Bunuel wrote:

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

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

_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372

2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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