Greeting cards

Probability Level 2

On Diwali, all the students of a class send greeting cards to one another . If the postmen deliver 1640 greeting cards to the students of this class,then the number of students can be $\text{\_\_\_\_\_\_\_\_\_\_}$ .

40 37 41 39

1 solution

Jus Jaisinghani
Jul 11, 2016

Lets suppose there were "n" no. of students,
each student has to give "n-1" greeting cards
So total greeting cards will be $n(n-1)$ but the postmen delivered 1640 cards
Thus $n(n-1)=1640$
$n^2-n-1640 =0$
$(n-41)(n+40)=0$
$i.e. n={41,-40}$
n cannot be negative ,Thus $n=\boxed{41}$