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

Question

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

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ManifestDreamMBA · Answer

Half people get for 6 times by the time of stop 7
First stop has then 2^6 = 64

OR do it backwards

Stop1 - 64
Stop2 - 32
Stop3 - 16
Stop4 - 8
Stop5 - 4
Stop6 - 2
Stop7 - 1

Aabhash777 · Answer

t0 = a
t1 = a
t2 = a/2
...
t7 = a/ (2^6) = 1

a = 64

Ans B IMO

azizlake · Answer

At stop 7, half of the people (P/2) = 1
At stop 7, P = 2.
Doing it backwards:
Stop 6 = 4
Stop 5 = 8
....
Stop 1= 128 (A)

rohitz98 · Answer

Considering 1 person gets down at 7th stop and at each of next stop half people get down
then 2 get down at 6th
 4 get down at 5th
 8 get down at 4th
 16 get down at 3rd
 32 get down at 2nd 
 64 get down at 1st

Hence at the start there would have been 64 x 2 = 128 members on bus  Option A

Dereno · Answer

Let us work from backwards to arrive at exact value at the start.

Stop 7 = S7 = 1

S6 = 2* S7 = 2

S5 = 2*2 = 4

S4 = 4*2 = 8

S3 = 8*2 = 16

S2 = 16*2 = 32

S1 = 32*2 =64

Option B

Ayeka · Answer

Half of the people get off at each station. 
Station 7 = 1 
S6= 2*1= 2
S5= 2*2= 4
S4= 2*4= 8
S3= 2*8= 16 
S2= 2*16= 32 
S1= 2*32= 64 
64 people were in bus at Station 1.

Answer: B

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

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GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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My Rewards