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

Question

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

LogicGuru1 · Accepted Answer

(1) The integer 11 is in  S , but 10 is not in  S .
Since numbers in the series S are consecutive, there cannot be any skipping among the number. 
If 10 is not there but 11 is there, then the series should start with 11
S={11,12,13,14,15}; 
out of these 12 and 14 are even
SUM OF THE SERIES CAN BE EASILY FOUND (11+12+13+14+15)
 SUFFICIENT

(2) The sum of the even integers in  S  is 26
Since there are total of 5 consecutive integers in the series so there are two possibilities

O+E+O+E+O=SUM TOTAL of the series (In this case there are two even numbers in the series)
E+O+E+O+E= SUM TOTAL of the series (In this case there are three even numbers in the series)

O+E+O+E+ O means two consecutive even number and the sum of these even number = 26
==>E+(E+2)=26 
==>2E=24
==>E=12
==> therefore First even = 12 ; second even (12+2) =14

EOEOE means there are three consecutive even numbers 
E+(E+2)+(E+4)=26
==>3E+6=26
==>3E=26-6
==> 3E= 20
==> E=20/3
==> E= 6.666666666

This value of E is NOT ACCEPTABLE because its not an integer value. Therefore it means that the Series E+O+E+O+ E cannot exist.

Therefore we that only two even number exist in series S such that their sum = 26 which we know are 12 & 14 (since only 12 +14 can yield 26)

SO in any case both cases gives unique values

ANSWER IS D

OptimusPrepJanielle · Answer

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

Smileyface123 · Answer

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...?

souvonik2k · Answer

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.

If u liked my post, press kudos!

Awaited · Answer

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.

Answer : D

Radheya · Answer

Hello dear  Smileyface123 
I hope you face always matches with your username!

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.

Salsanousi · Answer

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.

Answer choice D

anujpal · Answer

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

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!

unraveled · Answer

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 .
If 10 is not there, then 9 is not there as well. So we need to chose the numbers on other side i.e 11, 12, 13, 14 and 15.
Sum = 13 * 5 = 65

SUFFICIENT.

(2) The sum of the even integers in  S  is 26
26 = Even AND
Likely possibilities of numbers are 
1. O + E + O + E + O = O
2. E + O + E + O + E = E

But note that sum of 3 consecutive(or equally spaced numbers of the form (n-x)*n*(n+x) where x = 2, 4, 6...) evens would be an even number multiple of 3 i.e. 3*Even(3n). However, since 26 is not a multiple of 3, 2nd option is impossible.
Thus, only possible numbers are 12 and 14 that sum 26.

SUFFICIENT.

Answer D.

Basshead · Answer

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.

This tells us integers 11, 12, 13, 14, 15 are in the set. SUFFICIENT.

(2) The sum of the even integers in S is 26

This tells us the even integers are 12 and 14, meaning the other integers are 11, 13, 15. SUFFICIENT.

Also, if you don't see this right away, you can look at statement 1 as a clue. We can't get 26 any other way.

Answer is D.

ScottTargetTestPrep · Answer

Solution:

Question Stem Analysis:

We need to determine the sum of the 5 consecutive integers in set S.

Statement One Alone:

Since 11 is in S and 10 is not, 11 must be the smallest integer in S. Therefore, the sum of the 5 integers in S is 11 + 12 + 13 + 14 + 15 = 65. Statement one alone is sufficient.

Statement Two Alone:

Since there are 5 consecutive integers, either 2 of them are even (if the smallest integer is odd) or 3 of them are even (if the smallest integer is even). If 2 of them are even, we can let the smallest even integer be x, so the larger one is x + 2. We can create the equation:

x + x + 2 = 26

2x = 24

x = 12

This means the integers are 11, 12, 13, 14, and 15, and their sum is 65. If 3 of them are even, we can let the smallest even integer be y, so the larger two are y + 2 and y + 4, respectively. We can create the equation:

y + y + 2 + y + 4 = 26

3y = 20

y = 20/3

Since 20/3 is not an integer (let alone an even integer), it means there can’t be 3 even integers in S. So the only possible sum of the integers in S is 65. Statement two alone is sufficient.

Answer: D

BLTN · Answer

Dear  ScottTargetTestPrep 
how can we decipher from the prompt that the set cannot be the following
1, 3, 5, 7 , 9 
2 , 4, 6, 8, 10
or constitutive multiple of 5 etc.

In such cases 1st statement would be insufficient.

Thanks beforehand.

ScottTargetTestPrep · Answer

Because consecutive integers mean evenly spaced by one, not by two, which you show in your list.

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