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Is the product of four consecutive even integers positive?

The sum of these integers is positive but smaller than 20 The product of the middle two of these integers is positive

I got C

OA is A which i disagree can someone explain why its A

as for S1 we can have -2 0 2 4 sum is +ve and < 20 product is 0 which is not positive

In YES/No DS questions statement is sufficient if you can answer either definitive YES or definitive NO to the question

Is the product of four consecutive even integers positive?

First of all: the product of four consecutive even integers can be either 0 (when one of the eve integers is zero) or positive (when all integers are positive or negative).

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

If the greatest term is \(\geq{8}\), 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 \(product =0\), so in either case the product is NOT positives. Sufficient.

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

It's possible to have {0,2,4,6} --> product is zero OR {2,4,6,8} --> product is positive OR {-8,-6,-4,-2}--> product is positive. Not sufficient.

In YES/No DS questions statement is sufficient if you can answer either definitive YES or definitive NO to the question

Is the product of four consecutive even integers positive?

First of all: the product of four consecutive even integers can be either 0 (when one of the eve integers is zero) or positive (when all integers are positive or negative).

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

If the greatest term is \(\geq{8}\), 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 \(product =0\), so in either case the product is NOT positives. Sufficient.

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

It's possible to have {0,2,4,6} --> product is zero OR {2,4,6,8} --> product is positive OR {-8,-6,-4,-2}--> product is positive. Not sufficient.

Answer: A.

Hope it's clear.

Are negative numbers considered even or odd in GMAT? I also chose A but because there is only one possibility here {0,2,4,6}.
_________________

Do not forget to hit the Kudos button on your left if you find my post helpful

In YES/No DS questions statement is sufficient if you can answer either definitive YES or definitive NO to the question

Is the product of four consecutive even integers positive?

First of all: the product of four consecutive even integers can be either 0 (when one of the eve integers is zero) or positive (when all integers are positive or negative).

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

If the greatest term is \(\geq{8}\), 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 \(product =0\), so in either case the product is NOT positives. Sufficient.

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

It's possible to have {0,2,4,6} --> product is zero OR {2,4,6,8} --> product is positive OR {-8,-6,-4,-2}--> product is positive. Not sufficient.

Answer: A.

Hope it's clear.

Are negative numbers considered even or odd in GMAT? I also chose A but because there is only one possibility here {0,2,4,6}.

An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder.

An odd number is an integer that is not evenly divisible by 2.

Thus, according to the above both negative and positive integers can be even or odd. For example, -2 is even and -3 is odd.

P.S. Zero is an even integer. Zero is nether positive nor negative, but zero is an even number.
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