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If you have made mistakes, there is always another chance for you. You may have a fresh start any moment you choose, for this thing we call "failure" is not the falling down, but the staying down.

stmt 1 is sufficient, because the product will always be = 0, unique answer. so suff

in stmt 2, the 2 smallest integers can be -2 and -4, and the other two will be 0 and 2. In this case, product is 0, not positive. they could also be -8 and -6, then other two integers can be -4, -2 and then product will be positive. No unique answer, so insuff.

how will product be zero in statement 1
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Take the smallest 4 positive consecutive even integers and add them

2+4+6+8 >20 that means the 4 integers begin from 0 or less

Now it also says that their sum is positive but less than 20. Sum can only be positive if the 4 numbers have atleast few numbers that are positive, ie, all four cannot be negative. So these numbers must include zero as well, (zero is considered as an even integer)

If zero is one of them, product will always be zero

Take the smallest 4 positive consecutive even integers and add them

2+4+6+8 >20 that means the 4 integers begin from 0 or less

Now it also says that their sum is positive but less than 20. Sum can only be positive if the 4 numbers have atleast few numbers that are positive, ie, all four cannot be negative. So these numbers must include zero as well, (zero is considered as an even integer)

If zero is one of them, product will always be zero

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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

I think statement 1 is not sufficient, as we can have -2, 0, 2, 4 in which case the sum is 4 and the product of the four consecutive even integers is '0', which is neither +ve nor -ve.

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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