We are given two variables say S and G to be quantified as per the equation xS + yG = 35
Quote:
(1) The Swiss chocolate bars cost $3.50 per bar, and the German chocolate bars cost $2.50 per bar.
now we know it is actually 3.5x + 2.5y = 35. On initial analysis it might seem that this is not enough as it is one equation with two unknown variables, however do know that we are to find positive integer values for both and that decreases the probability of there being many different solutions especially for smaller numbers. What if, we can arrive at a single unique solution using this equation by trial and error?
Let's see:
we know that Sara purchased both, so neither value can be zero. That discards 10x3.5 = 35, i.e 10S as the answer, so number of S has to be less than 10. Working our way backwards, it will be important to establish a number where say 3.5a=2.5b. This is only true for when 3.5x5=17.5=2.5x7
Since 5S and 7G are the only possible solutions for 3.5x + 2.5y = 35 as x has to lie between 1 and 10, we have arrived at our unique solution. Note that the only scenario that has led to this solution is the fact that the shop is selling whole numbered- chocolate items.
(1) is sufficient.
Quote:
(2) Sara purchased 2 more German chocolate bars than she did Swiss chocolate bars.
We do not know how much they cost, it could be 10S and 50G or even 1S and 1G.
Not sufficient.
Answer: A
One trick to solving this quickly is to sneak a peek onto Statement (2) only for the values and check if (C) i.e, both statements together stand, it they do, try to arrive at those values using only Statement 1 and if at all there are alternative solutions. That is how you decide between (A) and (C)
These kind of questions are particularly to be expected when you are scoring well, so it is advisable to be on the lookout for prime number values and easily multiplicative numbers for such DS questions.