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

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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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GMAT 1: 750 Q49 V43 Re: If the set S consists of five consecutive positive integers, what is..  [#permalink]

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

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

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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

Statement 1) provides us that 11 is the smallest value so it is sufficient.

From it we can also extend that 11, 12, 13, 14, 15 are the values.

Now statement 2) It tells us that the sum of even integers is 26.

which is basically 12 + 14 = 26. Solving the first statement gives us some insight for the second statement.

If we try even numbers such as 2,3,4,5,6

Sum of even = 12

if we try 4,5,6,7,8

Sum of even = 18

If we try 6,7,8,9,10

Sum of even = 24

This would give us some sense that it will not happen unless we have only two even numbers.

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

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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[/quote]

Ans- Let the nos be : a-2d, a-d, a, a+d, a+2d.

1. it means 1st no is 11 so other nos will be 12, 13, 14, 15. SUM DONE.
2. Two case EOEOE or OEOEO.
EOEOE = a-2d + a + a+2d = 26 --> 3a = 26 (fraction - not possible as only integers are permitted)
OEOEO = a-d +a+d = 26 ---->2a =26 ..... a=13. Other nos will be 11, 12, 14, 15. SUM DONE.

Hope it helps! Re: If the set S consists of five consecutive positive integers, what is..   [#permalink] 03 Aug 2019, 06:46
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