Author 
Message 
TAGS:

Hide Tags

Senior Manager
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 439
Location: United Kingdom
Concentration: International Business, Strategy
GPA: 2.9
WE: Information Technology (Consulting)

If the 4 x 4 grid in the attached picture is filled with the
[#permalink]
Show Tags
31 Jan 2012, 19:25
Question Stats:
75% (02:16) correct 25% (02:23) wrong based on 170 sessions
HideShow timer Statistics
If the 4 x 4 grid in the attached picture is filled with the consecutive integers from 37 to 52, inclusive, so that every row, column and major diagonal sums to the same value, which of the following is a possible value of the sum of the four center cells of the grid (indicated by the shaded area)? (A) 124 (B) 153 (C) 178 (D) 192 (E) 214 Any idea how to approach this question please?
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Best Regards, E.
MGMAT 1 > 530 MGMAT 2> 640 MGMAT 3 > 610 GMAT ==> 730




SVP
Status: Top MBA Admissions Consultant
Joined: 24 Jul 2011
Posts: 1900

Re: Shaded part of the grid
[#permalink]
Show Tags
01 Feb 2012, 03:58
Sum of the numbers from 37 to 52 = (n/2)[2a + (n1)d] = (16/2) [74+15] = 8 * 89 = 712 Therefore the sum of all numbers in the grid = 712 If x is the sum of all numbers in a row/column/major diagonal, then 4x = 712 => x = 178 = sum of all numbers in any row = sum of all numbers in any diagonal = sum of all numbers in either major diagonal Now, consider the grid as follows: 1' 2' 3' 4' 5' 6' 7' 8' 9' 10' 11' 12' 13' 14' 15' 16' We know that 1' + 6' + 11' + 16' = 178 4' + 7' + 10' + 13' = 178 => 1' + 6' + 11' + 16' + 4' + 7' + 10' + 13' = 356 => 6' + 7' + 10' + 11' + 1' + 13' + 4' + 16' = 356 Also 5' + 6' + 7' + 8' + 9' + 10' + 11' + 12' = 356 and 1' + 5' + 9' + 13' + 4' + 8' + 12' + 16' = 356 => 6' + 7' + 10' + 11'  1'  13'  4'  16' = 0 Therefore 6' + 7' + 10' + 11' = 356/2 = 178 = sum of the middle four numbers Option (C).
_________________
GyanOne [www.gyanone.com] Premium MBA and MiM Admissions Consulting
Awesome Work  Honest Advise  Outstanding Results Reach Out, Lets chat!Email: info at gyanone dot com  +91 98998 31738  Skype: gyanone.services




Intern
Joined: 26 May 2016
Posts: 20

If the 4 x 4 grid in the attached picture is filled with the
[#permalink]
Show Tags
13 Jul 2016, 12:04
enigma123 wrote: If the 4 x 4 grid in the attached picture is filled with the consecutive integers from 37 to 52, inclusive, so that every row, column and major diagonal sums to the same value, which of the following is a possible value of the sum of the four center cells of the grid (indicated by the shaded area)?
(A) 124 (B) 153 (C) 178 (D) 192 (E) 214
Any idea how to approach this question please? I approached it this way: there are 16 cells; 37,38,39,...,52 can be denoted as 36+1,36+2,36+3,...,36+16 the total of 37+38+...+52 is therefore =36*16+16*17/2 =16(36+8.5) =16*44.5 =8*89 =4*178 =2*356 =712 The average value of a cell is 712/16 = 44.5 Attachment:
gmatclub.PNG [ 1.95 KiB  Viewed 4303 times ]
Also given : sum of values in column 2 = sum of values in column 3 = sum of values in row 2 = sum of values in row 3. To satisfy this, if we assigned the average value of a cell to each cell, the 4 cells will get a total of 44.5*4 = 178. Hence C is the answer.




Intern
Joined: 16 Jan 2012
Posts: 2

Re: If the 4 x 4 grid in the attached picture is filled with the
[#permalink]
Show Tags
08 Dec 2013, 08:01
In the last step "=> 6' + 7' + 10' + 11'  1'  13'  4'  16' = 0" how can we be sure that the +ve groupings and ve groupings each add up to 178 or 6' + 7' + 10' + 11' = 178. It could be 180 for 6' + 7' + 10' + 11' and 176 for  1'  13'  4'  16'. Am i missing something here?



Intern
Joined: 16 Jan 2012
Posts: 2

Re: If the 4 x 4 grid in the attached picture is filled with the
[#permalink]
Show Tags
08 Dec 2013, 08:02
In the last step "=> 6' + 7' + 10' + 11'  1'  13'  4'  16' = 0" how can we be sure that the +ve groupings and ve groupings each add up to 178 or 6' + 7' + 10' + 11' = 178. It could be 180 for 6' + 7' + 10' + 11' and 176 for  1'  13'  4'  16'. Am i missing something here?



