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# If the set S consists of five consecutive positive integers, what is..

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If the set S consists of five consecutive positive integers, what is..  [#permalink]

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22 May 2016, 23:07
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If the set $$S$$ consists of five consecutive positive integers, what is the sum of these five integers?

(1) The integer 11 is in $$S$$, but 10 is not in $$S$$.
(2) The sum of the even integers in $$S$$ is 26
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Re: If the set S consists of five consecutive positive integers, what is..  [#permalink]

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16 Jul 2016, 00:03
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nalinnair wrote:
If the set $$S$$ consists of five consecutive positive integers, what is the sum of these five integers?

(1) The integer 11 is in $$S$$, but 10 is not in $$S$$.
(2) The sum of the even integers in $$S$$ is 26

(1) The integer 11 is in $$S$$, but 10 is not in $$S$$.
Since number are consecutive, it there cannot be any skipping among the number. If 11 is there, then the series should start with 11
s={11,12,13,14,15}; 12 and 14 are even
SUFFICIENT

(2) The sum of the even integers in $$S$$ is 26
Now there are total of 5 integers. there are two possibilities
OEOEO OR EOEOE
OEOEO means two consecutive even ; sum of these is 26
==>E+(E+2)=26 ==>E=12, second even = 14
EOEOE means there are three consective even numbers
E+(E+2)+(E+4)=26
==>3E=20
==>E=20/3 NOT ACCEPTABLE because its not an integer value.

SO in any case both cases gives unique values

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Re: If the set S consists of five consecutive positive integers, what is..  [#permalink]

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23 May 2016, 00:09
1
nalinnair wrote:
If the set $$S$$ consists of five consecutive positive integers, what is the sum of these five integers?

(1) The integer 11 is in $$S$$, but 10 is not in $$S$$.
(2) The sum of the even integers in $$S$$ is 26

Statement 1: The integer 11 is in S, but 10 is not in S
This means the integers start from 11
The integers will be 11, 12, 13, 14, 15
We can find out the sum.
SUFFICIENT

NOTE: We do not need to find out the actual sum.

Statement 2: The sum of the even integers in S is 26
The only possible series is 11, 12, 13, 14, 15
We can find out the sum
SUFFICIENT

Correct Option: D
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Re: If the set S consists of five consecutive positive integers, what is..  [#permalink]

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13 Nov 2016, 23:05
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Sorry to bring this one back. By consecutive, do we just assume they mean x, x+1, x+2 or anything that has a pattern? ie. x+2, x+5, x+8...?
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Re: If the set S consists of five consecutive positive integers, what is..  [#permalink]

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14 Nov 2016, 00:08
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Smileyface123 wrote:
Sorry to bring this one back. By consecutive, do we just assume they mean x, x+1, x+2 or anything that has a pattern? ie. x+2, x+5, x+8...?

Since the question states 5 consecutive positive numbers, it means x, x+1, x+2....
Else, it would have been indicated about the pattern.
Hope it helps.

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Re: If the set S consists of five consecutive positive integers, what is..  [#permalink]

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24 Nov 2016, 03:28
Statement 1 : The integer 11 is in S, but 10 is not in S = It means it has to start from 11. Hence the count would start from 11,12,13,14,15 = Sufficient

Statement 2 : The sum of the even integers in SS is 26 = In this case only one set can be formed . 11,12,13,14,15 and in this sum of even numbers are 26 hence Sufficient.

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Re: If the set S consists of five consecutive positive integers, what is..  [#permalink]

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20 Sep 2018, 06:10
Smileyface123 wrote:
Sorry to bring this one back. By consecutive, do we just assume they mean x, x+1, x+2 or anything that has a pattern? ie. x+2, x+5, x+8...?

Hello dear Smileyface123

By consecutive integers the question will always mean a series of numbers, for example (1,2,3,4,5,6,....) or (10,11,12,13,14,...) or it can be any series with a common difference ( CD ) of 1.
So yes, they actually mean x, x+1, x+2, x+3 and so on.

On the other hand, x+2, x+5, x+8, x+11...and so on would be considered an evenly spaced set, which you can see has a common difference of 3 here.
Other examples of evenly spaced set :
1. x, x+10, x+20, x+30 and so on. CD = 10
2. 3,6,9,12,15..and so on. CD = 3 (series is a multiple of 3)
3. xy, xy +15, xy + 30, xy + 45...and so on. CD = 15

P.S - Set of consecutive numbers is always an evenly spaced set, but not vice versa.

I hope this helps.
Re: If the set S consists of five consecutive positive integers, what is.. &nbs [#permalink] 20 Sep 2018, 06:10
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# If the set S consists of five consecutive positive integers, what is..

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