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M12-21

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M12-21  [#permalink]

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New post 16 Sep 2014, 00:47
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How many integers in a group of 5 consecutive positive integers are divisible by 4?


(1) The median of these numbers is odd

(2) The average (arithmetic mean) of these numbers is a prime number

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Re M12-21  [#permalink]

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New post 16 Sep 2014, 00:47
Official Solution:


How many integers in a group of 5 consecutive positive integers are divisible by 4?

(1) The median of these numbers is odd. The median of the set with odd number of terms is just a middle term, thus our set of 5 consecutive numbers is: {Odd, Even, Odd, Even, Odd}. Out of 2 consecutive even integers only one is a multiple of 4. Sufficient.

(2) The average (arithmetic mean) of these numbers is a prime number. In any evenly spaced set the arithmetic mean (average) is equal to the median, so we have that mean=median=prime. Since it's not possible that median=2=even, (in this case not all 5 numbers will be positive), then median=odd prime, and we have the same case as above. Sufficient.


Answer: D
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Re: M12-21  [#permalink]

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New post 05 Jan 2016, 14:07
I understood solution, but I just wanted to know why exactly does 1 of the number will be divisible by 4? Is their any kind of rule here that i have missed. I took various different sets of positive consecutive numbers with median being odd and in all cases,one of the number was divisible by 4.
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Re: M12-21  [#permalink]

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New post 06 Jan 2016, 08:13
rhio wrote:
I understood solution, but I just wanted to know why exactly does 1 of the number will be divisible by 4? Is their any kind of rule here that i have missed. I took various different sets of positive consecutive numbers with median being odd and in all cases,one of the number was divisible by 4.


I think this is explained in the solution: out of 2 consecutive even integers only one is a multiple of 4.
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Re: M12-21  [#permalink]

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New post 12 Jan 2016, 05:40
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rhio wrote:
I understood solution, but I just wanted to know why exactly does 1 of the number will be divisible by 4? Is their any kind of rule here that i have missed. I took various different sets of positive consecutive numbers with median being odd and in all cases,one of the number was divisible by 4.


because the other no. will yield the reminder 2 and hence not divisible
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Re: M12-21  [#permalink]

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New post 12 Jan 2016, 07:48
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rhio wrote:
I understood solution, but I just wanted to know why exactly does 1 of the number will be divisible by 4? Is their any kind of rule here that i have missed. I took various different sets of positive consecutive numbers with median being odd and in all cases,one of the number was divisible by 4.



Hi,
In all cases, any number, n, will have only one number divisible by itself in 'n' consecutive numbers..
5 will have only one multiple in any 5 consecutive number because of the property of multiplication tables..
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Re: M12-21  [#permalink]

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New post 15 Jul 2016, 22:57
can someone explain me me how option 2 is right?

for eg 7 8 9 10 11
9 is a median and not prime so cannot determine . Ans should be just option A
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New post 15 Jul 2016, 23:13
r19 wrote:
can someone explain me me how option 2 is right?

for eg 7 8 9 10 11
9 is a median and not prime so cannot determine . Ans should be just option A


(2) says: The average (arithmetic mean) of these numbers is a prime number.

Why do you consider the case which contradicts the statement?
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Re: M12-21  [#permalink]

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New post 16 Jul 2016, 01:29
I considered 2 cases 1 2 3 4 5 and 7 8 9 10 11, for one we can determine and for other cannot .I misunderstood the question. Thanks for the help
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M12-21  [#permalink]

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New post Updated on: 27 Sep 2016, 06:32
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I think this is a poor-quality question. I think the wording of the question is confusing. And the grammar is incorrect too ("numbers" with "is")

How many numbers of 5 consecutive positive integers is divisible by 4?

Suggestion- How many integers in a group of 5 consecutive positive integers are divisible by 4?
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Originally posted by KarishmaParmar on 23 Sep 2016, 14:51.
Last edited by KarishmaParmar on 27 Sep 2016, 06:32, edited 1 time in total.
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Re: M12-21  [#permalink]

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New post 27 Sep 2016, 01:52
KarishmaParmar wrote:
I think this is a poor-quality question. I think the wording of the question is confusing. And the grammar is incorrect too (numbers with is)

How many numbers of 5 consecutive positive integers is divisible by 4?

Suggestion- How many integers in a group of 5 consecutive positive integers are divisible by 4?


Edited as suggested. Thank you.
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Re M12-21  [#permalink]

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New post 18 Nov 2017, 07:27
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. Is 2 divisible by 4?

Ans would be 1/2. Does it satisfy our condition?
Shouldn't we look for a whole number as an answer?

In refrence Statement 1, considering the set : (1, 2, 3, 4, 5)
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Re: M12-21  [#permalink]

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New post 18 Nov 2017, 07:47
jasanisanket24 wrote:
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. Is 2 divisible by 4?

Ans would be 1/2. Does it satisfy our condition?
Shouldn't we look for a whole number as an answer?

In refrence Statement 1, considering the set : (1, 2, 3, 4, 5)


Hi jasanisanket24

the question asks how many numbers in the set are divisible by 4. so 2 is not divisible by 4. Hence in the set (1,2,3,4,5) we have only 1 number that is divisible by 4. Hence the statement is sufficient.

Both statement 1 & 2 leads us to the conclusion that the consecutive set starts with an ODD integer. so the set will be of the form (odd,even,odd,even,odd)

hence there will be two even integers in the set and both will be consecutive even integers. out of any two consecutive even integers, only 1 is divisible by 4 (eg. 2,4; 4,6; 8,10....etc). SO we can conclude that there is only 1 number that is divisible by 4. Hence both the statements are sufficient
Re: M12-21 &nbs [#permalink] 18 Nov 2017, 07:47
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