Manager
Status: Work hard in silence, let success make the noise
Joined: 25 Nov 2013
Posts: 126
Location: India
Concentration: Finance, General Management
GMAT 1: 540 Q50 V15 GMAT 2: 640 Q50 V27
GPA: 3.11
WE: Consulting (Computer Software)

Re: If the 4 x 4 grid in the attached picture is filled with the
[#permalink]
Show Tags
10 Dec 2013, 09:16
This is just another great question. The difficulty level of this question is high and it didn't strike me how to do this question when I tried it in the first attempt.
_________________
Sahil Chaudhary If you find this post helpful, please take a moment to click on the "+1 KUDOS" icon. My IELTS 7.5 Experience From 540 to 640...Done with GMAT!!! http://www.sahilchaudhary007.blogspot.com



Intern
Joined: 31 Dec 2015
Posts: 1
GPA: 3.75

Re: If the 4 x 4 grid in the attached picture is filled with the
[#permalink]
Show Tags
04 Jan 2016, 19:57
I followed a rather simple approach. Since all the four sides and the major diagonal has same value. The sum of four center cell should also be the same. and it should be (37+38+51+52) = 178



Manager
Joined: 29 May 2016
Posts: 93

Re: If the 4 x 4 grid in the attached picture is filled with the
[#permalink]
Show Tags
13 Jul 2016, 22:31
mean of all 16 numbers is 44.5 take two number on right of this mean and take two number left , but they all are in such a way that mean is 44.5. so basically 44.5* 4 = 178



Director
Joined: 26 Oct 2016
Posts: 600
Location: United States
Concentration: Marketing, International Business
GPA: 4
WE: Education (Education)

Re: If the 4 x 4 grid in the attached picture is filled with the
[#permalink]
Show Tags
29 Dec 2016, 06:46
manojach87 wrote: enigma123 wrote: If the 4 x 4 grid in the attached picture is filled with the consecutive integers from 37 to 52, inclusive, so that every row, column and major diagonal sums to the same value, which of the following is a possible value of the sum of the four center cells of the grid (indicated by the shaded area)?
(A) 124 (B) 153 (C) 178 (D) 192 (E) 214
Any idea how to approach this question please? I approached it this way: there are 16 cells; 37,38,39,...,52 can be denoted as 36+1,36+2,36+3,...,36+16 the total of 37+38+...+52 is therefore =36*16+16*17/2 =16(36+8.5) =16*44.5 =8*89 =4*178 =2*356 =712 The average value of a cell is 712/16 = 44.5 Attachment: gmatclub.PNG Also given : sum of values in column 2 = sum of values in column 3 = sum of values in row 2 = sum of values in row 3. To satisfy this, if we assigned the average value of a cell to each cell, the 4 cells will get a total of 44.5*4 = 178. Hence C is the answer. It's a great solution.
_________________
Thanks & Regards, Anaira Mitch



Senior Manager
Status: Countdown Begins...
Joined: 03 Jul 2016
Posts: 277
Location: India
Concentration: Technology, Strategy
GPA: 3.7
WE: Information Technology (Consulting)

Re: If the 4 x 4 grid in the attached picture is filled with the
[#permalink]
Show Tags
29 Dec 2016, 20:16
I solved it in this way:
Min number is 37 so Min Sum of 4 numbers will be 37*4 = 148. (Option A out). Max Number is 52 so max sum of 4 numbers will be 52*4 = 208 (Option E out).
Because the numbers are uniformly distributed their sum should should lie in middle of 144 and 208 not towards any of these numbers.(Most likely B and D are out.) 148+208 = 356/2 = 178.
Hope this logic makes sense.



Intern
Joined: 06 May 2015
Posts: 22

Re: If the 4 x 4 grid in the attached picture is filled with the
[#permalink]
Show Tags
19 May 2017, 22:05
hello .
i blv we can solve it using algebra. sum of n numbers as we know Sn =n/2(2a +(n1)d Here d=1, n=16, a=37
we will get that sum of all from 3752 incl is 712. but we have to find sum in each column & dignoal uniform so =712/4 =178 hence ans is C



Manager
Status: Enjoying the Journey
Affiliations: ND
Joined: 26 Sep 2017
Posts: 114
WE: Marketing (Consulting)

Re: If the 4 x 4 grid in the attached picture is filled with the
[#permalink]
Show Tags
19 Jan 2018, 03:29
enigma123 wrote: If the 4 x 4 grid in the attached picture is filled with the consecutive integers from 37 to 52, inclusive, so that every row, column and major diagonal sums to the same value, which of the following is a possible value of the sum of the four center cells of the grid (indicated by the shaded area)?
(A) 124 (B) 153 (C) 178 (D) 192 (E) 214
Any idea how to approach this question please? Here's how I solved it the number of integers= 5237+1=16 The median (8th & 7th term)= (37+8)+(37+7)= 44&45 (No need to divide by 2) Add the previous number and the following number= 43+44+45+46= 178 (D)
_________________
"it takes more time to fix a mistake than to avoid one""Giving kudos" is a decent way to say "Thanks" and motivate contributors. Please use them, it won't cost you anythingHigh achievement always takes place in the framework of high expectation Charles KetteringIf we chase perfection we can catch excellence Vince LombardiGMAT Club Live: 5 Principles for Fast Math: https://gmatclub.com/forum/gmatclublive5principlesforfastmath251028.html#p1940045YouTube sessions by GMATNinja: https://gmatclub.com/forum/verballivewithgmatninjascpronounsthatparallelism250568.html#p1936104The Best SC strategies  Amazing 4 videos by Veritas: https://gmatclub.com/forum/thebestscstrategiesamazing4videosbyveritas250377.html#p1934575



