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

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Math Expert
Joined: 02 Sep 2009
Posts: 43810
Half the people on a bus get off at each stop after the first, and no [#permalink]

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23 Jan 2015, 06:05
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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.
[Reveal] Spoiler: OA

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Math Expert
Joined: 02 Aug 2009
Posts: 5652
Re: Half the people on a bus get off at each stop after the first, and no [#permalink]

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23 Jan 2015, 06:09
ans is B 64...
7th stop only one was left and in each preceding stop twice the nos ... there were so 6 stops before 7th
so 2^6= 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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29 Jan 2015, 00:35
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KUDOS

Let "x" be the people initially on the bus:

Stop Number ................................ People got down

1 ........................................................ $$\frac{x}{2}$$

2 .......................................................... $$\frac{x}{4} = \frac{x}{2^2}$$

3 ......................................................... $$\frac{x}{8} = \frac{x}{2^3}$$

For the seventh stop, people got down would be $$= \frac{x}{2^7} = 1$$

x = 128

People alighted on the first stop $$= \frac{128}{2} = 64$$
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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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29 Jan 2015, 12:32
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]

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02 Feb 2018, 11:26
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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04 Feb 2018, 11:59
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] 04 Feb 2018, 11:59
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