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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, 05:56
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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, 00:48.
Last edited by Bunuel on 09 Jul 2013, 05:56, 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, 06:33
23
7
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, 01:25
9
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, 08:55
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, 06:05
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, 04:29
4
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, 05:52
Thank you guys.... I really appreciate the job you are doing on this forum.. Keep it up...
Thanks Again for your great help...
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Re: odd multiples of 7?  [#permalink]

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New post 21 Jun 2010, 00:15
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, 00:43
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, 07:19
[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, 10:59
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, 09:06
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
Cheers!
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, 18:13
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, 08:22
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Re: What could be the range of a set consisting of odd multiples  [#permalink]

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New post 25 Feb 2018, 04:29
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Re: What could be the range of a set consisting of odd multiples &nbs [#permalink] 25 Feb 2018, 04:29
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