GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 25 Jan 2020, 06:43

### GMAT Club Daily Prep

#### 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

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

# Set A is composed of nine numbers, labeled A1 through A9. Set B is als

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 60647
Set A is composed of nine numbers, labeled A1 through A9. Set B is als  [#permalink]

### Show Tags

10 Nov 2014, 09:39
2
33
00:00

Difficulty:

95% (hard)

Question Stats:

27% (02:37) correct 73% (02:33) wrong based on 259 sessions

### HideShow timer Statistics

Tough and Tricky questions: Sets.

Set A is composed of nine numbers, labeled A1 through A9. Set B is also composed of nine numbers, labeled B1 through B9. Set B is defined as follows: B1 = 1 + A1; B2 = 2 + A2; and so on, including B9 = 9 + A9. How much larger is the sum of set B's mean and range than the sum of set A's mean and range?

A. 4
B. 9
C. 13
D. 17
E. cannot be determined

Kudos for a correct solution.

_________________
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1723
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: Set A is composed of nine numbers, labeled A1 through A9. Set B is als  [#permalink]

### Show Tags

Updated on: 11 Nov 2014, 19:12
5
Answer = E = Cannot be determined

Set A = { a1, a2 , a3 ......... a9}

Nowhere in the question its mentioned that a1 < a2 < a3 < .............. <a9 as we are "assuming" it to be "ideally"

Now, this will NOT make effect for computing mean, however will effect on computing "Range"

For Example:

Set A = {9, 8, 7, 6, 5, 4, 3, 2, 1}

Set B = {10, 10, 10, 10, 10, 10, 10, 10, 10, 10}

To calculate range of set A, it has to be re-organised from {1,2.......... 9}

Range = 8; Mean = 5

Set B

Range = 0; Mean = 10

Difference = -3

We may take multiple examples like this which will give different answers.

Bunuel: Thank you so much for indicating that C was incorrect answer

Originally posted by PareshGmat on 10 Nov 2014, 20:53.
Last edited by PareshGmat on 11 Nov 2014, 19:12, edited 2 times in total.
##### General Discussion
Manager
Joined: 03 Nov 2009
Posts: 54
Re: Set A is composed of nine numbers, labeled A1 through A9. Set B is als  [#permalink]

### Show Tags

10 Nov 2014, 11:54
1

Range of set B will always twice that of Set A in value.
if the Set A (1,2,3,4,5,6,7,8,9) - Range = 9-1 = 8
then Set B (2,4,6,8,10,12,14,16,18) - Range = 18-2 = 16

Mean of Set B will be twice that of Set A

if the Set A (1,2,3,4,5,6,7,8,9) - Mean = 45/9 = 5
then Set B (2,4,6,8,10,12,14,16,18) - Mean = 90/9 = 10

Set A (Range + Mean) = 8+5 = 13
Set B (Range + Mean) = 16+10 = 26

Set B (Range + Mean) - Set A (Range + Mean) = 26-13 = 13
Manager
Joined: 10 Sep 2014
Posts: 96
Re: Set A is composed of nine numbers, labeled A1 through A9. Set B is als  [#permalink]

### Show Tags

10 Nov 2014, 12:01
I am a bit old fashioned and just wrote it all out on paper and used the plug-in method. At first I chose #s for A and then I used the rule that was given to figure out the values for B. Calculations are below. This took me 2min25sec.

