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:

List A contains 5 positive integers, and the average (arithmetic mean) [#permalink]

Show Tags

28 Dec 2012, 19:12

2

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

55% (hard)

Question Stats:

68% (02:53) correct
32% (01:57) wrong based on 168 sessions

HideShow timer Statistics

List A contains 5 positive integers, and the average (arithmetic mean) of the integers in the list is 7. If the integers 6, 7, and 8 are in list A, what is the range of list A?

(1) The integer 3 is in list A. (2) The largest term in list A is greater than 3 times and less than 4 times the size of the smallest term.

Re: List A contains 5 positive integers, and the average (arithmetic mean) [#permalink]

Show Tags

28 Dec 2012, 20:46

1

This post received KUDOS

Archit143 wrote:

List A contains 5 positive integers and the Mean of integers in the list is 7. If the integers in the list are 6,7, and 8, What is the range of the list A?

1. the integer 3 is in the list A. 2. The Largest term in A is greater than 3 times and less than 4 times the size of the smallest term.

Hello, can anyone help me in decoding the Statement 2......

One approach is to remember one key thing. Since its given that 7 is the mean, and 6 & 8 are on either sides of mean, therefore the other two numbers, namely x and y have to be equally spaced on either side of the mean. The effect of +1 of 8 is equally compensated by the effect of -1 of 6. Hence for 7 to reman the mean of the set, the other numbers have to do so as well.

Statement 1) integer 3 is in the list A 3 is at a distance of 4 units from the mean on left hand side of number line. Therefore you are supposed to look for another number, but at the same distance on right hand side of the mean. \(7+4=11\) Hence the other number is 11. Now we know the smallest and the largest of the set. So range can be easily found out. Sufficient

Statement 2) The Largest term in A is greater than 3 times and less than 4 times the size of the smallest term.

One of the two numbers, the two that we don't know yet, have to be either side of the mean. Let the smaller one be x and the larger one be y. Since the set consists of positive numbers only, hence we have to check from 1 to 6. \(3x<y<4x\) Since only one number has to be on either side of the mean, hence the value of x comes out as 3 and y as 11. The smallest and the largest are known. Hence sufficient.

Re: List A contains 5 positive integers, and the average (arithmetic mean) [#permalink]

Show Tags

28 Dec 2012, 22:42

Thanx Marcab I got it if you can edit and one more line that is necessary constraint it will be easy i.e x+ y must be equal to 14.. I know its understood +1 dude Good going

List A contains 5 positive integers, and the average (arithmetic mean) of the integers in the list is 7. If the integers 6, 7, and 8 are in list A, what is the range of list A?

(1) The integer 3 is in list A. (2) The largest term in list A is greater than 3 times and less than 4 times the size of the smallest term.

Re: List A contains 5 positive integers, and the average (arithmetic mean) [#permalink]

Show Tags

16 Jun 2015, 04:18

1

This post received KUDOS

Bunuel wrote:

List A contains 5 positive integers, and the average (arithmetic mean) of the integers in the list is 7. If the integers 6, 7, and 8 are in list A, what is the range of list A?

(1) The integer 3 is in list A. (2) The largest term in list A is greater than 3 times and less than 4 times the size of the smallest term.

Kudos for a correct solution.

First put everything together: 5 Integers * Average of 7 = Sum of 35 for the whole List A. 6, 7 and 8 included equals 21. Therefore 2 integers left with a value of 14.

Statement 1: Sufficient The list contains 3, 6, 7, 8 and 11 as the last integer (all adding up to 35). Range = 11-3 = 8

Statement 2: Sufficient How can we split 14 so that the biggest Number of the List is > 3x smallest and <4x smallest. Only 3 and 11 fit. Range 11-3.

Answer D.
_________________

Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!

PS Please send me PM if I do not respond to your question within 24 hours.

Last edited by reto on 16 Jun 2015, 04:45, edited 1 time in total.

Re: List A contains 5 positive integers, and the average (arithmetic mean) [#permalink]

Show Tags

16 Jun 2015, 07:34

1

This post received KUDOS

Bunuel wrote:

List A contains 5 positive integers, and the average (arithmetic mean) of the integers in the list is 7. If the integers 6, 7, and 8 are in list A, what is the range of list A?

(1) The integer 3 is in list A. (2) The largest term in list A is greater than 3 times and less than 4 times the size of the smallest term.

Kudos for a correct solution.

Explaination : Let the two missing integers are x and Y. So list is x,y,6,7,8 and average is 7

Henc X + Y + 6+7+8 = 35 X + Y = 14.

If X = 1 and Y = 13 - range = 12 If X = 10 and Y = 4 Range = 6

Basically to find the range we need to find X and Y.

Statement 1 : The integer 3 is in list A. So either X or Y is 3, hence Either X or Y is 11. Consider X = 3 and Y = 11 Range = 8 - definite answer

Hence statement 1 is sufficient.

Statement 2 : The largest term in list A is greater than 3 times and less than 4 times the size of the smallest term. Consider extremes, consider Largest Term (Y) is equal to 3 time smallest term (x) X + y = 14 X + 3X = 14 4X = 14 X = 3.5 So one of the term has to less than 3.5

consider Largest Term (Y) is equal to 4 time smallest term (x) X + y = 14 X + 4X = 14 5X = 14 X = 2.8 so one of the term has to be more than 2.8

Only integer 3 satisfies these extremities, hence one of the missing integer is 3 and another is 11.

Range = 8

Hence statement 2 is sufficient.

Hence Option D, each of the statement is sufficient.

