sanju09 wrote:For a set of 3 numbers, assuming there is only one mode, does the mode equal the range?
[1] The median equals the range.
[2] The largest number is twice the value of the smallest number.
Hi there!
Beautiful problem, sanju.
From the question stem, we have only 3 possible scenarios... let us called them (I), (II) and (III) as follows:
(I) {a,a,a} with mode a and
with focus on the simplified question (on this particular case): a = 0 ?
(II) {a,a,b} (where a<b) with mode a and
with focus.... case): a = b-a, i.e., b = 2a ?
(III) {a,b,b} (where a<b) with mode b and
with focus... case): b= b-a, i.e., a = 0 ?
Now let us discuss each statement alone in each of the 3 scenarios/simplified questions shown above!
(1) SUFFICIENT:
(I) From this sttm we get a=0, answering in the affirmative;
(II) From this sttm we get a=b-a, again in the affirmative;
(III) From this sttm we get b=b-a, again in the affirmative;
(2) INSUFFICIENT:
(I) From this sttm we get a=2a, therefore a=0, answering in the affirmative; (
*)
(II) From this sttm we get b = 2a, again answering in the affirmative;
(III) From this sttm we get b = 2a, but here we have the possibility of answering in the negative: take a=1 and b=2;
Best Regards,
Fábio.
Post-Mortem:
Obs.1: the question stem should use the word "list" instead of "set", for technical reasons.
Obs.2: there is nothing wrong here, when there is only one number in the list, the largest and the smallest values coincide!
