# Mensa pattern recognition task - find the odd one out among 5 pictures of crosshatched lines

I have a question about the solution to this pattern recognition task:

I know that according to the book, the correct answer is E. The "argument" is: Vertical lines represent $$1$$ integer; horizontal lines represent $$5$$. The product of the number of lines on each end equals the sum of lines in the middle. But then not only E contradicts this structure, but B as well: the product of the number of lines on each end is $$6$$, the sum in the middle is $$16$$.

Any idea what might be the correct answer?

• I don't. (A) 4*3=10+2, (B) 3*2≠5+3, (C) 4*4=15+1, (D) 2*5=10, (E) 3*5≠10+2. Is there any context to restrict the possible answers? I mean - only in A is the number of lines not divisible by 3. Only D has a large square. There seems to be a number of possible solutions. – retzler May 23 '20 at 13:14

There are several ways one of the pattern differs from others. One for example

If you count ALL vertical and horizontal lines

A = 11

B = 9

C = 12

D = 9

E = 12

From this you can argue that A is the odd one out-- the only PRIME NUMBER or the pattern should have been 12,9,12,9,12. So A is the odd one

Another way is to count all the right (90 degree) angles

they are 24, 18, 18, 8, 24 so 8 is the only one not divisible by 3

All/any of them

because

E is the only one where the number of vertical bars is not a multiple of 3
D is the only one with 2 groups of vertical bars
C is the only one with left-right symmetry in number of vertical bars
B is the only one where the number of vertical bars in the leftmost group is equal to the sum of the numbers in the other groups
A is the only one with no other reason for being different

I don't think you can assume that there is an elegant, satisfying answer to this problem. If the people who provided the intended answer you cited are the same people who conceived the problem, there is obviously an error somewhere, possibly a mistake in the depiction of the "B" image. Unless you have reason to believe that this is a valid problem, and only your book's explanation is in error, I would recommend not spending time on this.

Another thing you could do is write to the book's publisher and point out the discrepancy you found. You would quite possibly get a detailed reply addressing the discrepancy.

There can be several answers to this: Assume the following format : $$d = (a + b)\times c$$ where, $$a$$ is the number of lines in the left end, b is the number of lines in the right end, and c is the number of intersection points between the "middle vertical line(s) and the horizontal lines". Now, for $$A: d = 28; B: d = 15; C: d = 24; D: d = 0; E: d = 32$$ Two conclusions since $$d$$ is ODD only for $$B$$, it is the odd one OR since all are positive numbers except $$0, D$$ (0 is neutral) is the odd one out. Another format (preserving the nomenclature for $$a,b,c$$), $$d = \frac{c}{a+b}$$ Now, for $$A: d = 4/7; B: d = 3/5; C : d = 3/8; D : d = 0; E:d=4/8$$ Two conclusions: 1. All are terminating decimals except $$A$$. Hence it is the odd one out. 2. All numbers are greater than $$0$$ except $$D$$. Hence it is the odd one out.