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# Half the people on a bus get off at each stop after the first, and no

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Re: Half the people on a bus get off at each stop after the first, and no [#permalink]
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7-5-6-4-3-2-1

1-2-4-8-16-32-64

I did this way. I know will take more time if the number were big.
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Re: Half the people on a bus get off at each stop after the first, and no [#permalink]
Bunuel wrote:
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

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Re: Half the people on a bus get off at each stop after the first, and no [#permalink]
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Bunuel wrote:
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

Kudos for a correct solution.

Let X be the number of people who got on to bus at Stop 1.
From stop 2 we have, $$\frac{x}{2} + \frac{x}{4} + \frac{x}{8} + \frac{x}{16} + \frac{x}{32} + \frac{x}{64} + \frac{x}{128.}$$
Given that $$\frac{x}{64} = 1.$$
Hence, $$X = 64$$.
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Re: Half the people on a bus get off at each stop after the first, and no [#permalink]
Hi All,

Since the answer choices are numbers, one of those numbers MUST be the number of people who got on the bus at the first bus stop. This means we can TEST THE ANSWERS.

We're told that there were 7 stops (counting the first stop where people got ON the bus). We're also told that HALF the people who were on the bus got off at each ensuing bus stop, until the 7th stop where just 1 person got off.

If 128 get on the bus at the 1st stop….
2nd stop: 64 get off, 64 still on
3rd stop: 32 get off, 32 still on
4th stop: 16 get off, 16 still on
5th stop: 8 get off, 8 still on
6th stop: 4 get off, 4 still on
7th stop: 2 get off, 2 still on……

In this scenario, 2 people got off the bus at the 7th stop. The question tells us that only 1 person was supposed to get off. This tells us that the original number of people is NOT 128 - this number is too big. So Answer A is NOT correct AND we know that there needs to be fewer people at the beginning. Since Answer A gives us DOUBLE the number of people getting off at the 7th stop, it's likely that starting with HALF of 128 will give us the correct answer.

If you create the same table (above), but start with the number 64, you will have 1 person getting off the bus at the 7th stop. This is a match for what the question describes.

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Re: Half the people on a bus get off at each stop after the first, and no [#permalink]
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Re: Half the people on a bus get off at each stop after the first, and no [#permalink]
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