During a 10-week summer vacation, was the average (arithmetic mean)

Question

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.

ID 00262

Bunuel · Accepted Answer

Let  c  be the average # of books that Carolyn read per week;
Let  j  be the average # of books that Jacob read per week;

Question is c>j?

(1)  2c>2j-5 , if  c=10<j=11  -->  2*10=20>2*11-5=17  BUT if  c=10>j=5  -->  2*10=20>2*5-5=5 , two different answers. Not sufficient.

(2) Clearly insufficient. In the second half of the 10 week period, Carolyn read 3 books more than Jacob. So her average for the second half will be greater than Jacob's, but we know nothing about the first half.

(1)+(2) Combined two statements also not sufficient to determine whether c>j.

Answer: E.

sanjoo · Answer

Bunuel..it is necessary to try with num..

i have done lyk this..take C as the average of carolyn and J as the avg of jacob..

2c>2j-5
2j-2c<5

(J-C)<5/2..

so we dont knw its positive or negative..if its positive that means J avg is more than carolyn and vice versa..

Statement 2 is insufficient..

both are still insufficient to give the ans ..

So e..

Bunuel · Answer

Yes, you can do this way as well.

mvictor · Answer

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

Kinshook · Answer

Asked:  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?

Let the average (arithmetic mean) number of books that Carolyn read per week be c
Let the average number of books that Jacob read per week be j

(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.
2c > 2j-5 => c>j may or may not be true
NOT SUFFICIENT

(2) During the last 5 weeks of the vacation, Carolyn read a total of 3 books more than Jacob.
No data is provided for first 5 weeks 
NOT SUFFICIENT

IMO E

Basshead · Answer

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

(1)  2C > 2J -5 
 2C - 2J = -5 
 C - J = -\frac{5}{2}

We can't say for certain whether Carolyn's average was higher or lower.

(2) Clearly insufficient.

(1&2) Combined, we still can't determine whether Carolyn's average is higher or lower. INSUFFICIENT.

Answer is E.

C6R391 · Answer

what does "greater than 5 less than" even mean lol?

Bunuel · Answer

Let  c  be the average # of books that Carolyn read per week;
Let  j  be the average # of books that Jacob read per week;

Then "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" would mean  2c>2j-5 .

gmat700s · Answer

Bunuel ,  Sajjad1994  kindly update the question tag to GMAT prep (it is part of Gmat Official practice question 1 )

Here is the official solution

Let C and J represent the average numbers of books Carolyn and Jacob read per week during their 10-week summer vacation. Determine if C > J, which is the same as determining if C –J is positive.

(1) It is given that 2C > 2J – 5, from which it follows that 2C – 2J > –5 and C –J > –​five halves​. Thus C –J could be positive, but it could also be negative; NOT sufficient.

(2) If C 2 and J 2 represents the numbers of books Carolyn and Jacob read during the last 5 weeks of the summer, then C 2 = J 2 + 3, but this is not enough information to determine if C > J, because the numbers of books Carolyn and Jacob read during the first 5 weeks of the summer are unknown. If C 2 = 20, from which it follows that J 2 = 17, and Carolyn read 20 books during the first 5 weeks of the summer, then C = ​the fraction with numerator 20 plus 20 and denominator 10​ = 4. If Jacob read 13 books during the first 5 weeks, then J = ​the fraction with numerator 17 plus 13 and denominator 10​ = 3 and C > J, but if Jacob read 43 books during the first 5 weeks, then J = ​the fraction with numerator 17 plus 43 and denominator 10​ = 6 and C < J; NOT sufficient.

Since the values for C –J obtained in the examples used for (2), namely 4 – 3 = 1 and 4 – 6 = –2, also satisfy (1) because each is greater than –​five halves​, it follows that (1) and (2) together are NOT sufficient.

The correct answer is E; both statements together are still not sufficient.

Varun291 · Answer

I got this wrong. Could someone help point my mistake out?

I got it as A because

2C>2J-5. Now I broke this C and J down into the average forumla. Assumed sum of C as a and Sum of books read by Jacob to be b and number of weeks in the denominator to be w. So you get

2(a/w)=2 (b/w)-5

w gets cancelled as its the same for both and you get 2a=2b-5

5= 2b-2a -> 5/2=b-a

Given the sum of books read by jacob is greater than Carolyn and number of weeks is the same, Jacob on average would have read more books.

Bunuel · Answer

We are given:

2(a/w) > 2(b/w) - 5 not 2(a/w) = 2(b/w) - 5. So:

2(a/10) > 2(b/10) - 5

a/5 > b/5 - 5

a > b - 25

25 > b - a

Gaurav07 · Answer

Can someone help me understand - in data sufficiency, the two stattements have to be considered true when we look at them right? for example here, if i consider statement 1, 2c/10 is greater than 2j/10 - 5, therefore since the statement says its greater, i can assume directly by solving that c is greater than j-2.5, therefore j is atleast 2.5 more than c? please correct me.

Bunuel · Answer

Assuming c and j are total number of books read over 10-week, we get:

2c/10 > 2j/10 - 5

c > j - 25

25 > j - c

j = 10 and c = 1, gives a NO answer
j = 1 and c = 10, gives a YES answer

bumpbot · Answer

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During a 10-week summer vacation, was the average (arithmetic mean)

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