MI3 wrote:Q. Set X consists of different positive numbers arranged in ascending order: K, L, M, 5, 7. If K, L and M are consecutive integers, what is the arithmetic mean of set X?
(1) The product K × L × M is a multiple of 6
(2) There are at least 2 prime numbers among K, L and M
IMO - A, am I correct?
Hi MI3, not quite.
If the numbers are positive, different, arranged in ascending order, and K, L, M are consecutive integers, then there are only two possible cases:
case a: K=1, L=2, M=3
case b: K=2, L=3, M=4
Each case will give a different arithmetic mean of set X.
At this point, we can rewrite our target question as "Which case is true?"
Statement 1: KLM is a multiple of 6
case a: KLM = (1)(2)(3) = 6, and 6 is a multiple of 6
case b: KLM = (2)(3)(4) = 24, and 24 is a multiple of 6
Case a and case b are both such that KLM is a multiple of 6.
So, this is not enough information to determine which case is true.
As such, statement 1 is not sufficient
Statement 2: There are at least 2 prime numbers among K, L and M
Well, case a has two primes among K, L and M (2 and 3), and case b has two primes among K, L and M (2 and 3).
So, this is not enough information to determine which case is true.
As such, statement 2 is not sufficient.
Statements 1 & 2
Both cases are such that KLM is a multiple of 6,
and both cases have two primes among K, L and M.
So, we still do not have enough information to determine which case is true.
As such, the answer is
E
Cheers,
Brent
