Of the marbles in a box, 2/5 are blue, 1/3 are red, and the rest are

Hello,
Greetings for the day!
At the outset, although this problem appears like a problem on Overlapping sets, it actually tests your understanding of concepts on mathematical operations done on fractions. It’s a good idea to actually solve this problem to see what we mean. So, here we go.

Since the two fractions we see are 2/5 and 1/3, let us assume 30x as the total number of marbles.

Now, you may have a question in your mind as to why we took 30x instead of just taking 30. If you observe the second statement, you can see that there are 36 marbles which are green or red. Had we taken just 30, it would have caused a confusion when Statement II had to analysed. Also, we do not know for sure how many marbles are actually there. So, to account for all these uncertainties, it is a good idea to involve a variable.

Okay, let’s try to analyse the question statement now. The question says that 2/5th of the marbles are blue. This means 2/5th of 30x are blue. Therefore, 12x marbles are blue. In a similar manner, we can ascertain that 10x and 8x are the respective numbers of red and green marbles.
Also, it is said that half the marbles are large and half are small. So, we have 15x large and 15x small marbles.

If we have to answer the question uniquely, we need a unique value for ‘x’. Whichever statement or combination will give us this will be sufficient.

Using statement I alone, we can say that there are 6x large blue marbles and 5x large red marbles. With this we can conclude that there are 4x large green marbles.
Therefore, there should be 6x small blue marbles, 5x small red marbles and 4x small green marbles since we have 12x blue, 10x red and 8x green marbles.

But knowing these split ups will not help us find a value of x. Hence, this data is insufficient. So, the answer options cannot be A or D. The possible answers are B, C or E.

Using statement II alone, we know that there are 36 large marbles which are green or red. But we do not know how many large green and red marbles are there, individually.
Hence, insufficient! So, the answer cannot be B. The possible answers are C or E.

When we combine both the statements, we can see that, from statement I, there are 5x large red marbles and 4x large green marbles; from statement II, we know that the addition of these two values should give us 36. So, we can definitely calculate a unique value of x and hence answer the question uniquely.

So, the correct answer is option C.

As demonstrated in the first half of this explanation, it is important to solve these kind of problems on fractions, by assuming values which represent a common multiple of the denominators. It is not a great idea to follow the conventional approach of taking the total number of marbles as ‘x’ and then applying the fractions on x. This will only prolong the solution and put an unnecessary load on your mental faculties.

Hope this helps!
Arvind,
CrackVerbal Prep Team