vaivish1723 wrote:

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 the vacation, Carolyn read a total of 3 books more than Jacob.

my approach to prove that A, B, and C are not sufficient.

1. suppose average for C is 4, and so is for J.

2x4=8

2x4 - 5 = 3

so A for C > than A for J.

but it can be that A read 5/week and J read 4/week

10>3 true again, but values differ.

A and D are out

2. clearly insufficient.

B is out.

1+2

40 total books

C in first 5 weeks read 40/2 -3 = 17 books, and 23 in last 5 weeks

J on the contrary read 20 books in the first 5 weeks, and 20 in the last 5 weeks.

satisfies both 1 and 2, but averages are equal

now.

suppose C=5books/week = 50 books total

J = 4books/week = 40 total

C during first 5 weeks read 46 books, and 4 in the last 5 weeks

J read 39 in the first 5 weeks, and 1 in the last 5 weeks.

again, satisfies both conditions from 1 and 2..

2 outcomes - C is out