Question

-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

Answer 1

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

Answer 2

Actually its B)17

Answer 3

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?

Answer 4

wait just a minute

Answer 5

im typing the solution

Answer 6

oh wait, I see, the four that don't belong are 49, 25, 9, and 1

Answer 7

your right! how did you figure that out?

Answer 8

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

Answer 9

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

Answer 10

and the others? 25,9 and 1?

Answer 11

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)

Answer 12

great,thanks

Answer 13

do you see why, or should I explain it more ... I sorta botched the whole initial explanation thing ;)

Answer 14

nah i think i got :)

Answer 15

awesome :D