Sudoku DS problem from OG13

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[email protected]: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Wed Sep 12, 2012 5:37 pm

by [email protected] » Sat Dec 15, 2012 9:32 am

Eachof the letters inthe table above represents one of the numbers 1, 2, or 3, and each of these numbers occurs exactly once ineach 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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Source: Beat The GMAT — Data Sufficiency | Sat Dec 15, 2012 9:32 am

[email protected]: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Wed Sep 12, 2012 5:37 pm

by [email protected] » Sat Dec 15, 2012 10:26 am

Sorry let me post the matrix here

r s t
u V w
X y 1

Imagine the matrix is 3x3 ( above)

103. Eachof the letters inthe table above represents one of the numbers 1, 2, or 3, and each of these numbers occurs exactly once ineach row and exactly once in each column. What is the value of r ?
(1) v + z = 6
(2) s + t + u + x = 6

From (1) we can get V=Z=3 ( Sufficient)
From (2) we can ger 1,1,1,3 or 1,1,2,2
Of these 1,1,1, is not possible since it would be mean that there is 1,1 in one column or row which is not possible according to the statement so my answer is D

The OG answer is A since it does not take into consideration 1,1,2,2 from (2) . I am not able to understand why OG is not even considering 1,1,2,2 ?

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sat Dec 15, 2012 11:08 am

[email protected] wrote:
r s t
u V w
X y 1

Imagine the matrix is 3x3 ( above)

103. Eachof the letters inthe table above represents one of the numbers 1, 2, or 3, and each of these numbers occurs exactly once ineach 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

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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