What could be the range of a set consisting of odd multiples of 7?
A. 21
B. 24
C. 35
D. 62
E. 70
The OA is E .
I don't understand this PS question. What is the range of a set of numbers? How can I find it with an infinite set?
Experts, I need your help, please.
Hi VJesus12,
Let's take a look at your question.
Range of a set is the difference between the largest value and the smallest value of that set.
We are asked to find the range of a set consisting of odd multiples of 7.
Odd multiples of 7 will be:
$$7\times1,\ 7\times3,\ 7\times5,\ 7\times7,\ ...,\ 7\times\left(2n+1\right)$$
Range = Largest Odd Multiple - Smallest Odd Multiple
$$Range=\left[7\times\left(2n+1\right)\right]-\left[7\times1\right]$$
$$Range=7\left[\left(2n+1\right)-1\right]$$
$$Range=7\left[2n+1-1\right]$$
$$Range=7\left[2n\right]$$
2n represents an even number, therefore, range will be an even multiple of 7.
We need to check all the given options and find which one is an even multiple of 7.
Option
A: 21 = 7 x
3 ; 21 is an odd multiple of 7.
Option
B: 24; it is not a multiple of 7.
Option
C: 35 = 7 x
5 ; 35 is an odd multiple of 7.
Option
D: 62; It is not a multiple of 7.
Option
E: 70; 7 x
10 ; 70 is an even multiple of 7.
Which shows that the range of a set consisting of odd multiples of 7 is 70.
Therefore, Option
E is correct.
Hope it helps.
I am available if you'd like any follow up.
