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

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 =

Cheers,
Brent

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

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

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

Answer: Option D

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