Data Sufficiency

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.

radhika1306 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.

Answer should be A.

Statement 2 just does not give enough information. However if you convert the information given in statement 1 you get the following equation -

2c > 2J - 5, where c & j stand for the average no of books read by each person.

No matter what value you put for X, Y will have to be greater than X to satisfy the equation.

Is this the correct answer?

Correct thanks

ri2007 wrote:

radhika1306 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.

Answer should be A.

Statement 2 just does not give enough information. However if you convert the information given in statement 1 you get the following equation -

2c > 2J - 5, where c & j stand for the average no of books read by each person.

No matter what value you put for X, Y will have to be greater than X to satisfy the equation.

Is this the correct answer?

I don't understand how though.

If 2c>2J-5: if c=5, j=4, the statement holds. Is c=5 and j=6, the statement still holds.

TT

You are correct, thanks for pointing out my mistake.

To be honest I was hoping some one else would read ur comment and give the correct solution:)

Am not sure if I am reading statement 1 in the right way but here is how it could be written -

5> 2C<2J?

average number of books that Carolyn read was greater
than 5 less than twice the average number of books that Jacob read per week

So statement 1 is enough ???

Is E or A? I think it's E but could be tricy than I think..

It's (e), not enough information.

Statement (1) was correctly translated as:

2C > 2J - 5

As TT pointed out, we can pick numbers that make C>J and that make J>C. Therefore, statement (1) by itself isn't sufficient.

Statement (2) was simpler.. it says that in the second half of the period, Carolyn read an extra 3 books, total. We know that her average for the last half will be greater than J's, but we know nothing about the first half, so (2) is also insufficient.

When we combine the statements, we're still out of luck. We can pick the exact same numbers suggested by TT and satisfy both statements, so we can still get both a yes and a no answer: insufficient.