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

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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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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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:

GMAT assassins aren't born, they're made,
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!

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).

GMAT assassins aren't born, they're made,
Rich

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.

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.

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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Let there be 2P and 1T per province. (Total P = 10, each province has 1/10th of 10 = 1T)
Therefore, fraction of traditionalists = \(\frac{(1*5)}{(2*5)+(1*5)}\)
\(=\frac{5}{15} = \frac{1}{3}\)

What makes me confused is the word "entirely" > "Each province consists entirely of Progressives and Traditionalists" so I thought each province suppose to have ONLY Progressive OR Traditionalists.

Hi bbb123,

The prompt tells us that "....EACH province consists ENTIRELY of Progressives AND Traditionalists".... meaning that each province includes a certain number of Progressives AND a certain number of Traditionalists... and NO OTHER types of people.

Based on what you described about your original interpretation of the prompt, were you able to get to any of the 5 answer choices?

One of the great aspects of certain PS questions on the GMAT is that if you misinterpret the prompt (or make a little math mistake), then you won't end up with any of the answers.... and THAT is proof that you made a mistake (so that you can go back and try to find/fix it). Unfortunately, other types of Quant questions include answers that are the RESULT of a little mistake that the writers anticipate that some Test-takers will make. This is one of the reasons why it's so important to do ALL of your work on your pad (and NEVER "in your head").

GMAT assassins aren't born, they're made,
Rich

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