Arithmetic mean

[MI3]

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?

[Brent@GMATPrepNow]

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

[MI3]

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

Thank you for the detailed explanation, Brent.

[goalevan]

One note:

Statement 1 does not add any information to the question stem. For any n, n(n + 1)(n + 2) will contain at least one factor of 2 and at least one factor of 3, and thus at least one factor of 6. The product of three consecutive integers is always a multiple of 6.

When a statement adds no information to the question stem, you can eliminate the answer choice of that statement (either A or B) along with C and D.