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Each of the letters in the table above represents one of the [#permalink]

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07 Dec 2012, 10:08

14

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A

B

C

D

E

Difficulty:

65% (hard)

Question Stats:

60% (02:35) correct
40% (01:32) wrong based on 983 sessions

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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?

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.

Since v and z are 1, 2, or 3, then v=z=3. So, we have 3 in the second and third columns, which mean that neither s nor t can be 3, which means that r must be 3. Sufficient.

(2) s + t + u + x = 6.

We can have two combinations of the numbers to satisfy s + t + u + x = 6:

1+1+1+3=6 OR 1+1+2+2=6. The first case is not possible since in this case three letters out of s, t, u and x would be 1, which would mean that either in the first row or in the first column we have the same number 1.

So, we have 1+1+2+2=6 case, which means that r must be 3 (since no other number in the first column or the first row is 3). Sufficient.

Re: Each of the letters in the table above represents one of the [#permalink]

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18 Jun 2013, 02:34

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This post received KUDOS

Walkabout wrote:

Attachment:

Table.png

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

For St 1, we are given that v+z=6...since possible nos are only 1,2 and 3, we can conclude that v=z=3. Since v and z are in row 2 and row 3 then number 3 in row 1 has to be at position of r -----> r= 3. Cancelling option B, C and E

From st 2, we have s+t+u+x= 6 and 2r+s+u+t+x= 12....solving for r we get r--->3

Hence ans should be D
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Re: Each of the letters in the table above represents one of the [#permalink]

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09 Aug 2014, 17:19

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Re: Each of the letters in the table above represents one of the [#permalink]

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26 Oct 2015, 08:06

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Re: Each of the letters in the table above represents one of the [#permalink]

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05 Aug 2016, 10:43

Top Contributor

Walkabout wrote:

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?

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

Re: Each of the letters in the table above represents one of the [#permalink]

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10 Sep 2016, 07:35

Walkabout wrote:

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, which is possible only for 3+3 since there is one 3, in middle and last colomn, the only possible value for r is 3....sufficient 2. s + t + u + x = 6....this is possible for combinations, 1+2 + 1+2 or 2+1 + 1+2 and so on....as each number should occur only once, r has to take value of 3...sufficient

so answer is D
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Re: Each of the letters in the table above represents one of the
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10 Sep 2016, 07:35

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