GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 05 Dec 2019, 13:45

Close

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
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.

Close

Request Expert Reply

Confirm Cancel

In a numerical table with 10 rows and 10 columns, each entry is either

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Board of Directors
User avatar
D
Joined: 01 Sep 2010
Posts: 3417
In a numerical table with 10 rows and 10 columns, each entry is either  [#permalink]

Show Tags

New post 25 Jul 2017, 11:27
6
Top Contributor
93
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

72% (02:45) correct 28% (02:36) wrong based on 1253 sessions

HideShow timer Statistics

In a numerical table with 10 rows and 10 columns, each entry is either a 9 or a 10. If the number of 9s in the nth row is n – 1 for each n from 1 to 10, what is the average (arithmetic mean) of all the numbers in the table?

A. 9.45

B. 9.50

C. 9.55

D. 9.65

E. 9.70

_________________
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59561
In a numerical table with 10 rows and 10 columns, each entry is either  [#permalink]

Show Tags

New post 25 Jul 2017, 23:10
24
18
carcass wrote:
In a numerical table with 10 rows and 10 columns, each entry is either a 9 or a 10. If the number of 9s in the nth row is n – 1 for each n from 1 to 10, what is the average (arithmetic mean) of all the numbers in the table?

A. 9.45

B. 9.50

C. 9.55

D. 9.65

E. 9.70


We have 10*10 = 100 entries.

"The number of 9s in the nth row is n – 1 for each n from 1 to 10" means that:
In the 10th row the number of 9s is 10 - 1 = 9;
In the 9th row the number of 9s is 9 - 1 = 8;
In the 8th row the number of 9s is 8 - 1 = 7;
...
In the 1st row the number of 9s is 1 - 1 = 0.

Thus, the total number of 9s is 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 9*(9 + 1)/2 = 45.

The number of 10s is therefore 100 - 45 = 55.

The average of all numbers = (45*9 + 55*10)/100 = 9.55.

Answer: C.

P.S. Below is an image for better understanding:
Image

Attachment:
Untitled.png
Untitled.png [ 8.57 KiB | Viewed 22030 times ]
Most Helpful Community Reply
Current Student
User avatar
D
Joined: 12 Aug 2015
Posts: 2548
Schools: Boston U '20 (M)
GRE 1: Q169 V154
GMAT ToolKit User
Re: In a numerical table with 10 rows and 10 columns, each entry is either  [#permalink]

Show Tags

New post 05 Aug 2017, 23:13
14
4
Painful question.

I feel this question is just pure lengthy and nothing else.

Here is what I did -->

Sum => 1000-(1+2+3+4+5+6+7+9) => 1000-(45) => 955

Total spaces => 100

Mean => 955/100 => 9.55



_________________
General Discussion
Intern
Intern
avatar
B
Joined: 02 Oct 2014
Posts: 10
GMAT ToolKit User Reviews Badge
Re: In a numerical table with 10 rows and 10 columns, each entry is either  [#permalink]

Show Tags

New post 01 Aug 2017, 19:39
2
1
Key formula to note: Avg of an evenly spaced set = \(\frac{(First + Last)}{2}\)

Yellow part sum: 9 ( 1 + 2 + 3 ..... 9) = 9 * (Avg * 9) = 9 * [(9+1)/2]*9 = 45 * 9 = 405
This also hints there are 9 9s

Green part sum: 10 ( 1 + 2 + 3 .... 10) = 10 * 5.5*10 = 550
There are 10 10s

Total elements = 10 * 10 = 100

Thus Avg =
(550+405)/100 = 9.55 (C)
Intern
Intern
avatar
Joined: 25 Jul 2017
Posts: 7
Re: In a numerical table with 10 rows and 10 columns, each entry is either  [#permalink]

