Carolyn read per week

[Needgmat]

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.

OAE

[GMATGuruNY]

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.

Let C = Carolyn's average number of pages per week and J = Jacob's average number of pages per week.

Statement 1:
2C > 2J-5.
C > (2J-5)/2.

Let J=3, with the result that C > 1/2.

Case 1: C=1
In this case, C<J.
Case 2: C=4
In this case, then C>J.
INSUFFICIENT.

Statement 2:
In Case 1, J's total for all 10 weeks = 10*3 = 30, while C's total for all 10 weeks = 10*1 = 10.
The following distribution is possible:
In the last 5 weeks, C reads 3 books, while J reads 0 books.
In the first 5 weeks, C reads 7 books, while J reads 30 books.
Thus, Case 1 also satisfies Statement 2.
In Case 1, C<J.

In Case 2, J's total for all 10 weeks = 10*3 = 30, while C's total for all 10 weeks = 10*4 = 40.
The following distribution is possible:
In the last 5 weeks, C reads 3 books, while J reads 0 books.
In the first 5 weeks, C reads 37 books, while J reads 30 books.
Thus, Case 2 also satisfies Statement 2.
In Case 2, C>J.
INSUFFICIENT.

Statements combined:
Cases 1 and 2 satisfy both statements.
In Case 1, C<J.
In Case 2, C>J.
INSUFFICIENT.

The correct answer is E.

[Brent@GMATPrepNow]

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.

OAE

Target question: During a 10-week summer vacation, was the average number of books that Carolyn read per week greater than the average number of books that Jacob read per week?

Let C = average number of books per week that Carolyn read
Let J = average number of books per week that Jacob read

REPHRASED target question: Is C > J ?

Statement 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.
So, statement 1 tells us that: 2C > 2J - 5
There are several pairs of values that satisfy this condition. Here are two:
Case a: C = 2 and J = 3, in which case C < J
Case b: C = 5 and J = 3, in which case C > J
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: During the last 5 weeks of the vacation, Carolyn read a total of 3 books more than Jacob.
This tells us nothing about the first 5 weeks of the vacation, so we have cannot determine the total number of books read over the 10-week period, which means Carolyn or Jacob could have read the most books.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
From statement 1, we were able to come up with 2 possible, conflicting cases:
Case a: C = 2 and J = 3, in which case C < J
Case b: C = 5 and J = 3, in which case C > J

In case a, Carolyn's average of 2 books/week, means she read a total of 20 books over the 10-week period, and Jacob's average of 3 books/week, means she read a total of 30 books over the 10-week period. Notice that it's quite possible that, during the last 5 weeks, Carolyn read a total of 3 books more than Jacob. So, case a could satisfy both conditions.
Likewise, case b could satisfy both conditions.

Since the two possible cases, yield different answers to the target question, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent