zahraf wrote:
If x and y are both positive integers, x is a multiple of 3 and y is a multiple of 21, is xy a multiple of 75?
1) x is a multiple of 9.
2) y is a multiple of 25.
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.
There are 2 variables and 0 equation.
Thus C is the answer most likely.
This question is a key question by VA method, since it is related to Integers. By CMT(Common Mistake Type) 4A, we should check the answer A or B too.
We can express as follwings.
\(x = 3a\) and \(y = 21b\) for some integers \(a\) and \(b\).
The question if \(xy\) is a multiple of \(75\) is equivalent to the question if \(ab\) is a multiple of \(25\) since \(xy = 3a \cdot 21b = 3^2 \cdot 7 \cdot ab\) an \(75 = 3 \cdot 5^2\).
Condition 1)
Since \(x = 3a\) is a multiple of \(9\), \(a\) is a multiple of \(3\). We can determine from this condition if \(ab\) is a multiple of \(25\) or not.
Thus this is not sufficient.
Condition 2)
Since \(y = 21b\) is a multiple of \(25\), \(b\) must be a multiple of \(25\). Thus \(ab\) is also a multiple of \(25\).
Thus this condition is sufficient.
Therefore, B is the Answer
Normally for cases where we need 2 more equations, 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 C has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) together. Here, there is 70% chance that C is the answer, while E has 25% chance. These two are the key questions. 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 according to DS definition, we solve the question assuming C would be our answer hence using 1) and 2) together. (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
_________________