Show Tags

New post 06 Aug 2017, 02:12
1
2
We can do it following way also to be quick -
Assume al lnumbers were 10, then the sum would have been 10*10(rows)*10(columns) = 1000
Now, this sum is diminshed by including some 9s in the rows in a specific pattern. So remove the extra counted 1 (10-9 = 1) from above sum.
There are 0+1+2+3+4+5+6+7+8+9 = 45 9s. Hence, subtract 45 from 1000.
This gives 955 which is the sum of all numbers on the grid.
Hence, average = 955/100 = 9.55
C
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2809
Re: In a numerical table with 10 rows and 10 columns, each entry is either  [#permalink]

Show Tags

New post 09 Aug 2017, 13:34
1
1
carcass wrote:
In a numerical table with 10 rows and 10 columns, each entry is either a 9 or a 10. If the number of 9s in the nth row is n – 1 for each n from 1 to 10, what is the average (arithmetic mean) of all the numbers in the table?

A. 9.45

B. 9.50

C. 9.55

D. 9.65

E. 9.70


Since the table has 10 rows and 10 columns there are 100 spots in the table.

So we see there are:

For row 1: n = 1 and there are (n - 1) = (1 - 1) = 0. Thus, there are 0 nines in row 1

For row 2: n = 2 and there are (n - 1) = (2 - 1) = 1. Thus, there is 1 nine in row 2.

For row 3: n = 3 and there are (n - 1) = (3 - 1) = 2. Thus, there are 2 nines in row 3, and so on.

We can see that a pattern emerges.

So the number of nines is:

0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45

Because there are 100 numbers in the entire table, we have (100 - 45) = 55 tens.

Thus, the average of the 45 nines and 55 tens is:

[9(45) + 10(55)]/100 = (405 + 550)/100 = 9.55

Answer: C
_________________

Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Manager
Manager
User avatar
G
Joined: 22 May 2015
Posts: 125
Re: In a numerical table with 10 rows and 10 columns, each entry is either  [#permalink]

Show Tags

New post 21 Aug 2017, 08:17
1
1st row has 0 9's
2nd row has 1 9's
.....
10th row has 9 9's

No of 9's = 1+2.....+9 = 45.

=> No of 10's = 55

So total sum of numbers = (45*9)+(55*10) = 955

Mean = 955/100 = 9.55
_________________
Consistency is the Key
Manager
Manager
User avatar
B
Joined: 26 Feb 2018
Posts: 54
WE: Sales (Internet and New Media)
Re: In a numerical table with 10 rows and 10 columns, each entry is either  [#permalink]

Show Tags

New post 16 Mar 2018, 11:31
stonecold , could you explain , in the sum section how did you take 1000 - rest
_________________
" Can't stop learning and failing"
Senior Manager
Senior Manager
User avatar
P
Joined: 10 Apr 2018
Posts: 267
Location: United States (NC)
In a numerical table with 10 rows and 10 columns, each entry is either  [#permalink]

Show Tags

New post 15 Aug 2018, 21:58
1
Bunuel wrote:
carcass wrote:
In a numerical table with 10 rows and 10 columns, each entry is either a 9 or a 10. If the number of 9s in the nth row is n – 1 for each n from 1 to 10, what is the average (arithmetic mean) of all the numbers in the table?

A. 9.45

B. 9.50

C. 9.55

D. 9.65

E. 9.70


We have 10*10 = 100 entries.

"The number of 9s in the nth row is n – 1 for each n from 1 to 10" means that:
In the 10th row the number of 9s is 10 - 1 = 9;
In the 9th row the number of 9s is 9 - 1 = 8;
In the 8th row the number of 9s is 8 - 1 = 7;
...
In the 1st row the number of 9s is 1 - 1 = 0.

Thus, the total number of 9s is 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 9*(9 + 1)/2 = 45.

The number of 10s is therefore 100 - 45 = 55.

The average of all numbers = (45*9 + 55*10)/100 = 9.55.

Answer: C.

