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If the 4 x 4 grid in the attached picture is filled with the [#permalink]

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31 Jan 2012, 19:25

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81% (01:35) correct
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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)?

Sum of the numbers from 37 to 52 = (n/2)[2a + (n-1)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

Re: If the 4 x 4 grid in the attached picture is filled with the [#permalink]

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15 Nov 2013, 22:23

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Re: If the 4 x 4 grid in the attached picture is filled with the [#permalink]

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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?

Re: If the 4 x 4 grid in the attached picture is filled with the [#permalink]

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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?

Re: If the 4 x 4 grid in the attached picture is filled with the [#permalink]

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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.
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Re: If the 4 x 4 grid in the attached picture is filled with the [#permalink]

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11 Jul 2015, 17:11

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Re: If the 4 x 4 grid in the attached picture is filled with the [#permalink]

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04 Jan 2016, 19:57

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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

If the 4 x 4 grid in the attached picture is filled with the [#permalink]

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13 Jul 2016, 12:04

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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

Re: If the 4 x 4 grid in the attached picture is filled with the [#permalink]

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13 Jul 2016, 22:31

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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

Re: If the 4 x 4 grid in the attached picture is filled with the [#permalink]

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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

Re: If the 4 x 4 grid in the attached picture is filled with the [#permalink]

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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.

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