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 2 years ago
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
 2 years ago
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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RoamingBlue
 2 years ago
Best ResponseYou've already chosen the best response.07x7 = 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

RoamingBlue
 2 years ago
Best ResponseYou've already chosen the best response.049, 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?

RoamingBlue
 2 years ago
Best ResponseYou've already chosen the best response.0oh wait, I see, the four that don't belong are 49, 25, 9, and 1

umar284
 2 years ago
Best ResponseYou've already chosen the best response.0your right! how did you figure that out?

RoamingBlue
 2 years ago
Best ResponseYou've already chosen the best response.0because 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

RoamingBlue
 2 years ago
Best ResponseYou've already chosen the best response.0and 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

umar284
 2 years ago
Best ResponseYou've already chosen the best response.0and the others? 25,9 and 1?

RoamingBlue
 2 years ago
Best ResponseYou've already chosen the best response.0for 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)

RoamingBlue
 2 years ago
Best ResponseYou've already chosen the best response.0do you see why, or should I explain it more ... I sorta botched the whole initial explanation thing ;)
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