Re: List A contains 5 positive integers, and the average (arithmetic mean) [#permalink]

Show Tags

16 Jun 2015, 09:09

2

This post received KUDOS

Bunuel wrote:

List A contains 5 positive integers, and the average (arithmetic mean) of the integers in the list is 7. If the integers 6, 7, and 8 are in list A, what is the range of list A?

(1) The integer 3 is in list A. (2) The largest term in list A is greater than 3 times and less than 4 times the size of the smallest term.

Kudos for a correct solution.

Solution -

Average of the list is (6+7+8+x+y) = 7*5 = 35 -> x+y=14.

Stmt 1 - (6+7+8+3+y) = 35 - > Missing number from the list is y=11 ---> Range = 11-3 = 8. Sufficient.

Stmt 2 - The largest term y in list is greater than 3 times and less than 4 times the size of the smallest term x.

3x<y<4x -> After substituting y=14-x in the inequality 3x<14-x<4x -> 4x<14<5x. The only integer x satisfy the given inequality is x=3 (9<14<15).

Re: List A contains 5 positive integers, and the average (arithmetic mean) [#permalink]

Show Tags

16 Jun 2015, 10:02

1

This post received KUDOS

Bunuel wrote:

List A contains 5 positive integers, and the average (arithmetic mean) of the integers in the list is 7. If the integers 6, 7, and 8 are in list A, what is the range of list A?

(1) The integer 3 is in list A. (2) The largest term in list A is greater than 3 times and less than 4 times the size of the smallest term.

Kudos for a correct solution.

Given : Five Positive integers have 7 as average. If the integers 6, 7, and 8 are in list A, let us assume that other two integers are x and y.

So, \((x + y + 6 + 7 + 8) / 5 = 7\) => \(x + y + 21 = 35\) => \(x+y=14\) So (x,y) can be (1,13), (2,12), (3,11), (4,10), (5,9), (6,8), (7,7), (8,6), (9,5), (10,4), (11,3), (12,2) or (13,1). Now, 1.) The integer 3 is in list A. So lets say, x = 3, that means y will be 11 (14-3).

So the list A is (3,6,7,8,11) And Range of A is 8 (11-3).

SUFFICIENT.

(2) The largest term in list A is greater than 3 times and less than 4 times the size of the smallest term. \(3*smallest term < largest term < 4*smallest term.\) Now we will check this condition for (x,y) as (1,13), (2,12), (3,11), (4,10), (5,9), (6,8) or (7,7). As we can see, out of the values of (x,y) specified above only for (3,11) or (11,3) the list A satisfies this condition. So the list A is (3,6,7,8,11) And Range of A is 8 (11-3). Hence again SUFFICIENT.

List A contains 5 positive integers, and the average (arithmetic mean) of the integers in the list is 7. If the integers 6, 7, and 8 are in list A, what is the range of list A?

(1) The integer 3 is in list A. (2) The largest term in list A is greater than 3 times and less than 4 times the size of the smallest term.

The average of all five integers in the set is 7. Three of the integers in the set are given (6, 7, and 8) and they all have an average of 7. Therefore, the floating terms in this problem must also have an average of 7. If we assign x and y to represent these terms, we have:

(x + y)/2 = 7; x + y = 14.

Our rephrased question is thus, “Given that x + y = 14, what is either x or y?” Once we know one of the values, we can solve for the other, and thereby determine the range of the set.

(1) SUFFICIENT: If 3 is one of the unknown integers, the other must be 11. The range is thus 11 – 3 = 8.

(2) SUFFICIENT: This statement might seem a little too vague to be sufficient, but by visually listing the possible pairs that add up to 14, we can rule out pairs that don't fit the constraint from this statement:

Notice that the pairings represent the constraint x + y = 14. Visually, this means that x and y are balanced around 7.

Among these pairs: 8 is 1.33 times the size of 6 (the ratio is too low). 9 is 1.8 times the size of 5 (the ratio is too low). 10 is 2.5 times the size of 4 (the ratio is too low). 11 is 3.66 times the size of 3 (an acceptable ratio). 12 is 6 times the size of 2 (the ratio is too high).

Only one pair of integers results in a ratio strictly between 3 and 4. The unknown terms must therefore be 3 and 11, and the range is 11 – 3 = 8.

The correct answer is D.

In this problem we saw the constraint x + y = 14: a fixed sum. Another common constraint is a fixed difference, such as a – b = 2. A fixed difference can be represented visually as a fixed distance between a and b on the number line, with a to the right because it is larger. That distance could move left or right:

Re: List A contains 5 positive integers, and the average (arithmetic mean) [#permalink]

Show Tags

26 May 2016, 11:44

(6+7+8+x+y)/5 = 7

Since the average of 6+7+8 is 7, the average of x+y must be 7 as well.

(x+y)/2 = 7 ---> x+y = 14

1.) The integer 3 is in the list A 3+y = 14 ---> y =11 so range = 3-11 SUFF

2.) The largest term in list A is greater than 3 times and less than 4 times the size of the smallest term In order for x+y = 14, x and y must be the smallest and largest numbers in the set. 3x = y ---> 4x = 14 x = 3.5 4x = y ---> 5x = 14 x = 2.8 If x is an integer then x = 3 and y = 11 SUFF

Re: List A contains 5 positive integers, and the average (arithmetic mean) [#permalink]

Show Tags

13 Oct 2016, 16:54

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

There’s something in Pacific North West that you cannot find anywhere else. The atmosphere and scenic nature are next to none, with mountains on one side and ocean on...

This month I got selected by Stanford GSB to be included in “Best & Brightest, Class of 2017” by Poets & Quants. Besides feeling honored for being part of...

Joe Navarro is an ex FBI agent who was a founding member of the FBI’s Behavioural Analysis Program. He was a body language expert who he used his ability to successfully...