Consecutive integers

[crackgmat007]

Can someone explain why stmt 1 is sufficient?

OA - D

[sreak1089]

Let us says the numbers are a1, a2, a3, ... aN
Stmt # 1 stays: (a1 x a2 x a3 .. X aN) / (a1 + a2 + a3 + ... + aN) is -ve

For the sum of abs values of consequtive integers to be different from the sum of values of consequtive inetegers, some values of the consequtive integers should be -ve and others should be posititve. If all the nos are -ve or all the nos are positive, above equation will be +ve.

Sincce the eqn is -ve, I guess there should be some +ve and some -ve numbers and hence their sum will not be equal to their absolute sum.
Hence stmt # 1 is sufficient. I think.

[crackgmat007]

Thanks for the explanation.

Actually, after thinking again, here is my explanation:

If there are even number of negative consecutive numbers. In this case, product of the consecutive numbers will be positive, but the sum will be negative, hence the quotient will be negative. Hence their sum will be equal to their absolute sum. --Y

If there are odd number of negative consecutive numbers. In this case, product of the consecutive numbers will be negative, so is the sum. Hence stmt 1 is not met.

However, if there are some +ve and some -ve numbers, product will be 0 (consecutive integers). In this case, quotient cannot be negative. Stmt 1 is not met.

Hence there is only one possibility, there are even number of the negative consecutive numbers.

Hence stmt 1 is sufficient coz to get a negative quotient, there must be even number of negative consecutive numbers.

Is the above logic correct?