Data Sufficiency

ardz24 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

What's the best way to determine whether statement 1 is sufficient? Can any experts help?

Given:

1. 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.

S: {5, 10, 15, 20, 25, ...} such that the last term of the set < K, where K is a positive integer not divisible by 5.

Say, for an example, K = 26, 27, 28, or 29, then S: { 5, 10, 15, 20, 25};

However, if for an example, K = 31, 32, 33, or 34, then S: { 5, 10, 15, 20, 25, 30};

2. The mean of Set S is not divisible by 5.

Since Set S is an equally spaced set, its arithmetic mean (average) would be the value of the middle-most term, if the number of terms (it is given as N) is odd; however, the arithmetic mean (average) would be the average of the two middle-most terms, if the number of terms (N) is even.

Example 1: Say, S: {5, 10, 15, 20, 25}; we see that the number of terms (N) is odd, thus the mean = 15, which is divisible by 5, so the number of terms (N) cannot be odd.
Example 2: Say, S: {5, 10, 15, 20, 25, 30}; we see that the number of terms (N) is even, thus the mean = (15 + 20)/2 = 17.5, which is NOT divisible by 5, so the number of terms (N) is even.

So, we concluded that N is even but it is not divisible by 5 (given).

Let's take each statement one by one.

(1) N < 52

The set of N would be {48, 46, 44, 42, 38, 36, 34, 32, 28,...}; note that N is even but not divisible by 5, thus, we excluded all odd and 50, 40, 30, 20, and 10.

The statement is clearly insufficient as there is no unique value of N. Insufficient.

(2) K/5 > 48

=> K > 5*48

=> The last term of Set S is greater than equal to the 48th multiple of 5.

=> N can be anything 48, 52, 54, 56, 58, 62...; note that N is even but not divisible by 5.

The statement is clearly insufficient as there is no unique value of N. Insufficient.

(1) and (2) together

There is only one value of N is common and that is 48. Thus, N = 48. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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