-7,-5,-3,-1,0,1,3,5,7 How many distinct products can be obtained by multiplying pairs of numbers from the list above? A)9 B)17 C)19 D)21 E)31

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-7,-5,-3,-1,0,1,3,5,7 How many distinct products can be obtained by multiplying pairs of numbers from the list above? A)9 B)17 C)19 D)21 E)31

Mathematics
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7x7 = 49 7x5 = 35 7x3 = 21 7x1 = 7 7x0 = 0 don't need to do 5x7 because we already did 7x5 5x5 = 25 5x3 = 15 5x1 = 5 don't need to do 3x7 because we already did 3x7 don't need to do 3x5 because we already did 3x5 don't need to do 5x0 because we already did 7x0 3x3 = 9 3x 1 = 3 don't need to do 3x0 because we already did 7x0 don't need to do 1x7 because we already did 7x1 don't need to do 1x5 because we already did 5x1 don't need to do 1x3 because we already did 3x1 1x1= 1 don't need to do 1x0 because we already did 1x0 counting all the different answers we got, the total number of POSITIVE combinations is: 11 zero can't be negative but if we'd multiplied each of the other 10 by a negative value we would have got another unique value (for instance 1x -1 = -1 so we add 10 more to the count of possible combinations 11+10 = 21 possible combinations
Actually its B)17
49, -49, 35, -35, 21, -21, 7, -7. 25, -25, 15, -15, 5, -5, 9, -9, 3, -3, 1, -1, 0 I count 21 ... which 4 don't you think belong?

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wait just a minute
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oh wait, I see, the four that don't belong are 49, 25, 9, and 1
your right! how did you figure that out?
because you cannot get positive 49 from any of the combinations you would need to multiply -7 times -7 or 7 times 7 to get a positive result
and you only have one negative seven and one positive seven ... so there's no way you can multiply two sevens (from your list) to get a positive ... it can only be negative
and the others? 25,9 and 1?
for the same reason ... you can't get 25 because your fives are positive and negative, and you always get negative when you multiply positive by negative ... same for 9 (threes) and 1 (ones)
great,thanks
do you see why, or should I explain it more ... I sorta botched the whole initial explanation thing ;)
nah i think i got :)
awesome :D

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