iampancham21 wrote:
In a group of 62 children, more of the children were born on a Friday than on any other day of the week. What is the least possible number of children in the group who were born on a Friday?
A. 11
B. 10
C. 9
D. 8
E. 7
We know that more of children were born on a Friday than on any other day of the week. So, if x children were born on a Friday,
at most x - 1 children could have been born on any of the other 6 days. To minimize x, we need to maximize the sum of the children born on any of the other 6 days.
Now, if x - 1 children were born on each of the other 6 days and x on Friday, we will have 6(x - 1) + x = 62, which gives x = 9.something. x must be integer, so let's try 9 and 10.
If x = 9, then
at most 8 children could have been born on any of the other 6 days, giving the sum of 9 + 6*8 = 57, which is less than 62. So, {8, 8, 8, 8, 8, 8, 9} is not possible.
If x = 10, then
at most 9 children could have been born on any of the other 6 days, giving the sum of 10 + 6*9 = 64, which is more than 62 but we if 8 children were born on 2 of the days, then the sum will be exactly 62: {8, 8, 9, 9, 9, 9, 10}.
Answer: B.