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 equations ensures a solution.
Nate Dogg sings hooks for two different prices: $52 for an EP and $58 for an LP. How many EP hooks did he sing?
(1) Nate sang a total of 9 hooks
(2) Nate earned $492 from singing hooks
Looking at the original condition, we can notice that this is a typical 2by2 question in GMAT test and the table is as below.
There are 2 variables (a,b) and we need 2 equations to match the number of variables and equations. Since there is 1 each in 1) and 2), C is likely the answer. Using both 1) & 2) together, a+b=9, 52a+56b=492 gives us b=4,a=5 and thus C is the answer. But hidden integer questions such as this question usually turns out to be common mistake type 4(A), thus we should try using the conditions separately. Using 1) and 2) separately, in case of 2) we have 52a+56b=492, 26a+29b=246 and since (26,29) is relative prime numbers (pair whose common factor is 1) a and b is a positive integer. Normally there is only 1 answer for the pair. Looking at 2), we have 26a+29b=246 and the answer is a=5, b=4, a unique answer. The condition is sufficient, therefore the answer is B. This is 5051 level question.
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