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.

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

Attachment:

GCDS sondenso If the average (arithmetic mean) of the assessed (20151202).jpg [ 30.93 KiB | Viewed 1378 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.

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare

The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.

Find a 10% off coupon code for GMAT Club members.

Unlimited Access to over 120 free video lessons - try it yourself

See our Youtube demo