A1=3 B1= 4
A2=4 B2 = 6
A3=5 B3=8
A4=6 B4=10
A5=7 B5=12
A6=8 B6=14
A7=9 B7=16
A8=10 B8=18
A9=11 B9=20
mean= sum/9 = 7 mean= sum/9 = 12
range= 11-3 = 8 range = 20-4 = 16
mean + range: 15 mean + range: 28

(set B mean + range) - (set A mean + range) = 28 - 15 = 13

Math Expert
Joined: 02 Sep 2009
Posts: 60647
Re: Set A is composed of nine numbers, labeled A1 through A9. Set B is als  [#permalink]

### Show Tags

11 Nov 2014, 03:49
1
C is not correct. Anyone else?
_________________
Intern
Joined: 09 Sep 2014
Posts: 1
Re: Set A is composed of nine numbers, labeled A1 through A9. Set B is als  [#permalink]

### Show Tags

11 Nov 2014, 07:58
Set A - A1, A2, A3, A4 and so on......

Set B: A1 +1, A2 +2, A3+ 3, A4+4 ,A+5...-> 1+2+3+4+5+6+7+8+9 = 45/9 =5 (mean of set B)
Range of set B from 1 to 9 = 8

Set A: B1-1, B2-2, B3-3, B4-4, B5-5....-> -1-2-3-4-5-6-7-8-9 = -45/9 = -5 ( mean of set A)
Range of set A from -1 to -9 = 8

5+8 = 13
-5+8= 4

Hence 13-4= 9

Does it make any sense or have I broken all math rules ? ☺
I am new here.
Thank You !
Math Expert
Joined: 02 Sep 2009
Posts: 60647
Re: Set A is composed of nine numbers, labeled A1 through A9. Set B is als  [#permalink]

### Show Tags

12 Nov 2014, 04:19
PareshGmat wrote:
Answer = E = Cannot be determined

Set A = { a1, a2 , a3 ......... a9}

Nowhere in the question its mentioned that a1 < a2 < a3 < .............. <a9 as we are "assuming" it to be "ideally"

Now, this will NOT make effect for computing mean, however will effect on computing "Range"

For Example:

Set A = {9, 8, 7, 6, 5, 4, 3, 2, 1}

Set B = {10, 10, 10, 10, 10, 10, 10, 10, 10, 10}

To calculate range of set A, it has to be re-organised from {1,2.......... 9}

Range = 8; Mean = 5

Set B

Range = 0; Mean = 10

Difference = -3

We may take multiple examples like this which will give different answers.

Bunuel: Thank you so much for indicating that C was incorrect answer

Yes, the correct answer is E.
_________________
Intern
Joined: 28 Oct 2014
Posts: 2
Re: Set A is composed of nine numbers, labeled A1 through A9. Set B is als  [#permalink]

### Show Tags

12 Nov 2014, 05:23

A (A1+.....+A9)
B (B1+.....+B9) = (A1+.....+A9) + 45

A

Mean = (A1+....+A9)/9
Range = A9-A1

B

Mean = (A1+...+A9+45)/9 = (A1+....+A9)/9 + 5
Range = A9+9-(A1+1) = A9-A1+8

Combining

(A1+....+A9)/9 + 5+ A9-A1+8 - ((A1+....+A9)/9+A9-A1) = 5+8 = 13

Answer C - In my view
Math Expert
Joined: 02 Sep 2009
Posts: 60647
Re: Set A is composed of nine numbers, labeled A1 through A9. Set B is als  [#permalink]

### Show Tags

12 Nov 2014, 05:26
viniciuszds wrote:

A (A1+.....+A9)
B (B1+.....+B9) = (A1+.....+A9) + 45

A

Mean = (A1+....+A9)/9
Range = A9-A1

B

Mean = (A1+...+A9+45)/9 = (A1+....+A9)/9 + 5
Range = A9+9-(A1+1) = A9-A1+8

Combining

(A1+....+A9)/9 + 5+ A9-A1+8 - ((A1+....+A9)/9+A9-A1) = 5+8 = 13

Answer C - In my view

Note that the Official Answer is E, not C.
_________________
Intern
Joined: 28 Oct 2014
Posts: 2
Re: Set A is composed of nine numbers, labeled A1 through A9. Set B is als  [#permalink]

### Show Tags

12 Nov 2014, 12:31
Bunuel wrote:
viniciuszds wrote:

A (A1+.....+A9)
B (B1+.....+B9) = (A1+.....+A9) + 45

A

Mean = (A1+....+A9)/9
Range = A9-A1

B

Mean = (A1+...+A9+45)/9 = (A1+....+A9)/9 + 5
Range = A9+9-(A1+1) = A9-A1+8

Combining

(A1+....+A9)/9 + 5+ A9-A1+8 - ((A1+....+A9)/9+A9-A1) = 5+8 = 13

Answer C - In my view

Note that the Official Answer is E, not C.

