While I & II can be true, examples can be found that show they are not always true (for example, 2²/2²is odd and 4²/2²is even).

III is always true – a square even number is always divisible by four, and the distributive property tell us that adding two numbers with a common factor gives a sum that also has that factor.

Sconsists of all even integers. If we were to increase each of these even numbers by 2, then we would get another set of even numbers, because adding 2 to an even number yields an even number. In other words,Talso consists entirely of even numbers.

In order to find the mean ofT, we would need to add up all of the elements inTand then divide by however many numbers are inT. If we were to add up all of the elements ofT, we would get an even number, because adding even numbers always gives another even number. However, even though the sum of the elements inTmust be even, if the number of elements inTwas an even number, it's possible that dividing the sum by the number of elements ofTwould be an odd number.

For example, let's assumeTconsists of the numbers 2, 4, 6, and 8. If we were to add up all of the elements ofT, we would get 20. We would then divide this by the number of elements inT, which in this case is 4. The mean ofTwould thus be 20/4 = 5, which is an odd number. Therefore, the mean ofTdoesn't have to be an even number.

Next, let's analyze the median ofT. Again, let's pretend thatTconsists of an even number of integers. In this case, we would need to find the average of the middle two numbers, which means we would add the two numbers, which gives us an even number, and then we would divide by two, which is another even number. The average of two even numbers doesn't have to be an even number, because dividing an even number by an even number can produce an odd number.

For example, let's pretendTconsists of the numbers 2, 4, 6, and 8. The median ofTwould thus be the average of 4 and 6. The average of 4 and 6 is (4+6)/2 = 5, which is an odd number. Therefore, the median ofTdoesn't have to be an even number.

Finally, let's examine the range ofT. The range is the difference between the smallest and the largest numbers inT, which both must be even. If we subtract an even number from another even number, we will always get an even number. Thus, the range ofTmust be an even number.

Of choices I, II, and III, only III must be true.

The answer is III only.

Take a known common factor of two and rewrite the fraction.

Dividing the number 143 into 16, the coefficient is 8 since:

There is a remainder of fifteen, which is.

Combining the coefficient and the remainder as a mixed fraction, this can be rewritten as:

The answer is: