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DILR Practice Set – 12

DILR Practice Set – 12

Refer to the data below and answer the ques ons that follow.


D1, D2, D3, D4, D5, D6, D7, D8, D9, D10, D11 and D12 are the twelve districts in three states namely S1, S2 and S3 in a country named Taveuni. Sugarcane is produced only in these districts of Taveuni.

The following table gives informa on on the total produc on of sugarcane in the twelve districts of Taveuni, when expressed as a percent of the total produc on of sugarcane in the country.

image

The following table gives informa on on the total produc on of sugarcane in the three states of Taveuni, when expressed as a percent of the total produc on of sugarcane in the country.

image

It is known that each state has exactly four districts out of the twelve districts men oned. Each district can lie in only one state.

Please ensure your answer is entered accurately. Double-check your work.

1. If the district D3 is in state S2, in which state is the district D10 in?
  • S1
  • S2
  • S3
  • The district D3 cannot lie in state S2
It can be seen that the percent production in the twelve states are 2%, 3%, 5%, 6%, 7%, 8%, 9%, 10%, 11%, 12%, 13% and 14%. Three districts of state S1 together have total production of 47%. The sum of 47% can be obtained using four of the given numbers as follows: 1. 14% + 12% + 11% + 10% 2. 14% + 13% + 11% + 9% 3. 14% + 13% + 12% + 8% Three districts of state S3 together have total production of 18%. The sum of 18% can be obtained using four of the given numbers as follows: 1. 2% + 3% + 5% + 8% 2. 2% + 3% + 6% + 7% Combining these two, we get the following possibilities. image If D3 is in S2, possibility 3 is applicable. In that case, D10 is in state S1. Hence, [1].

Please ensure your answer is entered accurately. Double-check your work.

2. If the district D8 is in state S2, which state is the district D9 in?
  • S1
  • S2
  • S3
  • Cannot be determined
It can be seen that the percent production in the twelve states are 2%, 3%, 5%, 6%, 7%, 8%, 9%, 10%, 11%, 12%, 13% and 14%. Three districts of state S1 together have total production of 47%. The sum of 47% can be obtained using four of the given numbers as follows: 1. 14% + 12% + 11% + 10% 2. 14% + 13% + 11% + 9% 3. 14% + 13% + 12% + 8% Three districts of state S3 together have total production of 18%. The sum of 18% can be obtained using four of the given numbers as follows: 1. 2% + 3% + 5% + 8% 2. 2% + 3% + 6% + 7% Combining these two, we get the following possibilities. image If D8 is in S2, either possibility 1 or 2 is applicable. In possibility 1, D9 is in state S2 while in possibility 2, D9 is in state S1. Hence, [4].

Please ensure your answer is entered accurately. Double-check your work.

3. If the district D2 is not in state S2 and the district D5 is not in state S1, which state is the district D9 in?
  • S1
  • S2
  • S3
  • Cannot be determined
It can be seen that the percent production in the twelve states are 2%, 3%, 5%, 6%, 7%, 8%, 9%, 10%, 11%, 12%, 13% and 14%. Three districts of state S1 together have total production of 47%. The sum of 47% can be obtained using four of the given numbers as follows: 1. 14% + 12% + 11% + 10% 2. 14% + 13% + 11% + 9% 3. 14% + 13% + 12% + 8% Three districts of state S3 together have total production of 18%. The sum of 18% can be obtained using four of the given numbers as follows: 1. 2% + 3% + 5% + 8% 2. 2% + 3% + 6% + 7% Combining these two, we get the following possibilities. image If the district D2 is not in state S2 and the district D5 is not in state S1, possibility 4 is applicable. Hence, [2].

Please ensure your answer is entered accurately. Double-check your work.

4. For how many districts out of 12, can the state in which they fall in can be uniquely determined?
  • 0
  • 1
  • 2
  • More than 2
It can be seen that the percent production in the twelve states are 2%, 3%, 5%, 6%, 7%, 8%, 9%, 10%, 11%, 12%, 13% and 14%. Three districts of state S1 together have total production of 47%. The sum of 47% can be obtained using four of the given numbers as follows: 1. 14% + 12% + 11% + 10% 2. 14% + 13% + 11% + 9% 3. 14% + 13% + 12% + 8% Three districts of state S3 together have total production of 18%. The sum of 18% can be obtained using four of the given numbers as follows: 1. 2% + 3% + 5% + 8% 2. 2% + 3% + 6% + 7% Combining these two, we get the following possibilities. image We can determine that the districts D4 and D11 are definitely in the state S3, while the district D12 is in the state S1. Hence, [4].
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