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If the average (arithmetic mean) of the assessed values of x houses is $212,000 and the average of the assessed values of y other houses is $194,000, what is the average of the assessed values of the x+y houses?

(1) x+y=36

(2) x=2y

This is a '2by2'question, one of the most common type of questions in GMAT math

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GCDS sondenso If the average (arithmetic mean) of the assessed (20151202).jpg [ 30.93 KiB | Viewed 5650 times ]
We have 2 variables (x,y) and 2 equations are given by the 2 conditions, which gives (C) high chance of being the answer

Looking at the conditions together, x=24, y=12 so this seems sufficient, but this is a commonly made mistake; if we look at the conditions separately,

condition 2 contains ratios and when one condition contains numbers and another contains ratios, there is high chance the one with ratio is the answer, so if condition 2 is examined,

average assessed value= (212,000x+194,000y)/(x+y)=(212,000*2y+194,000y)/(2y+y).

y can be canceled out, so the condition is sufficient and the answer becomes (B).

For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% 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 C 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, D or E.

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