disembarks at the 7th stop.

The correct answer is B.

[ErikaPrepScholar]

Another approach to this question is to work backward. We know that at each stop, half the number of people who are on the bus get off of the bus, while half of the people stay on the bus. So before any stop, there are twice as many people on the bus as the number of people who leave the bus. Similarly, before any stop, there are twice as many people on the bus as the number of people who stay on the bus.

So if one person gets off at the 7th stop, there must have been two people (twice as many) on the bus after the 6th stop:

7th stop --> 1 person
6th stop --> 2 people

If 2 people stay on the bus after the 6th stop, there must have been 4 people (twice as many) on the bus after the 5th stop:

5th stop --> 4 people

We can keep working backward, doubling the number of people until we get to the first stop:

4th stop --> 8 people
3rd stop --> 16 people
2nd stop --> 32 people
1st stop --> 64 people

So the correct answer is B.

[Scott@TargetTestPrep]

Half the people on a bus get off at each stop after the first, and no one gets on after the first stop. If only one person gets off at stop number 7, how many people got on at the first stop?

A. 128
B. 64
C. 32
D. 16
E. 8

We can work backward to solve this problem. If only 1 person gets off at stop 7, there must be 2 people who get off at stop 6, 4 at stop 5, 8 at stop 4, 16 at stop 3 and 32 at stop 2. Notice that at stop 7, there must be 1 person left on the bus also, thus the total number of people who got on the bus at stop 1 is:

1 + 1 + 2 + 4 + 8 + 16 + 32 = 64

Answer: B