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 a certain store purchased a computer game and then sold it for $50, was the store's gross profit from the purchase and sale of the game less than $8?
(1) The store 's gross profit from the purchase and sale of the game was less than 25 percent of the amount for which the store purchased the game
(2) The store 's gross profit from the purchase and sale of the game was greater than 10 percent of the amount for which the store purchased the game
For questions regarding inequalities, if the range of the question includes that of the condition, the condition becomes the answer.
If we modify the question a little, p(profit)=50-c(purchase price).
p=50-c, where p<8.
From condition 1, p<0.25c=c/4 --> 4p<c. If we substitute in c=50-p, 4p<50-p, 5p<50, p<10. This is not sufficient
For condition 2, p>0.1c=c/10 --> 10p>c. If we substitute in c=50-p. 10p>50-p, 11p>50, p>50/11=4.5...., so this is also not a sufficient condition.
Looking at the conditions together, 4.5....<p<10.... So this is still not sufficient as the range of the question does not include the range of the conditions; the answer becomes (E)
For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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