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## explain

tagged by: Brent@GMATPrepNow

This topic has 3 expert replies and 2 member replies
src_saurav Master | Next Rank: 500 Posts
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#### explain

Sun May 31, 2015 10:12 pm

00:00

A

B

C

D

E

# Global Stats

Difficult

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

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

### GMAT/MBA Expert

Brandon@VeritasPrep Junior | Next Rank: 30 Posts
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Sun May 31, 2015 10:30 pm
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!

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cans Legendary Member
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Mon Jun 01, 2015 3:05 am
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.

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GMATGuruNY GMAT Instructor
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Mon Jun 01, 2015 4:07 am
src_saurav wrote:
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.

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Brent@GMATPrepNow GMAT Instructor
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Mon Jun 01, 2015 7:08 am
Quote:
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

Cheers,
Brent

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nikhilgmat31 Legendary Member
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Thu Jun 04, 2015 1:12 am
I remember solving this question OG 12..
Good question

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