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# Retirement

## Question

The retirement age in Bolandia will be raised from 66 to 67 over two years: every six months the minimum age will jump up by 3 months. Anyone over the retirement age on the date they apply will immediately get a free retired-person’s bus pass.

How much younger could one person with a free retired-person’s bus pass be than someone not able to get one?

A  It’s not possible to be younger.

B  Just under 3 months.

C  Just under 6 months.

D  Just under 1 year

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Hi bonanova, I can assure you it's no homework, but then again why should you believe me?   I found the problem interesting and I wanted to share it.

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It's not possible to be younger. (?) :S

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Hi bonanova, I can assure you it's no homework, but then again why should you believe me?   I found the problem interesting and I wanted to share it.

I believe you, antel0pe, simply because you say so. Multiple choice is a fav of teachers.

Thanks for contributing.

Because my answer is totally intuitive.

I'd def pick C or D - must have an answer, and B can't be right.

Of the two I'd pick D.

The reason is the C would be easier to imagine.

D makes the better puzzle.

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Hi bonanova, I can assure you it's no homework, but then again why should you believe me? I found the problem interesting and I wanted to share it.

I believe you, antel0pe, simply because you say so. Multiple choice is a fav of teachers.

Thanks for contributing.

Because my answer is totally intuitive.

I'd def pick C or D - must have an answer, and B can't be right.

Of the two I'd pick D.

The reason is the C would be easier to imagine.

D makes the better puzzle.

Nice meta argument, bonanova.

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Let the younger person apply for a bus pass on the same day he reaches 66, and this day happens immediately before the day the minimum age becomes 67. On that same day, let the older person be two days shy of 67. On the subsequent day, the older 66-year-old would not be permitted to apply for a bus pass, as the minimum age would be 67, and he would still be shy by 1 day. Thus, the answer is D, the younger would be just under 1 year younger and have a free bus pass, while the elder could not get one (until the next day).

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Let the younger person apply for a bus pass on the same day he reaches 66, and this day happens immediately before the day the minimum age becomes 67. On that same day, let the older person be two days shy of 67. On the subsequent day, the older 66-year-old would not be permitted to apply for a bus pass, as the minimum age would be 67, and he would still be shy by 1 day. Thus, the answer is D, the younger would be just under 1 year younger and have a free bus pass, while the elder could not get one (until the next day).

This is incorrect because the minimum requirement only advances three months at a time. It does not suddenly jump forward by a year.

However, by the same reasoning, a person can be younger by just under three months. The answer is B.

Edited by gavinksong
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Let the younger person apply for a bus pass on the same day he reaches 66, and this day happens immediately before the day the minimum age becomes 67. On that same day, let the older person be two days shy of 67. On the subsequent day, the older 66-year-old would not be permitted to apply for a bus pass, as the minimum age would be 67, and he would still be shy by 1 day. Thus, the answer is D, the younger would be just under 1 year younger and have a free bus pass, while the elder could not get one (until the next day).

This is incorrect because the minimum requirement only advances three months at a time. It does not suddenly jump forward by a year.

However, by the same reasoning, a person can be younger by just under three months. The answer is B.

As a person does not necessarily apply for the free bus pass when he reaches retirement age, it matters not the interval of advancement, but at what point (day) it changes. The 3-month intervals only represent a cycle. The unit (day) prior to the point of change is the point open to a given minimum age, and then is closed to that age the day following. As age is measured in years -- not 3 month intervals, the maximum length between two ages of the same age would be under 1 year. What occurs is that this maximum span of age for two 66-year-olds, though not the same two 66-year-olds as they all age during the intervals, happens 4 times in the two year cycle.

Edited by DejMar
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The answer is B. gavinksong is correct, and DejMar also deserves some credit for providing the reasoning behind it.

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I apologize to gavinksong, he is correct.  I guess lack of sleep had my mind thinking a bit off.

Consider the regulation required a minimum age of 66 years and 9 months for the bus pass. Let the younger reach this minimum on December 31 of the second year of Bolandia's minimum age schedule. The following day, January 1 of the third year, the minimum age would be 67. The maximum age the elder could be and not be able to apply for the bus pass at this time, would be an age of 66 years, 11 months and a day short of another month. Thus the maximum age differences between the elder and younger is (B) just under 3 months (66yr 11mo ~30da  -  66yr 9mo 0 da = 0yr 2mo ~30da).

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