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number properties

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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number properties

by sud21 » Thu Jan 19, 2012 11:05 pm
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
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by neelgandham » Fri Jan 20, 2012 7:07 am
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
v + z = 6, implies v=z=r = 3. Sufficient to answer the question
2) s + t + u + x = 6
r+s+t = 6, r+u+x = 6. Adding these equations you get r+s+t+r+u+x=12
2r+(s+t+u+x) = 12
2r + 6 = 12
r = 3
Sufficient to answer the question

Answer D
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by Brent@GMATPrepNow » Fri Jan 20, 2012 11:00 am
sud21 wrote: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
Statement 1:
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)
As such, statement 1 is SUFFICIENT

Statement 2:
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
As such, statement 2 is SUFFICIENT

Answer = D

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Brent
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