I have a math problem....?

Question

My first language is Chinese, so i don`t really understand this question at all, can someone plz help me ?

A set of numbers has a range of 20. A second set of numbers has a range of 30. The two sets of numbers are combined into a new set.

a)What is the smallest possible range of the new set? Explain

b)Can you state a value for the greatest possible range of the new set? Explain.

Answer 1

If a set of numbers has a range of 20, it means the difference between the highest and lowest numbers in the set is twenty...so the numbers could range from 1 to 20, or 129 to 148 (for example).

a.) If the values of all the numbers in the first set lie within the range of the numbers in the second set, then the smallest possible range of the new set is achieved, which would be 30. (Ex: Set 1: 10-29 Set 2: 5-34. Combined Set Range: 5-34, range 30)

b.) Since the range does not tell whether or not any numbers are in common, it is possible that one range is as low as you want and the other as high as you want...this means that their range could be as far as you like, as so there is no value for the greatest possible range.

Answer 2

The range of a set of numbers is the largest one minus the smallest one. E.g. the range of {83, 26, 75, 32, 11, 42} is 83 - 11 = 72. You can also think of it as the largest value you get by subtracting one element from another.

(a) We know in the second set there are two numbers that are 30 apart, so those two numbers will be in the new set and will still be 30 apart. So the range of the new set is at least 30. If the elements of the first set are all between the smallest and largest values of the second set, the range of the new set will be 30, otherwise it will be larger.

(b) No, there is no upper limit to the range of the new set. For instance, let the first set be {0, 20} and the other set be {x-30, x}. The combined set is {0, 20, x-30, x}; for x>30 the smallest element will be 0 and the largest will be x, so the range of the combined set will be x. So we can make the combined range as large as we like; there is no upper bound.

Answer 3

The range is the largest number minus the smallest number in the set. So for the first set, the largest number minus the smallest number gives you 20. For the second, it gives you 30.
The first question is saying if you combine both sets of numbers into one big set, what is the smallest possible range? In other words, when you do the largest number minus the smallest number of the new set, what is the smallest possible value?
The second question is asking for the greatest possible value of the range of the new set.

Answer 4

a) If you were given only integers for the set of numbers, The range is still 30. It is impossible to find a smaller range because no matter what, you will always have the smallest number of set 2 be in the new set. If the smallest number of the 1st set was smaller than the smallest number of set 2, the range will be highest number of set 2 or set 1 minus that number. If that were to be, subtracting from set 2 will always be >30 Subtracting from set 1 will be useless because If the the smallest digit of set one were The smallest possible is thus 30
The greatest possible is infinity.
No matter what you'll get:
high#set1 or set2 - small#set1 or set2 in which the small number can approach a number near -infinity and the high number can be near infinity.

Answer 5

the first part would be 30- the smallest possible range. Because the set with the range of 20 could "fit" inside the one with the range of thirty.

The second part in a little trickier, so someone else can have a stab at that one.

Answer 6

the smallest possible range is 30
assume set 1 is something like (0,10,20) and set 2 is (0,10,30)
combine and you get (0,0,10,10,20,30) or a range of 30-0 or 30

the greatest possible range is infinite
also imagine the set 1 of (0,10,20) and set 2 is (infinity-30, infinity-10, infinity)
combine and you get from 0 to infinity, or an infinite maximum range

Answer 7

a) 30
The set of numbers in the first set could all fall within the numbers of the second set. So the minimum set of numbers would be the larger of the two sets.

b) 20 + 30 = 50
If the set of numbers in both sets are totally different, then there would be 50 different numbers.