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A certain country is divided into 5 provinces. Each province consists

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A certain country is divided into 5 provinces. Each province consists  [#permalink]

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New post 28 Jul 2015, 13:54
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A certain country is divided into 5 provinces. Each province consists entirely of Progressives and Traditionalists. If each province contains the same number of Traditionalists and the number of Traditionalists in any given province is 1/10 the total number of Progressives in the entire country, what fraction of the country is Traditionalist?

A) 1/5
B) 1/3
C) 1/2
D) 2/3
E) 4/5

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Re: A certain country is divided into 5 provinces. Each province consists  [#permalink]

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New post 28 Jul 2015, 15:08
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Harley1980 wrote:
A certain country is divided into 5 provinces. Each province consists entirely of Progressives and Traditionalists. If each province contains the same number of Traditionalists and the number of Traditionalists in any given province is 1/10 the total number of Progressives in the entire country, what fraction of the country is Traditionalist?

A) 1/5
B) 1/3
C) 1/2
D) 2/3
E) 4/5

Dear Harley1980,
This is a great question, and I am happy to help. :-)

There is some number of Progressives in the country as a whole. Call that number P.

In each province, the number of traditionalists is P/10 = 0.1*P

In five provinces, the number of traditionalist would be that times five, 0.5*P. In other words, the number of traditionalist is half the number of progressives.

Let T be the total number of traditionalists. Then P = 2T, and the total population in the country is 3T. T is 1/3 of this. OA = (B).

Does all this make sense?
Mike :-)
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Re: A certain country is divided into 5 provinces. Each province consists  [#permalink]

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New post 28 Jul 2015, 15:12
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Harley1980 wrote:
A certain country is divided into 5 provinces. Each province consists entirely of Progressives and Traditionalists. If each province contains the same number of Traditionalists and the number of Traditionalists in any given province is 1/10 the total number of Progressives in the entire country, what fraction of the country is Traditionalist?

A) 1/5
B) 1/3
C) 1/2
D) 2/3
E) 4/5


Let T be the number of traditionalists in 1 province and P1, P2, P3,P4,P5 be the number of progressives in the 5 provinces.

Total P = P1+P2+P3+P4+P5

Per the question, T = P/10 ---> P =10T

Thus fraction of traditionalists = Total number of traditionalists / Total People = \(\frac{5T}{5T+P}\) =\(\frac{5T}{5T+10T}\) = 1/3. B is the correct answer.
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Re: A certain country is divided into 5 provinces. Each province consists  [#permalink]

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New post 28 Jul 2015, 20:20
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Hi All,

This question can be solved by TESTing VALUES.

We're given a series of facts to work with:
1) There are 5 provinces
2) Each province includes a certain number of Progressives and a certain number of Traditionalists
3) Each province has the SAME number of Traditionalists; the number of Traditionalists in each province = 1/10 the TOTAL number of Progressives in the ENTIRE COUNTRY.

We're asked 'what fraction of the COUNTRY is TRADITIONALISTS?'

If we say that each province has 10 Traditionalists in it, then we can calculate the TOTAL number of Progressives in the ENTIRE COUNTRY....

10 = (1/10)(ALL Progressives)
100 = All Progressives

Since there are 5 provinces, each with 10 Traditionalists in it, there are (5)(10) = 50 Total Traditionalists

50 Traditionalists + 100 Progressives = 150 Total people.

Since we're asked for the fraction that is Traditionalists.... 50/150 = 1/3

Final Answer:

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A certain country is divided into 5 provinces. Each province consists  [#permalink]

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New post Updated on: 22 Jan 2016, 23:07
EMPOWERgmatRichC wrote:
Hi All,

This question can be solved by TESTing VALUES.

We're given a series of facts to work with:
1) There are 5 provinces
2) Each province includes a certain number of Progressives and a certain number of Traditionalists
3) Each province has the SAME number of Traditionalists; the number of Traditionalists in each province = 1/10 the TOTAL number of Progressives in the ENTIRE COUNTRY.

We're asked 'what fraction of the COUNTRY is TRADITIONALISTS?'

If we say that each province has 10 Traditionalists in it, then we can calculate the TOTAL number of Progressives in the ENTIRE COUNTRY....

10 = (1/10)(ALL Progressives)
100 = All Progressives

Since there are 5 provinces, each with 10 Traditionalists in it, there are (5)(10) = 50 Total Traditionalists

50 Traditionalists + 100 Progressives = 150 Total people.

Since we're asked for the fraction that is Traditionalists.... 50/150 = 1/3

Final Answer:

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Rich


Hi Rich, I followed the same steps as you have mentioned above, but was'nt able get to the final answer. I have highlighted where i went wrong and I have a doubt: in the highlighted part are we allowed to plug in 10 for all the 5 province and then add 100 Progressives? I mean out of 5 provinces should'nt there be atleast one progressives? Please help!
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Originally posted by Sash143 on 22 Jan 2016, 13:24.
Last edited by Sash143 on 22 Jan 2016, 23:07, edited 1 time in total.
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Re: A certain country is divided into 5 provinces. Each province consists  [#permalink]

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New post 22 Jan 2016, 13:37
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Hi Sash143,

When TESTing VALUES on this question, you can use ANY number of Traditionalists (I simply chose 10 because it made all of the numbers 'round numbers'). The prompt tells us that the number of Traditionalists is the SAME in all 5 provinces, so you MUST multiply your Value by 5 (to find the TOTAL number of Traditionalists). Whatever number you Test ALSO impacts the TOTAL number of Progressives in the country (you have to multiply that Value by 10 to get the Total number of Progressives).

The prompts asks us to consider the WHOLE COUNTRY, so we don't actually have to count up the number of Traditionalists in each province (we already know THAT Total).

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Re: A certain country is divided into 5 provinces. Each province consists  [#permalink]

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New post 16 Sep 2016, 07:49
Harley1980 wrote:
A certain country is divided into 5 provinces. Each province consists entirely of Progressives and Traditionalists. If each province contains the same number of Traditionalists and the number of Traditionalists in any given province is 1/10 the total number of Progressives in the entire country, what fraction of the country is Traditionalist?

A) 1/5
B) 1/3
C) 1/2
D) 2/3
E) 4/5


traditionalists let's say is X in each province. 5 provinces = 5x.
let's say progressives in each province is Y. total progressives in all provinces = 5y.
we are told that x (traditionalists in each province) is equal to 1/10 of the total progressives (5y) so x=5y/10 or y/2. since we have 5x total = 5y/2.
the total number of population is thus 5y+5y/2 or 15y/2. now..we need to find the ratio of traditionalists to total number of people.
5y/2 divide by 15y/2 = 1/3. B.
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Re: A certain country is divided into 5 provinces. Each province consists  [#permalink]

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New post 16 Oct 2018, 00:06
This can definitely be done using the abstract method, but here I'm just sharing the number picking technique for this question:

Say there are 100 Progressives in the country.
This means that each province has 10 Traditionalists, so there are 50 Traditionalists in the whole country,
Hence the total population of the country: 100+50=150
The number of traditionalists amounts to 50/150 i.e. 1/3 of the total population.
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Re: A certain country is divided into 5 provinces. Each province consists  [#permalink]

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New post 16 Oct 2018, 00:19
Harley1980 wrote:
A certain country is divided into 5 provinces. Each province consists entirely of Progressives and Traditionalists. If each province contains the same number of Traditionalists and the number of Traditionalists in any given province is 1/10 the total number of Progressives in the entire country, what fraction of the country is Traditionalist?

A) 1/5
B) 1/3
C) 1/2
D) 2/3
E) 4/5



Take one line at a time:

A certain country is divided into 5 provinces.
- 5 provinces

Each province consists entirely of Progressives and Traditionalists. If each province contains the same number of Traditionalists
- Say each province has T traditionalists so total 5T traditionalists

and the number of Traditionalists in any given province is 1/10 the total number of Progressives in the entire country,
- T = (1/10)*Total Progressives
This means 5T = (5/10)*Total Progressives

what fraction of the country is Traditionalist?

Total Traditionalists = (1/2)*Total Progressives

Total Traditionalists/Total Progressives = 1/2

Total Traditionalists = 1/3 of All

Answer (B)
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Re: A certain country is divided into 5 provinces. Each province consists   [#permalink] 16 Oct 2018, 00:19
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