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.
On a camping trip, x campers each paid y dollars for food. What percent of the total food expenses did each camper pay?
(1) If there were one few camper, each camper would owe 1 dollar more.
(2) If there were half as many campers, each camper would owe 7 dollars more.
If we modify the question, we want to know y/xy=1/x=? the conditions are sufficient if they have data about 'x' If we simplify the 2 conditions, the question asks 1/x=?
Condition 1) (x-1)(y+1)=xy, or xy-y+x-1=xy, or y=x-1
Condition 2) (x/2)(y+7)=xy, or (y+7)/2=y, y+7=2y, y=7.
There are 2 variables (x,y) and 2 equations are given from the 2 conditions so there is high chance (C) will be our answer, and (C) is , in fact, our answer.
For cases where we need 2 more equation, 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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