Manager
Status: Enjoying the Journey
Affiliations: ND
Joined: 26 Sep 2017
Posts: 114
WE: Marketing (Consulting)

Re: If the 4 x 4 grid in the attached picture is filled with the
[#permalink]
Show Tags
19 Jan 2018, 04:11
manojach87 wrote: enigma123 wrote: If the 4 x 4 grid in the attached picture is filled with the consecutive integers from 37 to 52, inclusive, so that every row, column and major diagonal sums to the same value, which of the following is a possible value of the sum of the four center cells of the grid (indicated by the shaded area)?
(A) 124 (B) 153 (C) 178 (D) 192 (E) 214
Any idea how to approach this question please? I approached it this way: there are 16 cells; 37,38,39,...,52 can be denoted as 36+1,36+2,36+3,...,36+16 the total of 37+38+...+52 is therefore =36*16+16*17/2 =16(36+8.5) =16*44.5 =8*89 =4*178 =2*356 =712 The average value of a cell is 712/16 = 44.5 Attachment: gmatclub.PNG Also given : sum of values in column 2 = sum of values in column 3 = sum of values in row 2 = sum of values in row 3. To satisfy this, if we assigned the average value of a cell to each cell, the 4 cells will get a total of 44.5*4 = 178. Hence C is the answer. I believe there's a simpler way to calculate the total: [#of items (first term+last term)] /2 = 16 (37+52)/2= 8*89= 712
_________________
"it takes more time to fix a mistake than to avoid one""Giving kudos" is a decent way to say "Thanks" and motivate contributors. Please use them, it won't cost you anythingHigh achievement always takes place in the framework of high expectation Charles KetteringIf we chase perfection we can catch excellence Vince LombardiGMAT Club Live: 5 Principles for Fast Math: https://gmatclub.com/forum/gmatclublive5principlesforfastmath251028.html#p1940045YouTube sessions by GMATNinja: https://gmatclub.com/forum/verballivewithgmatninjascpronounsthatparallelism250568.html#p1936104The Best SC strategies  Amazing 4 videos by Veritas: https://gmatclub.com/forum/thebestscstrategiesamazing4videosbyveritas250377.html#p1934575



Intern
Joined: 19 Jul 2017
Posts: 40

If the 4 x 4 grid in the attached picture is filled with the
[#permalink]
Show Tags
30 Jun 2018, 11:26
enigma123 wrote: If the 4 x 4 grid in the attached picture is filled with the consecutive integers from 37 to 52, inclusive, so that every row, column and major diagonal sums to the same value, which of the following is a possible value of the sum of the four center cells of the grid (indicated by the shaded area)?
(A) 124 (B) 153 (C) 178 (D) 192 (E) 214
Any idea how to approach this question please? 10If the 4 x 4 grid in the attached picture is filled with the consecutive integers from 37 to 52, inclusive, so that every row, column and major diagonal sums to the same value, which of the following is a possible value of the sum of the four center cells of the grid (indicated by the shaded area)? (A) 124 (B) 153 (C) 178 (D) 192 (E) 214 37 38 39 40 178 44 43 42 41 178 45 46 47 48 178 52 51 50 49 178 178 178 178 178 C
_________________
He gives power to the faint; and to them that have no might he increases strength. Isaiah 40:29
You never FAIL until you stop TRYING



Director
Joined: 31 Jul 2017
Posts: 510
Location: Malaysia
GPA: 3.95
WE: Consulting (Energy and Utilities)

Re: If the 4 x 4 grid in the attached picture is filled with the
[#permalink]
Show Tags
30 Jun 2018, 21:07
enigma123 wrote: If the 4 x 4 grid in the attached picture is filled with the consecutive integers from 37 to 52, inclusive, so that every row, column and major diagonal sums to the same value, which of the following is a possible value of the sum of the four center cells of the grid (indicated by the shaded area)?
(A) 124 (B) 153 (C) 178 (D) 192 (E) 214
Any idea how to approach this question please? The Sum will be two of the least number (37+38) + tow of the max (51 + 52) = 178
_________________
If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!



NonHuman User
Joined: 09 Sep 2013
Posts: 13575

Re: If the 4 x 4 grid in the attached picture is filled with the
[#permalink]
Show Tags
20 Oct 2019, 11:26
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.
_________________




Re: If the 4 x 4 grid in the attached picture is filled with the
[#permalink]
20 Oct 2019, 11:26






