Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

range of set A is R. if a number with value R is added to the set will the range increase?

all numbers in A are >0 mean of the new set is smaller than R

Stmt 1: Range = largest no. - smallest no.
If all numbers in A > 0, then the smallest no. > 0. Therefore, R must be lesser than the largest number. Hence, the range will not change on adding R to the set. Sufficient.
This is of course assuming that sets contain distinct numbers. If the largest and smallest are equal, then R = 0 and this violates stmt 1.

Stmt 2: I think this is not sufficient, but I cannot be sure.

range of set A is R. if a number with value R is added to the set will the range increase?

all numbers in A are >0

mean of the new set is smaller than R

Answer: E

stat 1: If the numbers in set A are distinct, then since R=largest no.- smallest no. R will always be smaller than the largest number and therefore, the range will never increase. However if the numbers in set A are the same then the Range can increase.

Eg: Set A = {1,1,1} R=0
New Set A ={0,1,1,1} R=1

Insuff.

Stat 2:

Eg 1:
Set A = {1,2,6} R=5 Mean=3
New Set A= {1,2,5,6} R=5 Mean=3.5
Range remains the same

Eg 2:
set A={-3,-2,-1} R=2 Mean =-2
new set A={-3,-2,-1,2} R=5 Mean = -1
Range increases from 2 to 5

range of set A is R. if a number with value R is added to the set will the range increase?

(1) all numbers in A are >0

(2) mean of the new set is smaller than R

Range = maxA - minA = R

(1) The range will increase only if R > maxA; otherwise the range would just stay the same.

All #s in A are >0, therefore R = maxA - minA < maxA. Then, the range will not increase. Suff.

(2) The mean does not bring terminating information. All numbers but one could be positive and still we wouldn't have enough grounds to know for sure whether including that R number would increase the range of the set. Insuff.

range of set A is R. if a number with value R is added to the set will the range increase?

all numbers in A are >0

mean of the new set is smaller than R

I think C.
1) Say Set A = {1,2,3}, Range = 2. Inserting 2 will not increase range.
Say Set A = {6,7,8}, Range = 2. Inserting 2 will increase range.

2) Mean of the new set is smaller than R.
Set A = {A1,A2,A3}
Range = A3 - A1
Mean of new set= (A1+A2+A3+A3-A1)/4 = (A2+2*A3) /4
Knowing that mean of new set is smaller than R:
=> (A2+2*A3) / 4 < R
=> (A2+2*A3) / 4 < (A3 - A1)
=> A2 + 2*A3 < 4*A3 - 4*A1
=> 4*A1 + A2 - 2*A3 < 0
=> A2 / 2 < A3 - 2*A1
We want to know if A3-A1 < 0 or A3-A1 > 0. This doesn't tell anything.

If all values are positive, however, this means that A3-2*A1 is positive. This also means that A3-A1 is positive.

range of set A is R. if a number with value R is added to the set will the range increase?

all numbers in A are >0

mean of the new set is smaller than R

(1) Suppose A = {2,5}- answer no
Suppose A ={2,3}- answer yes

NOT SUFF

(2) A = {-3,3} yes
A= {0,0,4} no

NOT SUFF

(T) Suppose A' = A U {R}. If all the members of A are positive, R is less than the greatest element.
If the mean of the set A´ is less than R, there is at least one element in A' , and thus in A, that is less than R. Thus R is neither the smallest nor the greatest element in A', and the range of A' = range of A