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Set S consists of all the positive multiples of 5 that are less than K

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Set S consists of all the positive multiples of 5 that are less than K [#permalink]

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Set S consists of all the positive multiples of 5 that are less than K, and K is a positive integer not divisible by 5. The mean of Set S is not divisible by 5. Let N be the number of members of the set. N is not divisible by 5. What does N equal?

(1) N < 52
(2) K/5 > 48

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[Reveal] Spoiler: OA

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Set S consists of all the positive multiples of 5 that are less than K [#permalink]

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New post 18 Mar 2015, 13:25
From the problem statement,

5n < k < 5n+5
n < k/5 < n+1
(k/5) - 1 < n <k/5

Since, mean of S is not divisible by 5, n has to be even.
and since n is not divisible by 5, therefore it is not a multiple of 10.

(1) n < 52
This is clearly INSUFFICIENT since n can be any even no. < 52 as long as it's not a multiple of 10

(2) k/5 > 48 => k/5-1 > 47 => n > 47
This is INSUFFICIENT as well since n could take any even value > 47 as long as it is not a multiple of 10.

From (1) , (2)

47 < n < 52

So the only possible value of n can be 48. Hence, both together are SUFFICIENT.

Answer is C.

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Re: Set S consists of all the positive multiples of 5 that are less than K [#permalink]

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Bunuel wrote:
Set S consists of all the positive multiples of 5 that are less than K, and K is a positive integer not divisible by 5. The mean of Set S is not divisible by 5. Let N be the number of members of the set. N is not divisible by 5. What does N equal?

(1) N < 52
(2) K/5 > 48

Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION:

This is a tricky problem, because there are several constraints in the problem. first of all, the number of members is N, so the numbers in the set go from 5 to 5N. The integer K has the quality that 5N < K < (5N + 5), because K is bigger than the biggest member of the set, but 5N has to be the largest multiple of 5 less than K.

We know that the mean of the set is not divisible by 5, and this is important. For an evenly spaced set, the mean & median are identical. If there were an odd number of members, the mean & median would simply be the middle number on the list, and this of course would be some multiple of 5. The fact that mean & median is not divisible by 5 necessarily means that there must be an even number of members on the list. This way, the mean & median would be the average of the middle two numbers, which would be a non-integer, certainly not an integer divisible by 5. Therefore, N is an even number.

Finally, we are also told that N itself is not divisible by 5—an odd constraint that may be relevant.

Statement #1: Here, N could be any even number less than 52, as long as it’s not divisible by 5. It could be {48, 46, 44, 42, 38, ….} Multiple possibilities. This statement, alone and by itself, is not sufficient.

Statement #2: The statement tells us that K > 5*48, so it could be that N = 48, so that K would be between 5(48) and 5*(49). That’s a possibility, or N could be any larger even number that is not divisible by 5. N could be {48, 52, 54, 56, 68, 62, …} Again, multiple possibilities. This statement, alone and by itself, is not sufficient.

Combined statements: with both constraints, the only possible value if N = 48. The statements together are sufficient.

Answer = (C)
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Re: Set S consists of all the positive multiples of 5 that are less than K [#permalink]

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Re: Set S consists of all the positive multiples of 5 that are less than K [#permalink]

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New post 15 Jan 2017, 21:24
I don't understand why n>47.
Why can't be N any even number less than 48? N could be also 40 or 32, why would it be wrong?

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Re: Set S consists of all the positive multiples of 5 that are less than K [#permalink]

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New post 07 Aug 2017, 22:48
[quote="Bunuel"]Set S consists of all the positive multiples of 5 that are less than K, and K is a positive integer not divisible by 5. The mean of Set S is not divisible by 5. Let N be the number of members of the set. N is not divisible by 5. What does N equal?

(1) N < 52
(2) K/5 > 48


5N < K < (5N + 5)
I didnt understand how you got this equation

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Re: Set S consists of all the positive multiples of 5 that are less than K [#permalink]

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New post 09 Aug 2017, 02:15
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machiavelli wrote:
Bunuel wrote:
Set S consists of all the positive multiples of 5 that are less than K, and K is a positive integer not divisible by 5. The mean of Set S is not divisible by 5. Let N be the number of members of the set. N is not divisible by 5. What does N equal?

(1) N < 52
(2) K/5 > 48


5N < K < (5N + 5)
I didnt understand how you got this equation


Set S has N terms in it, and K is the highest term, which is not a multiple of 5.

Set S = {5,10,15,.............,5N,K}
=> 5N is the highest multiple of 5 in the Set, and K is greater than 5N as per the constraints in the question
=> K > 5N
Since K has to be the largest term in the set, and 5N has to the largest multiple of 5 in the set, we can write the equation as
5N + 5 > K > 5N

E.g.
S = {5,10,15,20,21}
Here K = 21
5N = 20 (The largest multiple of 5 in the set) => N = 4 (# of Multiples of 5)

Does this help?
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Re: Set S consists of all the positive multiples of 5 that are less than K   [#permalink] 09 Aug 2017, 02:15
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