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.

A student has decided to take GMAT and TOEFL examinations, for which he has allocated a certain number of days for preparation. On any given day, he does not prepare for both GMAT and TOEFL. How many days did he allocate for the preparation?

(1) He did not prepare for GMAT on 10 days and for TOEFL on 12 days.

(2) He prepared for either GMAT or TOEFL on 14 days.

->When you modify the original condition and question, this question is frequently given on GMAT math, which is “2 by 2 question” like the table below.

Attachment:

GCDS cyberjadugar A student has decided (20151210).jpg [ 27.69 KiB | Viewed 953 times ]
There are 3 variables(a, b, c), which should match with the number of equations. Therefore, 3 equations are needed. For 1), 1 equation, for 2) 1 equation, so we need 1 more equation. So, E is likely to be the answer. In 1) & 2),

1) Two equations b+c=10, a+c=12

2) One equation a+b=14

Based on 1) and 2), the answer is unique, which is sufficient. Therefore, the answer is C.

-> 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.

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