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

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What could be the range of a set consisting of odd multiples  [#permalink]

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New post Updated on: 09 Jul 2013, 06:56
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What could be the range of a set consisting of odd multiples of 7?

A. 21
B. 24
C. 35
D. 62
E. 70

Originally posted by dimitri92 on 27 May 2010, 01:48.
Last edited by Bunuel on 09 Jul 2013, 06:56, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: odd multiples of 7?  [#permalink]

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New post 31 May 2010, 07:33
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amitjash wrote:
I am sorry... I may sound a bit stupid but still i dont understand. First of all i dont understand what does it mean by range and why range must be even multiple of 7?


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 range of a set is the difference between the largest and smallest elements of a set.

Set consists of odd multiples of 7 (numbers of a type \(7*odd\)), so there can be following elements: ..., -7, 7, 21, 35, ...

The range of this set would be: \(7*odd_{max}-7*odd_{min}=7(odd_{max}-odd_{min})=7*even\), (as odd-odd=even). So the range is even multiple of 7.

Answer: E.

Hope it's clear.
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Re: odd multiples of 7?  [#permalink]

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New post 27 May 2010, 02:25
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E.

A set of odd multiples of 7 would be something like 7, 21, 35, 49....

The range would always be an even number multiple of 7.
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Re: odd multiples of 7?  [#permalink]

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New post 30 May 2010, 09:55
dimitri92 wrote:
What could be the range of a set consisting of odd multiples of 7?
a)21
b)24
c)35
d)62
e)70


I like the question.

The range of the set of multiples of 7 must be even multiple of 7. Which is only 70 among the answer choices.
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Re: odd multiples of 7?  [#permalink]

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New post 31 May 2010, 07:05
I am sorry... I may sound a bit stupid but still i dont understand. First of all i dont understand what does it mean by range and why range must be even multiple of 7?
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Re: odd multiples of 7?  [#permalink]

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New post 01 Jun 2010, 05:29
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As I know range means : Largest no. - Smallest no. in a set.
And as per the question its asking what could be the range .

Odd multiples of 7 means 7 *(2k+1) ..so smallest in this set can me where k=0 i.e 7
and largest in this set can be 7*(2k+1) where k is some finite max number.
So Range = 7*(2k+1) - 7 = 14k . This range should be in the form of a multiple of 14 , and as per the options I can see only 70 is the multiple of 14 .

Answer E
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Re: odd multiples of 7?  [#permalink]

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New post 01 Jun 2010, 06:52
Thank you guys.... I really appreciate the job you are doing on this forum.. Keep it up...
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Re: odd multiples of 7?  [#permalink]

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New post 21 Jun 2010, 01:15
1
range= last number( which is odd number) -first number( which is odd number too)
in this case, range = odd number - odd number = even number.
this narrow the answer to b,d, e
from property of factor: a multiple of 7 - multiple of 7= multiple of 7
so 70 is the only multiple of 7 among b,d and e
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Re: odd multiples of 7?  [#permalink]

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New post 22 Jun 2010, 01:43
Here you go:

Range = the difference between the greatest and the smallest numbers in the sequence. Our sequence is odd and is a multiple of 7. Every number in that sequence can be represented like this: 7*(2n+1) where n is any positive integer.

Range = 7*(2m + 1) - 7*(2n + 1) = 7*2*(m-n) = 14 * (m-n).

m, n - any positive integers

The answer must be divisible by 14, which is only 70.

The correct answer is E.
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Re: odd multiples of 7?  [#permalink]

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New post 22 Jun 2010, 08:19
[quote="Fistail] I like the question.

The range of the set of multiples of 7 must be even multiple of 7. Which is only 70 among the answer choices.[/quote]

I was banging my head against the wall after reading the question. Thanks Fistail, never occured to me that it can be so easy to answer.
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Re: odd multiples of 7?  [#permalink]

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New post 23 Jun 2010, 11:59
you have taken 2n+1 as it says to find the odd no. range.....what if he says to find the even no. range then how should we move........
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Re: What could be the range of a set consisting of odd multiples  [#permalink]

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New post 23 Dec 2013, 10:06
dimitri92 wrote:
What could be the range of a set consisting of odd multiples of 7?

A. 21
B. 24
C. 35
D. 62
E. 70


Well it has to be a multiple of 7 and since Odd - Odd = Even, then only E fits the bill

Hope it helps
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J :)
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Re: What could be the range of a set consisting of odd multiples  [#permalink]

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New post 22 Jun 2015, 19:13
Bunuel wrote:
amitjash wrote:
I am sorry... I may sound a bit stupid but still i dont understand. First of all i dont understand what does it mean by range and why range must be even multiple of 7?


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 range of a set is the difference between the largest and smallest elements of a set.

Set consists of odd multiples of 7 (numbers of a type \(7*odd\)), so there can be following elements: ..., -7, 7, 21, 35, ...

The range of this set would be: \(7*odd_{max}-7*odd_{min}=7(odd_{max}-odd_{min})=7*even\), (as odd-odd=even). So the range is even multiple of 7.

Answer: E.

Hope it's clear.

Thank you!
I really like your post :thumbup:
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Re: What could be the range of a set consisting of odd multiples  [#permalink]

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New post 13 Dec 2016, 09:22
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Re: What could be the range of a set consisting of odd multiples  [#permalink]

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New post 15 Oct 2019, 20:00
dimitri92 wrote:
What could be the range of a set consisting of odd multiples of 7?

A. 21
B. 24
C. 35
D. 62
E. 70


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
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Re: What could be the range of a set consisting of odd multiples   [#permalink] 15 Oct 2019, 20:00
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