In the diagram above each of the letters represents one of the digits

Question

https://gmatclub.com/forum/download/file.php?id=34784

In the diagram above each of the letters represents one of the digits between 5 and 9, not inclusive. If each row and each column must be filled with distinct digits, what is the value of w?

(1) b + m = 15
(2) a + c = 13

mohshu · Answer

lets try this one...

stat 1: b+m = 15
b= 8 and m= 7 or
b=7 and n =8

in either case value of w = 6..suff

stat 2 : w can be 7 or 8,,not suff

ans A

addisubhashree · Answer

Where can I find the official solution to this? I am looking for a detailed approach to these questions.

chesstitans · Answer

perhaps, not so many people like and do these questions. It really surprises me that only 31% of people make it right.

NamVu1990 · Answer

I may have the answer to this:
From question: the numbers can only be 6, 7, or 8 and each letter is a distinct number
Statement 1:
b + m = 15

So b and m can be 7 or 8, can not be 6.
Look at the figure, if we know the value of b then a ,x, c, l (all the number next to it) can't have that value. Also, iof we know m, we know what k, l, c, z can't be.
So if b and m can be either 7 or 8, then c and l can be either 7 or 8, and only can be 6.

And if c = l = 6, a and k can't be 6, therefore w must be 6.

Statement 2: We can only conclude that b is 8, nothing more. W can be either 6, 7, or 8.

Took me a lot more than 2 minutes to solve.

GMATisLovE · Answer

Hi Bunuel,

I solved it by putting values in the different blocks, but it took me long time.

Do you have a simple mathematical solution?

chetan2u · Answer

Hi..
In these Q, the diagonals are two- one will have same digit and other will have all three different...
So..
wxz
abc
klm

Let's see the statements
1) b+m=15
So b and m are equal to 7 and 8 or 8 and 7..
So the diagonal wbm is having different digits or w is 6..
Solution otherwise..
l in third row and c in 2nd row cannot be 7or8 as they have both b and m in their rows, so c and I are 6.
Therefore k in 3rd row is equal to b.
Also a in 2nd row is equal to m.
First column is w+a+k=w+b+m=w+15=6+7+8, so w is 6
Sufficient

2) a+c is 13
So b is 8, but from this we cannot say which diagonal has different and which has same digits.
we can be anything 6 or 7 or 8
876
687
768

678
786
867

768
687
876

w can be 6 or 7 or 8

Insufficient

A

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In the diagram above each of the letters represents one of the digits

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