gracie wrote:
At the first meeting of the amputees’ support group, there were
93 fewer handshakes than there would have been if everyone
had at least one arm and shook hands once with everyone else.
The people with less than one arm made up 1/11 of the group.
How many of them were there?
A. 2
B. 3
C. 4
D. 5
E. 6
Source: me
perfect example to use the units digit to get the answer quick.
let's assume the answer is A, then (22*21)/2 - (20*19)/2 = 93?
we can actually ignore the second part (after the minus) of the equation because it will always end with a units digit of 0.
the first part will have a units digit of 1 --> (units digit of 2 * units digit of 1) / 2
for the rest
B) (33*32) / 2 --> (units digit 3 * units digit 2) / 2 = 3 (success)
C) (44*43) / 2 --> (units digit 4 * units digit 3) / 2 = 6 (fail)
D) (55*54) / 2 --> (units digit 5 * units digit 4) / 2 = 0 (fail)
E) (66*65) / 2 --> (units digit 6 * units digit 5) / 2 = 0 (fail)
Interesting approach, but I don't think the unit digit is correct for B, D and E. The even number will become half and that reduced number should be used to get the unit digit.