MathRevolution wrote:
[GMAT math practice question]
(number properties) If \(a, b\), and \(c\) are positive integers, what is the value of \(a+b+c\)?
1) \(a, b\) and \(c\) are three consecutive odd numbers in that order
2) \(20≤bc-ab≤24\)
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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
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Since we have \(3\) variables (\(a, b\), and \(c\)) and \(0\) equations, E is most likely the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.
Conditions 1) & 2)
Since \(a, b\), and \(c\) are three consecutive odd numbers in that order, we can put \(a = b – 2\) and \(c = b + 2.\)
\(bc – ab = b(b+2) – (b-2)b = b^2 + 2b – b^2 +2b = 4b\) and we have \(20≤4b≤24\) and dividing everything by \(4\) we get \(5≤b≤6.\)
Since \(b\) is an odd integer, we have \(b=5.\)
Then we have \(a = 3, b = 5, c = 7\) and \(a + b + c = 15.\)
Since both conditions together yield a unique solution, they are sufficient.
Since this question is a statistics question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.
Condition 1)
Since there are many possibilities for (a,b,c), the condition is obviously not sufficient.
Condition 2)
If \(a = 3, b = 5\) and \(c = 7\), then we have \(a + b + c = 15.\)
If \(a = 1, b = 5\) and \(c = 5\), then we have \(a + b + c = 11.\)
Since condition 2) does not yield a unique solution, it is not sufficient.
Therefore, C is the answer.
Answer: C
In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions when the answer is A, B, C or D.