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Is the product of four consecutive even integers positive? [#permalink]

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02 Mar 2008, 09:01

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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

1 - suff. must be 6,4,2,-2. Any other sequences make the sum >=20, 0 or negative. 2 - insuff. could be any of these: 4,2,-2,-4 OR 2,-2,-4,-6 OR -2,-4,-6,-8

1 - suff. must be 6,4,2,-2. Any other sequences make the sum >=20, 0 or negative. 2 - insuff. could be any of these: 4,2,-2,-4 OR 2,-2,-4,-6 OR -2,-4,-6,-8

It is A but not for your reason:

1. the integers must be consecutive: 2 and -2 aren't. thus the sum must be 0+2+4+6 or smaller. in any case it involves positive and negative integers and, thus, 0, which is in the middle. thus 1 is suff since the product is always 0.

2. in the case the first 2 integers are negative, we may have the other 2 negative, in which case the product would be positive, or one negative and the other 0, in which case the product is 0. insuff

1 - suff. must be 6,4,2,-2. Any other sequences make the sum >=20, 0 or negative. 2 - insuff. could be any of these: 4,2,-2,-4 OR 2,-2,-4,-6 OR -2,-4,-6,-8

It is A but not for your reason:

1. the integers must be consecutive: 2 and -2 aren't. thus the sum must be 0+2+4+6 or smaller. in any case it involves positive and negative integers and, thus, 0, which is in the middle. thus 1 is suff since the product is always 0.

2. in the case the first 2 integers are negative, we may have the other 2 negative, in which case the product would be positive, or one negative and the other 0, in which case the product is 0. insuff

I considered it, but then wasn't sure if 0 is even (guess need to brush up my number skills). Since it wouldn't change the result anyway I picked -2 to show different sequences. Anyhow later I went to wikipedia and confirmed that 0 is infact an even number!