## Discussion

Suppose half the people on a bus exit at each stop and no additional passengers board the bus. If on the third stop the next to last person exits the bus, then how many people were on the bus?

*This question is included in Nova Math - Problem Set B: Substitution (Plugging in), question #3

(A) | 20 |

(B) | ... |

(C) | ... |

(D) | ... |

(E) | ... |

(F) | ... |

The solution is

I dont understand at all how the count got to 2 passengers by rhe second stop !

Deena, in this case we work backward from the 3rd stop. One hint is given on the 3rd stop: "next to last person exits", which means that there are 2 people left before that next to last person exits.

The problem gave another hint / rule: "half the people exit at each stop". That means on the 2nd stop, before half the people exit, there must have been 2 x 2 or 4 people. After the exit, there are 2 people moving on to the 3rd stop.

Which brings us to stop number 1: there must have been 4 x 2 = 8 people before the stop.

The problem gave another hint / rule: "half the people exit at each stop". That means on the 2nd stop, before half the people exit, there must have been 2 x 2 or 4 people. After the exit, there are 2 people moving on to the 3rd stop.

Which brings us to stop number 1: there must have been 4 x 2 = 8 people before the stop.

Posted: 11/29/2012 20:41

I don't understand how the answer was 8

Iessa, please read the explanation and the thread. Your question had been answered before.

Iessa, please read the explanation and the thread. Your question had been answered before.

Posted: 09/24/2013 07:11

Don't understand how you got 8 if they didn't say how many passengers

Hi Lakeisha,

For efficiency, we started with 8 because we knew it was the answer!

If we started with (A) [20 people], then on the first stop half the people will exit. So, there are now 10 people left on the bus. After the second stop, half of the remaining 10 people will exit, so there are now 5 left. After the third stop, half of the remaining 5 people will exit the bus. But this is not possible because you cannot have 2 1/2 (= 5/2) people exit the bus.

For Choice (B), after the first stop, 8 people will remain on the bus. After the second stop, 4 people will remain on the bus. After the third stop, 2 people will remain on the bus. Since there are still two people on the bus, the NEXT TO LAST person has not yet exited the bus. So, there could not have been 16 people on the bus.

Choices (D) and (E) can be eliminated in similar ways.

Nova Press

For efficiency, we started with 8 because we knew it was the answer!

If we started with (A) [20 people], then on the first stop half the people will exit. So, there are now 10 people left on the bus. After the second stop, half of the remaining 10 people will exit, so there are now 5 left. After the third stop, half of the remaining 5 people will exit the bus. But this is not possible because you cannot have 2 1/2 (= 5/2) people exit the bus.

For Choice (B), after the first stop, 8 people will remain on the bus. After the second stop, 4 people will remain on the bus. After the third stop, 2 people will remain on the bus. Since there are still two people on the bus, the NEXT TO LAST person has not yet exited the bus. So, there could not have been 16 people on the bus.

Choices (D) and (E) can be eliminated in similar ways.

Nova Press