pmal04 wrote:

Is the product of four consecutive even integers positive?

1)The sum of these integers is positive but smaller than 20

2)The product of the smallest two of these integers is positive

Is this GmatClub question?

I think there is a problem with it.

First of all: the product of four consecutive even integers can be either 0 or positive.

(1) The sum of these integers is positive but smaller than 20:

If the greatest term is >=8, eg {2,4,6,8}, then the sum will be equal or more than 20.

If the smallest term <-2, eg {-4,-2,0,2}, then the sum won't be positive.

Hence this statement gives only TWO possible sets {0,2,4,6} and {-2,0,2,4} --> sum<20 and product =0, which is not positive hence sufficient to answer the question. Sufficient.

(2) The product of the smallest two of these integers is positive.

Well in this case the product of terms can be positive or zero:

{2,4,6,8} --> product positive, or

{-4,-2,0,2} --> product 0, hence not positive. or

{-8,-6,-4,-2} --> product positive.

Not sufficient.

Answer: A.

BUT: in DS statements never contradict. Which means that BOTH statement must be true. Now, from (1) we got that only possible sets are {-2,0,2,4} and {0,2,4,6}. If we take the statement (2) the product of the smallest two terms must be positive, but in these sets the product of smallest terms equals to zero (-2*0=0 and 0*2=0), which is not positive. Statements contradict.

If I'm not wrong in above, I'd suggest to change the statement (2) as follows:

(2) The product of the smallest two of these integers is

not positive.

In this case answer would be D.

OR

(2) The product of the middle two of these integers is positive.

In this case answer still would be A. As it's possible to have {0,2,4,6} --> product zero OR {2,4,6,8} --> product positive OR {-8,-6,-4,-2}--> product positive.

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