M23-37

Question

https://gmatclub.com/gmat-practice-tests/resources/import/img/M23-37.png 
 
In the table above, if  x ,  y , and  z  represent numbers, what is the value of  x + y + z  ?

(1) The sum of numbers in each row is equal.
 
(2) The sum of numbers in each column is equal.

Bunuel · Answer

Official Solution:

In the table above, if  x ,  y , and  z  represent numbers, what is the value of  x + y + z  ? 
 
(1) The sum of numbers in each row is equal.
 
This implies that  x+2+1=2+1+y=1+z+2 , which yields  x=y=z . However, this information is not sufficient to determine the value of  x+y+z .
 
(2) The sum of numbers in each column is equal.
 
This implies that  x+2+1=2+1+z=1+y+2 , which again yields  x=y=z . However, this information is still not sufficient to determine the value of  x+y+z .
 
(1)+(2) Combining both statements, we only know that  x=y=z , but this information is not sufficient to determine the value of  x+y+z .

Answer: E

alandizzle · Answer

i thought this question was fair and good.

mchoudh7 · Answer

Where it is mentioned that x, y and z should be distinct numbers?

Bunuel · Answer

It is not mentioned. If nothing is mentioned, then variables can represent distinct numbers as well as the same number.

ydmuley · Answer

(1) The sum of numbers in each of the rows is equal

This does not give us the values of  x, y and z , only gives information of  x =y = z , which is not sufficient to get the values of  x+y+z  as  x, y and z  can be any number and hence values will change.

Hence, (1) =====> is NOT SUFFICIENT

(2) The sum of numbers in each of the columns is equal

Once again, this does not give us the values of  x, y and z , only gives information of  x =y = z , which is not sufficient to get the values of  x+y+z  as  x, y and z  can be any number and hence values will change.

Hence, (2) =====> is NOT SUFFICIENT

Combining (1) & (2)

Even after combing we will know that x = y = z, and as the values are not provided we will not be able to find the value of  x + y + z

(1) & (2) =====> is NOT SUFFICIENT

Hence, Answer is E

Kimberly77 · Answer

How is x+2+1=2+1+y=1+z+2 gives x=y=z ?

What happened to 3? x+3 = 3+y = 3+z
 BrentGMATPrepNow , could you share your insights please? Thanks.

BrentGMATPrepNow · Answer

3-part equations such as x+3 = 3+y = 3+z behave the same way as 2-part equations. 
So, we can take:  x+3 = 3+y = 3+z 
And subtract 3 from all three parts to get:  x + 3  -3  = 3 + y  -3  = 3 + z  -3  
Simplify to get:  x = y = z

Alternatively, we can examine the equations in pairs. 
For example we know that:  x+3 = 3+y 
Subtract 3 from both sides of the equation to get:  x = y

Similarly, since we know  3+y = 3+z , we can subtract 3 from both sides of this equation to get:  y = z 
If  x = y  and  y = z , then it must be true that  x = y = z

Captain07 · Answer

I think this is a  high-quality  question and I agree with explanation. Explanation is good
Thank u

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

BottomJee · Answer

I think this is a  high-quality  question and I agree with explanation.

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