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Representation in a local community board is based on the [#permalink]

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10 Jan 2010, 13:32

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Representation in a local community board is based on the community’s population, with 25 board members representing the first 500,000 people, and each additional board member representing an additional 30,000 people. Is the population of the town less than 500,000?

(1) There were 23 members on the community board. (2) If the population were three times as large, the community board would have had 51 members.

Re: Representation in a local community board is based on the [#permalink]

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11 Jan 2010, 00:52

sagarsabnis wrote:

Representation in a local community board is based on the community’s population, with 25 board members representing the first 500,000 people, and each additional board member representing an additional 30,000 people. Is the population of the town less than 500,000?

(1) There were 23 members on the community board. (2) If the population were three times as large, the community board would have had 51 members.

here each of the 1st 25 members represent 20000 people [500000/25]

stmnt1 - 23 members will represent 23 * 20000 = 460000 people which is less than 500000. hence suff

stmnt2- total board members is 51 so 1st 25 represent 500000 people and remaining 26 will represent 26 * 30000 = 780000. So total population is 500000 + 780000 = 12 80 000 people. this is 3times the actual population so we have 1280000/3 which is less than 500000 as the actual population. hence suff

Re: Representation in a local community board is based on the [#permalink]

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11 Jan 2010, 17:16

Expert's post

kp1811 wrote:

sagarsabnis wrote:

Representation in a local community board is based on the community’s population, with 25 board members representing the first 500,000 people, and each additional board member representing an additional 30,000 people. Is the population of the town less than 500,000?

(1) There were 23 members on the community board. (2) If the population were three times as large, the community board would have had 51 members.

here each of the 1st 25 members represent 20000 people [500000/25]

stmnt1 - 23 members will represent 23 * 20000 = 460000 people which is less than 500000. hence suff

stmnt2- total board members is 51 so 1st 25 represent 500000 people and remaining 26 will represent 26 * 30000 = 780000. So total population is 500000 + 780000 = 12 80 000 people. this is 3times the actual population so we have 1280000/3 which is less than 500000 as the actual population. hence suff

D

The answer is correct but there is a little problem with solution:

For (1). As there are less than 25 members, there is less then 500,000 population;

For (2). Consider this statement to be as follows: If the population were three times as large, the community board would have had 58 members.

What would be the answer in this case? _________________

Re: Representation in a local community board is based on the [#permalink]

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12 Jan 2010, 18:50

Expert's post

sagarsabnis wrote:

Whats the problem in the solution given by kp1811

@Bunuel for your question for st2 the total comes as 246,000 apprx so again st2 is suff...

If statement (2) were: "If the population were three times as large, the community board would have had 58 members."

Then according the solution given in previous posts the answer would be: 25 members represent first 500,00; Remaining 33 will represent 33*30,000=990,000. Total 500,00+990,000=1,490,000. As this is 3 times the current population, so we have 1,490,000/3=~497,000<500,000, hence sufficient.

But this would be wrong. As 1,490,000 will be the lowest possible population for 58 members, the highest would be 1,490,000+29,999=1,519,999. Meaning that 25 members for 500,000 plus 990,000 for 33 remaining members plus 29,999 of population with no member at all. In the case of highest possible population for 58 members, current population would be 1,519,999/3=~506,666>500,000. We have two answers one less than 500,000 another more. Not sufficient.

In our original question range for 51 members would be from 1,280,000(500,00+26*30,000) to 1,309,999(500,00+26*30,000+29,999). But as 1,309,999 (highest possible population for 51 members) divided by 3 is also less than 500,000 this didn't affect the final answer.

We are given that after the first 500,000 people, each board member represents an additional 30,000 people. So, there will be a maximum of 30,000 - 1 = 29,999 people who can be without a board member.

For example, if there are 25 board members, the lowest population will be 500,000 and the highest population for the same number of board members would be 500,000 + (30,000 - 1) = 529,999.

Hence in this question when we are given the number of board members, we would need to consider the range of the population to see if the total population is less than 500,000 or not.

Re: Representation in a local community board is based on the [#permalink]

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26 May 2015, 22:18

SivaKumarP wrote:

sagarsabnis wrote:

ohhh... i didnt thought of 29,999 thanks a lot bunuel...

can anyone please explain from where did 29,999 has come?

For every 30,000 people, there is 1 member in the board. Now what if there are 30,000 +29,999 = 59,999 people ?? There will stillbe only 1 member in the board who represents these 59,999 people.

Had there been 30,000 + 30,000 = 60,000 people, only then can 2 members represent these 60,000 people in the board.

Also, had there been only 29,999 people, then "NO" member can represent these 29,999 people in the board, since 29,999 < 30,000.

Please take a look at Bunuel's question and his explanation to get a clear idea.

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