P.S. Below is an image for better understanding:
Image

Attachment:
Untitled.png



Hi loserunderachiever,

https://gmatclub.com/forum/download/file.php?id=36500

May be i can try to explain. View the figure above
Let's assume that each value in 10 rows and 10 columns is "10". Then then total sum of each columns would be 100 and there are 10 columns= 100*10= 100
Now since in every row there is one less 10 than previous and we have assumed the value of it 1 each more than actual ,we will subtract it from total.
In the ninth coloumn our assumed total is 100 but actually its 99 so we have taken 1 more than assumed value .
Now in column number 8 number our assumed total is 100 but actually it is 98 so its two more than assumed. Why because we assumed two "10's" in place of 9 so each contributes additional 1.
similarly up-to column number 1 where our assumed total is 100, but actually it has to be 91 . each of the 9 assumed 10's are contributing 1 each to total .

So 1000-(9+8+7+6+5+4+3+2+1+0)
is 1000-45
955
total number observations are 100

so avg = 955/100
9.55
Hence answer C
_________________
Probus

~You Just Can't beat the person who never gives up~ Babe Ruth
Manager
Manager
User avatar
S
Joined: 20 Jul 2018
Posts: 87
GPA: 2.87
Re: In a numerical table with 10 rows and 10 columns, each entry is either  [#permalink]

Show Tags

New post 02 Sep 2018, 19:30
Total entries of 9 and 10 are 100 in the table.
In first row number of 9’s are 0 as according to n-1
In second row number of 9’s are 1
In third, fourth, fifth,....,tenth rows are 2,3,4,5,6,7,8,9 respectively.
So total 9’s are 0+1+2+3+4+5+6+7+8+9=45
Total 10’s are =100-45=55
So total sum of entries is 45*9 + 55*10 = 955
Average is=Sum/total number of entries
Average=955/100=9.55

Posted from my mobile device
_________________
Hasnain Afzal

"When you wanna succeed as bad as you wanna breathe, then you will be successful." -Eric Thomas
Intern
Intern
User avatar
B
Joined: 26 Apr 2015
Posts: 19
Location: United States
GMAT 1: 680 Q47 V36
GMAT 2: 700 Q48 V38
GPA: 3.91
GMAT ToolKit User Reviews Badge
Re: In a numerical table with 10 rows and 10 columns, each entry is either  [#permalink]

Show Tags

New post 16 Oct 2018, 12:09
Bunuel wrote:
carcass wrote:
In a numerical table with 10 rows and 10 columns, each entry is either a 9 or a 10. If the number of 9s in the nth row is n – 1 for each n from 1 to 10, what is the average (arithmetic mean) of all the numbers in the table?

A. 9.45

B. 9.50

C. 9.55

D. 9.65

E. 9.70


Image

Attachment:
Untitled.png


Lengthy question for sure; not sure I'd be able to stick with it during test-like conditions.
Anyways, if you note that in rows 2-10 there is an equal number of 9s and 10s, you can calculate it as a weighted average between those rows and the first row:

\(\frac{((9x10)(9.50) + (10)(10))}{(10x10)}\) =8.55 + 1 = 9.55
Manager
Manager
User avatar
S
Joined: 17 Mar 2018
Posts: 71
Reviews Badge
In a numerical table with 10 rows and 10 columns, each entry is either  [#permalink]

Show Tags

New post 19 Nov 2018, 00:01
As per question, in 1 row the number of 9's are row number-1, and the remaining numbers in the row are 10s.
Hence, quickest way is to list number 9s by row number and 10s would be 10-9s (because only 10 numbers in each row)


Ans.= c
Attachments

Screen Shot 2018-11-19 at 11.03.07 AM.png
Screen Shot 2018-11-19 at 11.03.07 AM.png [ 25.27 KiB | Viewed 10469 times ]

Intern
Intern
avatar
B
Joined: 13 Mar 2019
Posts: 27
Re: In a numerical table with 10 rows and 10 columns, each entry is either  [#permalink]

Show Tags

New post 04 Aug 2019, 10:10
1
We just need to subtract (1+2+....9) from 1000 to get the total sum.
1000 - 45 = 955
So the Answer is 955/10.
Manager
Manager
avatar
S
Joined: 18 Jul 2019
Posts: 54
Premium Member Reviews Badge CAT Tests
Re: In a numerical table with 10 rows and 10 columns, each entry is either  [#permalink]

Show Tags

New post 29 Aug 2019, 00:38
carcass wrote:
In a numerical table with 10 rows and 10 columns, each entry is either a 9 or a 10. If the number of 9s in the nth row is n – 1 for each n from 1 to 10, what is the average (arithmetic mean) of all the numbers in the table?

