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W, X, Y and Z each represent a different number

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W, X, Y and Z each represent a different number

by vinni.k » Sun Oct 29, 2017 9:53 am

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W, X, Y and Z each represent a different number. If the sum of each column is shown beneath that column, and the sum of each row is shown beside that row, then n =

| X | W | X | Z | 3
|W| Y | X |W| 6
| Z | Y | X | X | 9
| Z | Z |W| Y | 0
------------------
|-2| 7 | n | 5 |

A) 6
B) 7
C) 8
D) 9
E) 10

OA is C

What is the better way to approach this question ?

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Last edited by vinni.k on Sun May 06, 2018 7:44 am, edited 2 times in total.
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by vinni.k » Tue Oct 31, 2017 10:12 am
Can anyone please help in this question ?
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by vinni.k » Sun May 06, 2018 7:45 am
How to approach this question ? Or Is there any better way to approach this question ?
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by GMATGuruNY » Sun May 06, 2018 8:35 am
vinni.k wrote:W, X, Y and Z each represent a different number. If the sum of each column is shown beneath that column, and the sum of each row is shown beside that row, then n =

| X | W | X | Z | 3
|W| Y | X |W| 6
| Z | Y | X | X | 9
| Z | Z |W| Y | 0
------------------
|-2| 7 | n | 5 |

A) 6
B) 7
C) 8
D) 9
E) 10
Sum of all 4 rows = 3 + 6 + 9 + 0 = 18.
Sum of all 4 columns = -2 + 7 + n + 5 = n + 10.
The values in blue must be EQUAL, since each represents the sum of all 16 values in the table.
Thus:
n+10 = 18
n=8.

The correct answer is C.
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by Brent@GMATPrepNow » Sun May 06, 2018 12:10 pm
vinni.k wrote:How to approach this question ? Or Is there any better way to approach this question ?
I believe Mitch has provided the best/fastest approach.

Cheers,
Brent
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by vinni.k » Mon May 07, 2018 1:22 am
Brent@GMATPrepNow wrote:
vinni.k wrote:How to approach this question ? Or Is there any better way to approach this question ?
I believe Mitch has provided the best/fastest approach.

Cheers,
Brent
Yes,

Thanks. Appreciate it.
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by Scott@TargetTestPrep » Tue May 08, 2018 3:18 pm
vinni.k wrote:W, X, Y and Z each represent a different number. If the sum of each column is shown beneath that column, and the sum of each row is shown beside that row, then n =

| X | W | X | Z | 3
|W| Y | X |W| 6
| Z | Y | X | X | 9
| Z | Z |W| Y | 0
------------------
|-2| 7 | n | 5 |

A) 6
B) 7
C) 8
D) 9
E) 10
We see that from the first row, we have 2X + W + Z = 3 and from the first column, X + W + 2Z = -2. If we subtract the 2nd equation from the first, we have X - Z = 5. Thus Z = X - 5. Plug this back to the first equation, we have:

2X + W + (X - 5) = 3

3X + W - 5 = 3

3X + W = 8

Notice that n as the sum of the 3rd column is 3X + W, so n must be 8.

Answer: C

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