Set X consists of different positive numbers arranged in ascending ord

Question

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

u0422811 · Accepted Answer

Enigma, I am inclined to agree with you on choice E. Here is my logic:

Statement 1 says - KxLxM is a multiple of 6. This could be either 1,2,3 which equals 6 (6 is a multiple of itself) or 2,3,4 (which equals 12 also a multiple of 6) - so insuff.
Statement 2 says - There are at least 2 prime numbers among K,L, and M - this since K,L,M has to be 1-4 and consecutive this gives us no new information - so insuff.

Taken together doesn't help us either.

Hence I am inclined to say E.

BDSunDevil · Answer

Thanks alinomoto. I see my bad. edited.

statement 2 gives us 2 possibilities: 234 or 123   Not sufficient

together: since K*L*M is multiple of 6, 234 and 123 are the only possibilities.
E

alinomoto · Answer

I don't think this is correct.

The only 3 consecutive positive integer combination under 5 could be 1,2,3 or 2,3,4.

Statement 1 also gives you the same 2 possibilities. K*L*M could be 1*2*3 = 6 a multiple of 6.

2*3*4 = 24 (also a multiple of 6). NOT SUFFICIENT.

Statement 2 is saying that it has 2 different primes and 2,3 are in both, so again, statement 2 is NOT SUFFICIENT.

1) & 2) combined don't help as both still give you either 1,2,3 or 2,3,4 and the means will be different depending on which 3 numbers k,l,m are.

OA should be E.

prashantshukla · Answer

I think that the correct answer is C as the number "1" is not a prime number.

The prime number series starts from 2 ie: 2,3,5,7,11....... !

Bunuel · Answer

No, the correct answer is E. Consider below examples:

K=1, L=2=prime, M=3=prime. 
K=2=prime, L=3=prime, M=4.

JAIN09 · Answer

K=3,L=4,M=5
IS THIS SET POSSIBLE.BECAUSE THE CONDITION GIVEN IS "ELEMENTS OF THE SET ARE IN ASCENDING ORDER"
MAKING 2 ELEMENTS EQUAL WILL NOT VIOLATE THE CONDITION

Bunuel · Answer

Given set is K, L, M, 5, 7. We are told that the set consists of  different  positive numbers arranged in ascending order.

Thus, set {K=3, L=4,  M=5, 5,  7} is not possible because there are two 5's there.

P.S. Please turn of caps lock when posting.

Sonia2023 · Answer

Good question:

Question stem: Numbers are different and arranged in ascending order so the range for K L M is 1 to 4.

Statement 1:
The product of 3 consecutive integers is always divisible by 6. Hence no new information. 
the numbers can be 1,2,3 or 2,3,4 
Not sufficient

Statement 2:
This is a trap as we might just think of 2,3,4 as 2 and 3 are the prime numbers. But even 1,2,3 has two primes. So this statement doesn't provide us anything new. Hence insufficient.

Combined:
Both the statements point to two cases so not sufficient.

Hence E.

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Set X consists of different positive numbers arranged in ascending ord

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Set X consists of different positive numbers arranged in ascending ord

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