Please look at this question:
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 middle two of these integers is positive
(C) 2008 GMAT Club - m17#27
Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient
Can me please somebody explain, why A is correct? I thought that following two sequences of even integers are possible in the case 1: -2,0,2,4 => sum is positive and product is zero, 2,4,6,8 => sum is positive and product is positive as well.
Let the consecutive even integers be
0 < x-2+x+x+2+x+4 < 20
0 < 4x + 4 < 20
0 < x+1 < 5
-1 < x < 4
The possible sets are:
Both cases; Product=0
Product is not +ve.
x(x+2) > 0
x<-2 or x>0
x=10; 8,10,12,14. product=+ve
x=-4; -6,-4,-2,0. product=0