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.
The table above shows the number of students in a certain high school class who are boys and the number of students in the class who are studying biology. What is the total number of students in the class?
(1) Of the boys in the class, 15 are studying biology.
(2) The number of girls in the class is twice the number of students in the class who are NOT studying biology.
When you modify the original condition and the question, it is frequently given in the Gmat Math test, which is “2 by 2” question like the table below.
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GCDS Bunuel The table above shows the number of students (20160106).jpg [ 40.42 KiB | Viewed 30536 times ]
In the table, there are 4 variables(a,b,c,d) and 2 equations(a+c=26, a+b=18), which should match with the number of equations. So you need 2 more equations, which is likely to make C the answer.
When 1) & 2), a=15 and c=11, b=3 is derived from c+d=2(b+d). Also, d=5 is derived from 11+d=2(3+d)=6+2d, which is unique and sufficient. Therefore, the answer is C. However, since this is integer question which is one of the key questions, apply the mistake type 4(A).
For 1), even if you know that a=15, you don’t know d, which is not sufficient. For 2), c+d=2b+2d and (a+c)-(a+b)=b+d, which is 26-18=b+d=8 is derived from c-b=b+d. So, the answer from a+b+c+d=a+c+b+d=26+8=34 is unique and sufficient. Therefore, the answer is not C but B. You need to get this type of questions correct to reach the score range 50-51.
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.