A. 9.45

B. 9.50

C. 9.55

D. 9.65

E. 9.70


You can also do it by another method where you find the sum of the rows.
1st row has all 10's and no 9's so the sum is 100
2nd row has 9 10's and 1 9's and the sum is 99
3rd row has 8 10's and 2 9's and the sum is 98
If you follow the pattern you will find out that the sum of rows goes on decreasing by one i.e 100,99,98,,97 so om upto 91.
In consecutive number series the middle value is the mean i.e (96+95)/2=95.5 {since there are 10 numbers, mean of the middle values, if there are odd no of numbers in series then the middlemost value}
Since there are 10 rows average is 95.5/10 i.e 9.55
Director
Director
User avatar
P
Joined: 18 Dec 2017
Posts: 819
Location: United States (KS)
Premium Member CAT Tests
Re: In a numerical table with 10 rows and 10 columns, each entry is either  [#permalink]

Show Tags

New post 05 Sep 2019, 08:04
2
Bunuel wrote:
carcass wrote:
In a numerical table with 10 rows and 10 columns, each entry is either a 9 or a 10. If the number of 9s in the nth row is n – 1 for each n from 1 to 10, what is the average (arithmetic mean) of all the numbers in the table?

A. 9.45

B. 9.50

C. 9.55

D. 9.65

E. 9.70


We have 10*10 = 100 entries.

"The number of 9s in the nth row is n – 1 for each n from 1 to 10" means that:
In the 10th row the number of 9s is 10 - 1 = 9;
In the 9th row the number of 9s is 9 - 1 = 8;
In the 8th row the number of 9s is 8 - 1 = 7;
...
In the 1st row the number of 9s is 1 - 1 = 0.

Thus, the total number of 9s is 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 9*(9 + 1)/2 = 45.

The number of 10s is therefore 100 - 45 = 55.

The average of all numbers = (45*9 + 55*10)/100 = 9.55.

Answer: C.

P.S. Below is an image for better understanding:
Image

Attachment:
Untitled.png


Hello Sir Bunuel
Is it okay to say: If we have same number of 9s and 10s then the average would have been 9.5 But since we have more 10s (one entire row without 9s) so the average will be slightly higher than 9.5 and Hence 9.55?
_________________
D-Day : 21st December 2019

The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long

Learn from the Legend himself: All GMAT Ninja LIVE YouTube videos by topic
You are missing on great learning if you don't know what this is: Project SC Butler
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59561
Re: In a numerical table with 10 rows and 10 columns, each entry is either  [#permalink]

Show Tags

New post 05 Sep 2019, 08:39
TheNightKing wrote:
Bunuel wrote:
carcass wrote:
In a numerical table with 10 rows and 10 columns, each entry is either a 9 or a 10. If the number of 9s in the nth row is n – 1 for each n from 1 to 10, what is the average (arithmetic mean) of all the numbers in the table?

A. 9.45

B. 9.50

C. 9.55

D. 9.65

E. 9.70


We have 10*10 = 100 entries.

"The number of 9s in the nth row is n – 1 for each n from 1 to 10" means that:
In the 10th row the number of 9s is 10 - 1 = 9;
In the 9th row the number of 9s is 9 - 1 = 8;
In the 8th row the number of 9s is 8 - 1 = 7;
...
In the 1st row the number of 9s is 1 - 1 = 0.

Thus, the total number of 9s is 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 9*(9 + 1)/2 = 45.

The number of 10s is therefore 100 - 45 = 55.