Tks! i saw my mistake, i assumed sets A and B as sequence, i can`t make this inference.
Director
Joined: 04 Aug 2010
Posts: 514
Schools: Dartmouth College
Re: Set A is composed of nine numbers, labeled A1 through A9. Set B is als  [#permalink]

### Show Tags

08 Sep 2018, 08:00
Bunuel wrote:

Tough and Tricky questions: Sets.

Set A is composed of nine numbers, labeled A1 through A9. Set B is also composed of nine numbers, labeled B1 through B9. Set B is defined as follows: B1 = 1 + A1; B2 = 2 + A2; and so on, including B9 = 9 + A9. How much larger is the sum of set B's mean and range than the sum of set A's mean and range?

A. 4
B. 9
C. 13
D. 17
E. cannot be determined

Case 1:
A = 0, 0, 0, 0, 0, 0, 0, 0, 0 --> range = 0, mean = 0, range + mean = 0
B = 1, 2, 3, 4, 5, 6, 7, 8, 9 --> range = 8, mean = 5, range + mean = 13
B's sum - A's sum = 13-0 = 13

Case 2:
A = 9, 8, 7, 6, 5, 4, 3, 2, 1 --> range = 8, mean = 5, range + mean = 13
B = 10, 10, 10, 10, 10, 10, 10, 10, 10 --> range = 0, mean = 10, range + mean = 10
B's sum - A's sum = 10-13 = -3

Since the two cases yield different results, the difference between B's sum and A's sum cannot be determined.

The use of the word larger in the question stem incorrectly implies that B's sum must be larger than A's sum.
To avoid this miscommunication, the question stem should simply ask for the difference between B's sum and A's sum.
_________________
GMAT and GRE Tutor
New York, NY

Available for tutoring in NYC and long-distance.
SVP
Joined: 03 Jun 2019
Posts: 1942
Location: India
GMAT 1: 690 Q50 V34
Re: Set A is composed of nine numbers, labeled A1 through A9. Set B is als  [#permalink]

### Show Tags

09 Sep 2019, 04:14
Bunuel wrote:

Tough and Tricky questions: Sets.

Set A is composed of nine numbers, labeled A1 through A9. Set B is also composed of nine numbers, labeled B1 through B9. Set B is defined as follows: B1 = 1 + A1; B2 = 2 + A2; and so on, including B9 = 9 + A9. How much larger is the sum of set B's mean and range than the sum of set A's mean and range?

A. 4
B. 9
C. 13
D. 17
E. cannot be determined

Kudos for a correct solution.

Given:
1. Set A is composed of nine numbers, labeled A1 through A9.
2. Set B is also composed of nine numbers, labeled B1 through B9.
3. Set B is defined as follows: B1 = 1 + A1; B2 = 2 + A2; and so on, including B9 = 9 + A9.

Asked: How much larger is the sum of set B's mean and range than the sum of set A's mean and range?

A = {A1,A2, ,,, A9}
B = {B1,B2,,,,B9} = {1+A1,2+A2,,,,,9+A9}

Mean of B = $$\frac{A1+A2+.... + A9 + 45}{9} = \frac{A1+A2 +... + A9}{9} + 5$$ = Mean of A + 5
Since we don't know minimum and maximum of numbers {A1,A2,,, A9}, Range can not be determined.

IMO E
Re: Set A is composed of nine numbers, labeled A1 through A9. Set B is als   [#permalink] 09 Sep 2019, 04:14
Display posts from previous: Sort by