tinayni552 wrote:
when checking both statements we have 4 different unknowns, I will presume that they are defined as a,b,c, and d. check the attached picture, we can derive 4 different equations. a+b=10 , b+d=20 , 30+a=c , c+d=60. I tried to solve them manually and the answer was a=10. I thought that maybe I missed something, and we know that the maximum number for a is 10, so I tried 9, which made c=39 and d=21, which is impossible because the maximum value of d+b is 20. So the only value that a can take is actually 10. C is the correct answer.
I think you're arriving at an incorrect conclusion because the equation I highlighted above is not right - it should read 20 + b = d.
You can write down four equations here in four unknowns, but the equations are not "independent", to use the technical term. You can derive one of the equations from the rest of them. If you take the first three equations and put the number alone on one side in each:
10 = a + b
20 = d - b
30 = c - a
and just add all three of those equations together, what you'll get is:
60 = c + d
which is the fourth equation. So the fourth equation isn't any new information, since you already know it using the first three equations, and you really only have 3 equations in 4 unknowns. You'll have an infinite number of solutions, though if you need the unknowns to represent non-negative integers, I think you'll find a can take any value between 0 and 10, inclusive, for eleven possible non-negative integer solutions.
The question does illustrate why counting equations and unknowns is generally not a successful strategy in DS questions, besides on the easiest questions. And for this question, you don't really need to use any algebra. We know about 50 of the cars using the two statements, but we don't know how the remaining 10 cars are divided between the two remaining categories - the cars with only power windows, and the cars with neither stereos nor power windows. So the answer is E.
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