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number properties

by sud21 » Thu Jan 19, 2012 11:28 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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Source: — Data Sufficiency |

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by Anurag@Gurome » Fri Jan 20, 2012 12:13 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
(1) v + z = 6 if v = z = 3 implies r = 3 (as each of these numbers occurs exactly once in each row and exactly once in each column); SUFFICIENT.

(2) s + t + u + x = 6, where s is not equal to t, and u is not equal to x.
Either 1 + 2 + 1 + 2 = 6 or 2 + 1 + 2 + 1 = 6 implies r = 3; SUFFICIENT.

The correct answer is D.
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by rijul007 » Fri Jan 20, 2012 1:13 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
1) v + z = 6
v=z=3

r s t
u 3 w
x y 3

neither x nor u can be 3
This implies r = 3

Sufficient

2) s + t + u + x = 6


r s t
u v w
x y z

Let us assume one of s and t is 3
Lets say s = 3 and t = 1

s+t+u+x=6
4+u+x = 6
u+x=2
u and x both cant be 1 [both are in the same column]

None of s,t,u and x is 3
hence r has to be 3

Sufficient


Option D
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