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Re: A worker’s account activities consist of three types of
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12 Oct 2015, 11:13
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 worker’s account activities consist of three types of transactions—deposits of $500 and withdrawals of either $300 or $400. Last week, did the worker have at least ten account transactions?
(1) Last week the worker had at least one of each of the three types of transactions.
(2) At the end of last week, the amount in the worker’s account was $1,600 more than at the beginning of the week.
This is a frequently tested question in nowadays Chinese math. Looking at the original condition, there are 3 variables (x,y,z) if we let x be the no. of deposits of $500, y for that of $300, and z for $400. We will therefore need 3 equations to match the numbers, but there are only 2 equations given from the 2 conditions, so (E) is likely to be our answer.
Looking at them in detail, x=6, y=2, z=2 and the answer to the question becomes ‘yes’, and this condition is sufficient. In other words, 500*6-300*2-400*2=1,600 and 6+2+2=10.
But for condition 2, the answer is ‘yes’ for x=6, y=z=2, but ‘no’ for x=4, y=0, z=1. So this condition is insufficient, and the answer becomes (C).
For cases where we need 3 more equation, 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.