What could be the range of a set consisting of odd multiples

[VJesus12]

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.

[harshitpuri]

ACTUALLY THE QUESTION 'IS WHICH ONE OF THEM CAN ONLY BE RANGE OF A SET CONTAINING ODD MULTIPLES OF 7?'

So the range of odd multiples of 7 is even multiple of 7 for ex-
(7,21)=14
7,35=28
so out of the options only 70 is even multiple of 7.\i.e 10

[EconomistGMATTutor]

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.

[Scott@TargetTestPrep]

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.

Since the range of a set of numbers is defined as the difference between the largest number and the smallest number in the set, we can just calculate the difference between odd multiples of 7. For example, the difference between 21 and 7 is 14, between 35 and 7 is 28, between 77 and 21 is 56.

From the above examples, we see that the difference between two odd multiples of 7 must be an even multiple of 7 or, equivalently, a multiple of 14. Therefore, the correct answer is 70 since it is the only number in the answer choices that is a multiple of 14.

Answer: E