In the addition table shown above, what is the value of m + n ?

In the addition table shown above, what is the value of m + n =?
A. -19
B. 4
C. 5
D. 6
E. 22

The sum of some value from the first row and and some value from the first column is given in the intersection boxes of these values.

So:

\(x+4=1\);

\(x=-3\).

\(y+4=-5\);

\(y=-9\).

\(x+e=-3+e=7\);

\(e=10\).

\(y+e=-9+10=n\);

\(n=1\).

\(z+e=z+10=10\);

\(z=0\).

\(z+4=0+4=m\);

\(m=4\).

Therefore, \(m+n=4+1=5\).

Answer: C.
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It will.

+ x y z
4 1 -5 m
e 7 n 10
f 2 -4 5

Take an aggressive approach. First find out what you want to know: m + n
m = 4 + z and n = e + y so you need 4 + z + e + y

Now, y is simple. 4 + y = -5 so y = -9
e and z are trickier. Looking at the 2nd column, if I have x, I can find e.
x is simple. 4 + x = 1 so x = -3
Now, e + x = 7 which means e -3 = 7 so e = 10
Only z remains. e + z = 10 so 10 + z = 10 giving me z = 0
I have all I needed. 4 + z + e + y = 4 + 0 + 10 -9 = 5
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the simplest way to do this is through a series of successive substitutions.
whenever there's a () in the working below, it means i have substituted a value that i found in an earlier step.

cheers.

x + 4 = 1
therefore, x = -3

y + 4 = -5
therefore, y = -9

x + e = 7
(-3) + e = 7
therefore, e = 10

y + e = n
(-9) + (10) = n
therefore, n = 1 ...(i)

z + e = 10
z + (10) = 10
therefore, z = 0

z + 4 = m
(0) + 4 = m
therefore, m = 4 ...(ii)

using (i) and (ii), m + n = 5

Ans = 5

4 + z = m
e + y = n
e + z = 10
4 + y = -5
4 + z + e + y = m + n
m + n = 10 - 5 = 5

On careful observation , this problem can be easily solved under 2 mins.

m +n = 4 +z + e +y = 4 +(z+e)+y = 4 +10+y = 14+y

solve y separately, y = -9 => m+n = 14-9 =5.

Answer is C.

How will I know that The sum of some value from the first row and and some value from the first column is given in the intersection box of these values. What is the mechanism?
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If you are not aware of the concept of 'addition table', the mechanism isn't intuitive. It might take some time to figure out. On the bright side, you now know the mechanism behind an addition table and if some other such concept does crop up in your actual GMAT, they will explain you how to arrive at the values. Very rarely will you see ambiguity in actual GMAT questions (If it does arise, they are quick to fix it.) So just know what this concept is and move on.
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This one is quite easy actually. I, frankly, do not think that this is 700-level. But then again, it is just my opinion.

Here is my explanation:

Question: m + n = ?

Now m = z + 4; n = y + e

Hence, m + n = z + 4 + y + e = (z + e) + (y + 4)

If you observe the table again, you know that (z + e) = 10 and (y + 4) = -5.

Add them to get m + n = 5

Answer: C

Q # 2 on my GMAT Prep test # 1... spent 5 minutes trying to figure it out and still couldn't. Now I am worrying more than ever about such ridiculous questions....

You don't have to worry. If this question was a part of GMAT at some time, it was a very very long time back. GMAT has been evolving and now if they use a term such as 'addition table', they are not going to assume that you know what it is. They will explain you what an addition table is i.e. they will tell you something like this" "An addition table is where numbers in the first row get added to numbers in the first column to give the results given in the grid e.g. 4 + X = 1, E + Y = N etc."
The stats related to every question are monitored and if they see inconsistencies, they filter them out e.g. if they see people getting more than Q49 but sitting on this 500 - 600 level question for 5 mins, they will figure out why and take action. In GMAT, the intent of the question will be very clear. You will only have to worry about 'how to get the answer' not 'what do they want'.
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We do not have to calculate value of any variable here. The solution can be simplified as below:
m=z+4 and n=y+e
Hence m+n = z+4+y+e = (y+4) + (z+e)
From yellow cell (y+4) = -5
From green cell (z+e) = 10

Substitute above in (m+n) equation
m+n = (y+4)+(z+e) = -5+10= 5

Hence choice(C) is the answer.

Answer: option C

Check solution as attached

\(m + n = 4 + z + e + y\)

\(4 + y = -5\)

\(z + e = 10\)

\(10 + (-5) = 5\)

Answer is C.
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10 years since this post was published and GMAC has decided to retain it on the GMAT prep mocks. It seems as though we must be prepared for such surprises.

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