During a 10 week summer vacation, was the average ( arithmetic mean) number of books that Carolyn read per week greater than the average number of books that Jacob read per week ?
1. Twice the average number of books that Carolyn read per week was greater than 5 less than twice the average number of books that Jacob read per week.
2. During the last 5 weeks of summer vacation, Carolyn read a total of 3 books more than Jacob.
answer is E
the way I solved was
considering statement I alone
let carolyn's average be 'C' and jacob's average is 'J'
then from 1 I have
2C> 2J-5
I plugged in some values for C & J
when C=2 & J=3 C<J so answer is NO
when C=5 & J=4 C>J so answer is YES
so clearly 1 is insufficient
consider statement 2
we don't know the exact value of the average number books read by both on the first 5 weeks so statement 2 is insufficient
Now considering both still the answer can be a 'yes' or 'no'
so neither statement is sufficient to answer the question and the answer is E.
Is the way I solved the best approach or can someone come up with a better way of solving this problem ?
Thanks
Lakshminarayan