There are 5 consecutive integers. If the product of the 5 nu

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There are 5 consecutive integers. If the product of the 5 numbers is not zero, what is the number of the negative numbers of them?

1) The greatest number of the 5 numbers is less than 5.
2) At least one of the 5 numbers is negative.


* A solution will be posted in two days.
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by sanju09 » Fri Feb 12, 2016 12:49 am
Max@Math Revolution wrote:There are 5 consecutive integers. If the product of the 5 numbers is not zero, what is the number of the negative numbers of them?

1) The greatest number of the 5 numbers is less than 5.
2) At least one of the 5 numbers is negative.


* A solution will be posted in two days.
This question is poorly worded, and on first look it doesn't seem to be genuine GMAT wordings. Proper wordings would have been like:

If the product of 5 consecutive integers is not zero, how many of those integers are negative?
(1) The greatest of the 5 consecutive integers is less than 5.
(2) At least one of the 5 consecutive integers is negative.

By saying that the product of 5 consecutive integers is not zero, they mean that 0 is not in the list. In other words, the 5 consecutive integers are either all positives or all negatives. So, a possible answer to the question in prompt (how many of those integers are negative?) is either 0 or 5. Let's examine each statement one by one:

(1) If the greatest of the 5 consecutive integers is less than 5, it means those cannot be 5 positive consecutive integers, otherwise we have to include 0, which is not permissible. Those must be negatives only and answer is 5. Sufficient
(2) If at least one of the 5 consecutive integers is negative, then all have to be negatives only, and answer is 5. [spoiler]Sufficient

Pick D
[/spoiler]
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by Max@Math Revolution » Sun Feb 14, 2016 10:32 pm
There are 5 consecutive integers. If the product of the 5 numbers is not zero, what is the number of the negative numbers of them?

1) The greatest number of the 5 numbers is less than 5.
2) At least one of the 5 numbers is negative.


In the original condition, it says there are 5 consecutive integers, which are n, n+1, n+2, n+3, n+4. So, you only need to figure out n. Thus, there is 1 variable, which should match with the number of equation. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
For 1), only like -5,-4,-3,-2,-1/-6,-5,-4,-3,-2... are valid and there are always 5 negative integers, which is unique and sufficient.
For 2), only like -5,-4,-3,-2,-1/-6,-5,-4,-3,-2... are valid and there are always 5 negative integers, which is unique and sufficient.
Therefore, the answer is D.
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