explain

[src_saurav]

r s t
u v w
x y z


103. 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

please help me with the first option.

My answer was B i could get 3 out of it.

[Brandon@VeritasPrep]

Statement 1 is also sufficient. If v+z = 6, then both v and z = 3. Because z = 3, w and t each equal either 1 or 2. Because v is 3, s and y each equal either 1 or 2. Therefore we know that s and t each equal either 1 or 2, and therefore that r must equal 3.

I hope this helps!

[cans]

Statement 1 is sufficient.
as v+z =6, both v and z have to be 3.
as each number occurs once in each row and once in each column,
row2, row3, column2 and column 3 already have 3.
thus in row 1, only column 1 can have 3 which is r.
thus r=3.

[GMATGuruNY]

r s t
u v w
x y z


103. 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

Statement 1: v+z = 6
Since v and z must each be 1, 2, or 3, the equation above is valid only if v=3 and z=3, implying the following grid:
r...s...t
u...3...w
x...y...3.

Since 3 must appear exactly once in every row and column, the grid must look like this:
3...s...t
u...3...w
x...y...3.
Thus, r=3.
SUFFICIENT.

Statement 2: s+t+u+x = 6
Since each row must be composed of 1, 2 and 3, the sum of each row = 1+2+3 = 6.
Thus, r+s+t = 6, implying that s+t = 6-r.
Since each column must be composed of 1, 2 and 3, the sum of each column = 1+2+3 = 6.
Thus, r+u+x = 6, implying that u+x = 6-r.
Substituting s+t = 6-r and u+x = 6-r into s+t+u+x = 6, we get:
(6-r) + (6-r) = 6
6-2r = 0
-2r = -6
r=3.
SUFFICIENT.

The correct answer is D.

[Brent@GMATPrepNow]

r s t
u v w
x y z

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

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

[nikhilgmat31]

I remember solving this question OG 12..
Good question

[Scott@TargetTestPrep]

r s t
u v w
x y z


103. 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

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