Each of the letters in the table above represents one of the

Question

https://gmatclub.com/forum/download/file.php?id=18863 Each of the letters in the table above represents one of the numbers 1, 2, or 3, and each of these numbers occurs exactly once in each row and exactly once in each column. What is the value of r? (1) v + z = 6 (2) s + t + u + x = 6 Table.png

Bunuel · Accepted Answer

https://gmatclub.com/forum/download/file.php?id=18863 Each of the letters in the table above represents one of the numbers 1, 2, or 3, and each of these numbers occurs exactly once in each row and exactly once in each column. What is the value of r? (1) v + z = 6. https://gmatclub.com/forum/download/file.php?id=18864 Since v and z are 1, 2, or 3, then v=z=3. So, we have 3 in the second and third columns, which mean that neither s nor t can be 3, which means that r must be 3. Sufficient. (2) s + t + u + x = 6. https://gmatclub.com/forum/download/file.php?id=18865 We can have two combinations of the numbers to satisfy s + t + u + x = 6: 1+1+1+3=6 OR 1+1+2+2=6. The first case is not possible since in this case three letters out of s, t, u and x would be 1, which would mean that either in the first row or in the first column we have the same number 1. So, we have 1+1+2+2=6 case, which means that r must be 3 (since no other number in the first column or the first row is 3). Sufficient. Answer: D. Table2.png Table1.png

m0h1t · Answer

For the seconds statement, I thought of it like this

r + u + x = 6
r + s + t = 6

2r + u + x + s + t = 12
2r+6=12 (Since, s+t+u+x=6)
2r=6
r=3

BrentGMATPrepNow · Answer

Target question :    What is the value of r?

Statement 1 : v+z = 6 
Step 1: If v+z=6, then v and z must both equal 3. 
Step 2: If each number occurs  exactly once  in each row and  exactly once  in each column, then s cannot equal 3 (since s and v are in the same column) and t cannot equal 3 (since t and z are in the same column). 
Step 3: If s and t cannot equal 3, then  r  must equal  3  (since each number occurs exactly once in each row)
Since we can answer the  target question  with certainty, statement 1 is SUFFICIENT

Statement 2  s+t+u+x = 6 : 
If each number occurs exactly once in each row and exactly once in each column, the sum of numbers in any row or column will always equal 6. 
So, r+s+t=6, and r+u+x=6
When we combine these two equations, we get
(r+s+t)+ (r+u+x)= 6+6
Simplify to get: 2r+(s+t+u+x)=12
Statement 2 tells us that s+t+u+x=6
When we add this to the equation 2r+(s+t+u+x)=12, we get: 2r+(6)=12
When we solve this, we get   r=3  
Since we can answer the  target question  with certainty, statement 2 is SUFFICIENT

Answer =  D

Cheers,
Brent

daviddaviddavid · Answer

I guess another good way to think about these problems is in terms of max., min., and extreme values.

i.e. min. value of s+t = 3 and min. value of u+x = also 3 --> and the only way to get 3 from s+t or 3 from u+x is by adding 2+1

therefore r must be 3

susheelh · Answer

This is how I approached it -

S1: Just thought - if there are two integers which can take value of 1 or 2 or 3 and the their sum is 6, what is the value of each integer? - it took few seconds to realize that both have to be 3. Meaning V = Z = 3. This also means that U and X cannot be 3 (this follows from the stem). This again means R MUST be 3. Suff

S2: Here I used Algebra. We have R+S+T = 6 and R+U+X = 6. Adding both you get 2R+S+T+U+X = 12. We can see that the Value in S2 can be substituted to get the value of R. Suff

Both statements individually sufficient. Answer is D

PS: People who have played Sudoku will find this one easier to tackle

ScottTargetTestPrep · Answer

Solution:

Question Stem Analysis:
 
We need to determine the value of r given that every variable in the table represents one of the numbers 1, 2, or 3.

Statement One Alone:

This means both v and z are 3. Recall that each of the numbers occurs exactly once in each row and exactly once in each column, which means there is a “3” in the first row. Since v and z are 3, neither u nor x can equal 3 (otherwise we have a row with two 3’s). Thus, it must be true that r = 3. Statement one alone is sufficient.

Statement Two Alone:

We see that 6 can be expressed as the sum of 1, 1, 2, and 2 or 1, 1, 1, and 3 if all addends have to be integers. However, since s and t are on the same row and u and x are on the same column, it must be the former; i.e. the sum of 1, 1, 2, and 2. Furthermore, it means one of the values of s and t is 1 and the other is 2. Lastly, since s and t are on the same row as r, r must be 3. (Alternatively, we can also argue that since one of the values of u and x is 1 and the other is 2 and they are on the same column as r, r must be 3). Statement two alone is sufficient.

Answer: D

GMATinsight · Answer

Answer: Option D

Video solution by  GMATinsight

https://www.youtube.com/watch?v=jYL55GS4OPU

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