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If K is a sequence of n consecutive integers, then what is the value

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Bunuel
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If K is a sequence of n consecutive integers, then what is the value [#permalink] New post   18 Jun 2020, 08:31
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If K is a sequence of n consecutive integers, then what is the value of n ?


(1) The sum of all terms in K is 21.
(2) The average (arithmetic mean) of all terms in K is less than 9.


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Re: If K is a sequence of n consecutive integers, then what is the value [#permalink] New post   18 Jun 2020, 08:43
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Bunuel wrote:
If K is a sequence of n consecutive integers, then what is the value of n ?


(1) The sum of all terms in K is 21.
(2) The average (arithmetic mean) of all terms in K is less than 9.


Question: n = ?

STatement 1: SUm of terms = 21
21 = 3*7
i.e. K = {0, 1, 2, 3, 4, 5, 6} i.e. n = 7
or K = {6, 7, 8} i.e. n = 3
NOT SUFFICIENT

STatement 2: The average (arithmetic mean) of all terms in K is less than 9
i.e. K = {0, 1, 2, 3, 4, 5, 6} i.e. n = 7
or K = {6, 7, 8} i.e. n = 3
NOT SUFFICIENT

COmbining teh statements

i.e. K = {0, 1, 2, 3, 4, 5, 6} i.e. n = 7
or K = {6, 7, 8} i.e. n = 3
NOT SUFFICIENT

Answer: Option E
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Re: If K is a sequence of n consecutive integers, then what is the value [#permalink] New post   19 Jun 2020, 04:11
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Bunuel wrote:
If K is a sequence of n consecutive integers, then what is the value of n ?


(1) The sum of all terms in K is 21.
(2) The average (arithmetic mean) of all terms in K is less than 9.


The sum of any list always equals n*average, where n is the number of terms. So from Statement 1, n*average = 21. But this is an equally spaced list, so average = median. So we know n*median = 21, and from this equation we can easily generate examples of lists that satisfy both Statements, by making n a divisor of 21. For example, n can be 3 and the median (and thus the average) can be 7, or n can be 7 and the median can be 3, among other possibilities (n can be 21 too, and if n is even, the median can be a non-integer so there are other possibilities besides these, but we don't need to consider them). So the answer is E.
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Re: If K is a sequence of n consecutive integers, then what is the value [#permalink] New post   19 Jun 2020, 05:00
1. The sum of all terms in K is 21.
>> 1+2+3+4+5+6=21
or
6+7+8= 21 (n=3)
or
21(n=1)
Not sufficient

2. The average (arithmetic mean) of all terms in K is less than 9.
>>1+2+3+4+5 (average = 3)
or
1+2+3+4= 10/4= 2.5(average)

Not sufficient

Both 1 and 2:
>> 1+2+3+4+5+6=21
or
6+7+8= 21
Not sufficient

Option E
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Re: If K is a sequence of n consecutive integers, then what is the value [#permalink]
19 Jun 2020, 05:00
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