# Mensa web test question #34

Doing the Mensa web IQ test at http://test.mensa.no/, I was puzzled by this exercise.

I understand that asking for answers like this kind of defeats the entire purpose of the test, but it's stuck bugging me. Does anybody else see some sort of a logic in this? Most questions in this test flow both left-to-right and top-to-bottom, but it's possible that this one doesn't because

the last question doesn't either.

• looks like a complicated version of Mendelian inheritance – ngn Jan 24 '18 at 21:51
• Finnish Mensa has a version of this test with the same "question" but the options are somewhat different, notably lacking both of the correct answers identified here :) mensa.fi/iq/index_2.html – Hemaolle Jul 31 '18 at 5:20

Discussing this with some friends, it was suggested that the correct choice is

5, ie. bottom row in the middle

because

the puzzle is a form of simple addition. The first two pictures are added together, producing the third picture. Overlapping squares produce a large square, but beyond that there is no "overflow" so a small square plus a large square still produces a single large square. Note that this solution only works without question when reading the puzzle left-to-right; when reading top-to-bottom, the meaning of the alignment of the picture (whether the squares are on top of or below the horizontal line) is unclear.

I gamed the test a little by repeating it and seeing how different choices for this question affect the scoring, and I think this answer could be correct, but am not completely sure.

EDIT: I gamed the test a bit more by selecting the top left choice on every question until 29, and selecting the correct choice after that; this way the test gives a score of 91 if all choices are correct, and 90 if there is one mistake after the 29th question. I went through all the possibilities for question 34, and it appears that there are two correct answers:

3 (top right) and 5 (bottom middle)

Which means that both this answer and the one by prog_SAHIL (and Jan Ivan, who also suggested the same choice albeit with a more mathematically sound reasoning!) are correct.

• I think that these tests are structured unilaterally- to work in all planes and directions - so the correct answer must be 'uni-directional', so to speak. – NexusInk Jan 25 '18 at 2:57

C(Top right)

Because

Every other image in the question grid has a mirror image about the horizontal axis except for the center one.

## Major Edit

I took the test and C(Top right) is indeed the correct answer.

• Can I know the reason for the downvote? – prog_SAHIL Jan 25 '18 at 9:33
• (I didn't downvote.) What do you mean by "C"? The choices are not labeled. – Joel Reyes Noche Jan 25 '18 at 9:52
• @JoelReyesNoche edited. – prog_SAHIL Jan 25 '18 at 10:03
• I agree, before looking at the alternatives I concluded that the answer should either be a straight line, or the center image but upside down, and there were no option with just a straight line. – klskl Jan 25 '18 at 12:55
• "Every other image in the grid" -- which grid? The question grid, or the answer grid, or both? This is a terrible explanation. – Rich Jan 25 '18 at 21:21

Well you have:

-0 -x -x
+x +y +z
-x -z -?

First thing you remove minus from rows (it is for confusion of the enemy only anyway):

0 x x
x y z
x z ?

So it is very easy:

0 is difference between x and x
x is difference between y and z
x is difference between z and ?

This results into

? should be y, so correct answer is top right

• I don't see how your reasoning ends up with that answer. If you look at the size of the pillars. the first row makes sense, but the second doesn't. X is not the difference between y and z, because the two wider pillars are not the same height. Could you please elaborate a bit more? – Mixxiphoid Jan 25 '18 at 12:06
• @Mixxiphoid as you can see pictures and addition does not work at all (others say solution would be x+z=z). So you have to think outside of the box and forget pictures. Also you are assuming that size of the pillars is wider = 2 narrower, which might not be true (it could count with complex numbers or whatsoever) – Jan Ivan Jan 25 '18 at 12:19
• I like this answer because it reduces the problem to a simple algebraic form, and produces a correct solution. It appears that there are in fact two correct solutions as far as the test scoring is concerned; I explain why this seems to be the case in my answer. – burneddi Jan 25 '18 at 14:08
• I am doubtful like @Mixxiphoid, in addition to his concerns - where does the assumption that y ° z a is commutative operation comes from? – wondra Jan 26 '18 at 10:06
• I suppose by "difference" you mean the absolute value of the difference? – Hans Jul 11 '18 at 18:25

I agree with @burneddi, that:

I won't repeat why it flows from left-to-right, but what happens with top-to-bottom is:

identical - addition with a limit of 'big square', except that the middle row is flipped upside down first before adding

• ... or, in other words, subtracted :) – Quentin Jan 25 '18 at 13:17

Left - to - right:

Right- to - left:

Subtraction

Top - to - Bottom:

Inverse Addition with loss of a square in the conversion

Bottom- to - top:

Inverse Subtraction while gaining a square in the conversion

That's the only way I can say it simply, so the answer you are looking for is:

Top Left

Bonus: Take into account that most of these exercises work in all directions .

The last exercise requires a vertical flip of the card and removing the overlapping pieces.

I agree that the answer is the

middle variant in the bottom solutions line

but with the different explanation.

in the first column going from upper to the bottom line of the table we see subtraction (not adding!)

in the second column we see that it could be subtraction again, with the ceiling - the square can be of size 1 or 2, but no size 3 exists. If the result is more than three by abs, it is cut to 2.

Using two these rules we are getting the mentioned solution number 5, and its existence hints that the solution is correct.

The correct answer is definitely the top left.
If we follow the left to right logic by rows then:
From the first row we can learn that we practice addition (no cubes + 2 cubes = 2 cubes). We also learn that it is significant whether the cubes are above or below the line.
From the second row we can learn that 3 small cubes equals 1 large cube(2 small cubes + 3 small cubes + 1 large cube = 5 small cubes + large cubes = 2 small cubes + 2 large cubes).
We also learn that small cubes "turn" to large cubes only if there is no more space for cubes on the line.Combining the conclusions above, the left boxes of the bottom row hold 2 large cubes and 4 small cubes below the line. This equals 3 large cubes + 1 small cube below the line as the top left option presents.The "mirroring" aspect is only distract in this particular question.
Thanks to iprep.online

Some alternate logic

Bottom middle

Because

Rule 1: The number of the big cubes is always staying the same or growing when going from left to right or top to bottom.

Rule 2: The big cubes are always on the same side.

If someone is still searching for the real answer it is

5, ie. bottom row in the middle

as suggested by burneddi, but he didn't gamed the test correctly, because that is the only correct answer. I opened a thread, because there is an inconsistency in this exercise (Mensa Norway Test Inconsistent Exercise).

• The test might have been changed. When I was doing it, I seem to remember 135 being the maximum score rather than the 145 that you mention in your thread. – burneddi Oct 31 '18 at 12:02

I would argue that top left is the correct value.

Addition is in base 3, a big square is equal to three smaller.

As people mentioned, squares above the line are positive, while squares below are negative.

If $$A$$, $$B$$ and $$C$$ are in a column (in this order), then $$C=A-B$$.

If $$A$$, $$B$$ and $$C$$ are in a row, then $$C=A+B$$.

Both the row-rule and column-rule gives the top left option as correct.