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Manager  Joined: 02 Dec 2012
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Each of the letters in the table above represents one of the  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 66% (01:57) correct 34% (02:02) wrong based on 2125 sessions

HideShow timer Statistics 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

Attachment: Table.png [ 6.87 KiB | Viewed 33781 times ]
Math Expert V
Joined: 02 Sep 2009
Posts: 58418
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13
15 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.

Attachment: Table2.png [ 7.02 KiB | Viewed 33107 times ]
Attachment: Table1.png [ 6.91 KiB | Viewed 33105 times ]

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

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2
For the seconds statement, I thought of it like this

r + u + x = 6
r + s + t = 6

2r + u + x + s + t = 12
2r+6=12 (Since, s+t+u+x=6)
2r=6
r=3
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Math Expert V
Joined: 02 Sep 2009
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Re: Each of the letters in the table above represents one of the  [#permalink]

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Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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

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1
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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Joined: 11 Dec 2012
Posts: 24
Re: Each of the letters in the table above represents one of the  [#permalink]

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Answer is D. Please see my solution below:
Attachments Each of the letters.JPG [ 82.48 KiB | Viewed 22579 times ]

GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4015
Re: Each of the letters in the table above represents one of the  [#permalink]

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5
Top Contributor 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

Attachment:
Table.png

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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GMAT 1: 700 Q49 V36 WE: Business Development (Computer Software)
Re: Each of the letters in the table above represents one of the  [#permalink]

Show Tags 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

Attachment:
Table.png

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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Manager  B
Joined: 26 Mar 2017
Posts: 106
Re: Each of the letters in the table above represents one of the  [#permalink]

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m0h1t wrote:
For the seconds statement, I thought of it like this

r + u + x = 6
r + s + t = 6

2r + u + x + s + t = 12
2r+6=12 (Since, s+t+u+x=6)
2r=6
r=3

I guess another good way to think about these problems is in terms of max., min., and extreme values.

i.e. min. value of s+t = 3 and min. value of u+x = also 3 --> and the only way to get 3 from s+t or 3 from u+x is by adding 2+1

therefore r must be 3
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Joined: 12 Jun 2016
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WE: Sales (Telecommunications)
Re: Each of the letters in the table above represents one of the  [#permalink]

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1
This is how I approached it -

S1: Just thought - if there are two integers which can take value of 1 or 2 or 3 and the their sum is 6, what is the value of each integer? - it took few seconds to realize that both have to be 3. Meaning V = Z = 3. This also means that U and X cannot be 3 (this follows from the stem). This again means R MUST be 3. Suff

S2: Here I used Algebra. We have R+S+T = 6 and R+U+X = 6. Adding both you get 2R+S+T+U+X = 12. We can see that the Value in S2 can be substituted to get the value of R. Suff

Both statements individually sufficient. Answer is D

PS: People who have played Sudoku will find this one easier to tackle _________________
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Joined: 23 Feb 2015
Posts: 1262
Re: Each of the letters in the table above represents one of the  [#permalink]

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Bunuel 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?

(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.

Attachment:
Table2.png
Attachment:
Table1.png

Bunuel
Thanks for your nice explanation.
If the statement 2 replaced with $$s+u+w+y=6$$, can we still have the correct answer D?
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VP  V
Joined: 23 Feb 2015
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Re: Each of the letters in the table above represents one of the  [#permalink]

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Bunuel 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?

(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.

Attachment:
Table2.png
Attachment:
Table1.png

Bunuel
Thanks for your nice explanation.
If statement 2 replaced with $$s+u+w+y=6$$, can we still have the correct answer D?

Hi Bunuel
It seems that you missed my post. May I have your opinion on this question, please?
Thanks__
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Manager  S
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Re: Each of the letters in the table above represents one of the  [#permalink]

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Bunuel 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?

(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.

Attachment:
Table2.png
Attachment:
Table1.png

Bunuel
Thanks for your nice explanation.
If statement 2 replaced with $$s+u+w+y=6$$, can we still have the correct answer D?

Hi Bunuel
It seems that you missed my post. May I have your opinion on this question, please?
Thanks__

YES, you will still have the answer as D.
The basic thing is that as s&y are in the same column and u&w in the same row. Hence, they will always be 1 & 2. You can make a box and check. None of them can be 3 bcs then we will have to repeat a 1, which is not allowed. Re: Each of the letters in the table above represents one of the   [#permalink] 23 Aug 2019, 01:53
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