In a museum X, a total entrance fee is $x plus $z each person greater

I also beleive it's C, any official answer?

Bunuel any thouhgs?

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

In a museum X, a total entrance fee is $x plus $z each person greater than 20. In a museum Y, a total entrance fee is $y plus $w each person greater than 30. When 40 persons enter in museums X and Y, is a total entrance fee of the museum X smaller than that of the museum Y?

1) x<y
2) z<w


When you modify the original condition and the question, x+20z<y+10w? becomes a question. There are 4 variables(w,x,y,z), which should match with the number of equations. So you need 4 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make E the answer.
When 1) & 2), x=z=1, y=w=2 -> yes and x=z=2, y=w=3 -> no, which is not sufficient.
Therefore, the answer is E.


 For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.

chetan2u VeritasKarishma Bunuel gmatbusters
I think this question needs some clarity.
Does the question give information this way - x+z>20 and y+w>30 ?
Or am I missing something?
MathRevolution

The question intends to say that the entry fee is $x flat fee for upto 20 people and then $z for each additional person.
Hence fee for 40 people = x + z*20

The same for museum Y - entry fee is $y flat fee for upto 30 people and then $w for each additional person
Hence fee for 40 people = y + w*10