The average of all numbers = (45*9 + 55*10)/100 = 9.55.

Answer: C.

P.S. Below is an image for better understanding:
Image

Attachment:
Untitled.png


Hello Sir Bunuel
Is it okay to say: If we have same number of 9s and 10s then the average would have been 9.5 But since we have more 10s (one entire row without 9s) so the average will be slightly higher than 9.5 and Hence 9.55?

_______________________
Yes, that would be correct.
Director
Director
User avatar
P
Joined: 18 Dec 2017
Posts: 819
Location: United States (KS)
Premium Member CAT Tests
Re: In a numerical table with 10 rows and 10 columns, each entry is either  [#permalink]

Show Tags

New post 05 Sep 2019, 08:47
Quote:
_______________________
Yes, that would be correct.


Thank you!
_________________
D-Day : 21st December 2019

The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long

Learn from the Legend himself: All GMAT Ninja LIVE YouTube videos by topic
You are missing on great learning if you don't know what this is: Project SC Butler
Director
Director
User avatar
V
Joined: 24 Oct 2016
Posts: 580
GMAT 1: 670 Q46 V36
GMAT 2: 690 Q47 V38
In a numerical table with 10 rows and 10 columns, each entry is either  [#permalink]

Show Tags

New post Updated on: 24 Nov 2019, 14:46
carcass wrote:
In a numerical table with 10 rows and 10 columns, each entry is either a 9 or a 10. If the number of 9s in the nth row is n – 1 for each n from 1 to 10, what is the average (arithmetic mean) of all the numbers in the table?

A. 9.45

B. 9.50

C. 9.55

D. 9.65

E. 9.70


We'll have a 10*10 matrix.

1st row will have 0 9's and 10 10's. => Sum of 1st row = 100
10th row will have 9 9's and 1 10 => Sum of 10th row = 9*9 + 10*1 = 91

Method 1: Shorter



Avg of 1st row: 10
Avg of 10th row: 9.1

Avg of Avg = (10 + 9.1)/2 = 9.55

Method 2: Longer



If you notice, we have a sequence of consecutive integers (CI).
Mean of CI = (91 + 100)/2 = 95.5

Total sum = 95.5 * 10

Avg = (95.5 * 10)/100 = 9.55

ANSWER: C

Originally posted by dabaobao on 31 Oct 2019, 03:53.
Last edited by dabaobao on 24 Nov 2019, 14:46, edited 1 time in total.
Intern
Intern
User avatar
B
Joined: 07 Aug 2018
Posts: 3
Re: In a numerical table with 10 rows and 10 columns, each entry is either  [#permalink]

Show Tags

New post 31 Oct 2019, 17:28
What should be the average time to solve this question? It is taking around 4 minutes to solve this one.
Director
Director
User avatar
P
Joined: 18 Dec 2017
Posts: 819
Location: United States (KS)
Premium Member CAT Tests
Re: In a numerical table with 10 rows and 10 columns, each entry is either  [#permalink]

Show Tags

New post 31 Oct 2019, 17:34
Dream2020 wrote:
What should be the average time to solve this question? It is taking around 4 minutes to solve this one.


I see I took 2:01 back when I solved it. On average, you should take only about 2 minutes for any question on GMAT. You can stretch it to 2:30 only if you know you're going somewhere with it and you know that you will get the right answer. Otherwise you should mark it randomly and move on.

Note: If you are still learning and practicing then it is okay to take longer but still you should be keeping an eye on the clock.

Hope that helps!

Dream2020
_________________
D-Day : 21st December 2019

The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long

Learn from the Legend himself: All GMAT Ninja LIVE YouTube videos by topic
You are missing on great learning if you don't know what this is: Project SC Butler
GMAT Club Bot
Re: In a numerical table with 10 rows and 10 columns, each entry is either   [#permalink] 31 Oct 2019, 17:34

Go to page    1   2    Next  [ 22 posts ] 

Display posts from previous: Sort by

In a numerical table with 10 rows and 10 columns, each entry is either

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne