Hello,
This problem involves using the minimization concept in a subtle way, but the core of the problem involves addition of positive integers, which is the main concept being tested here. So, as with most Data Sufficiency questions, it is always a good idea to try and figure out the concept/s which are being tested in the question, rather than just trying values.
This is a Data Sufficiency question which demands a definite value as an answer.
The data given in the question statement mentions that each of the 5 persons viz, A, B, C, D and E recieved at least 1 chocolate out of a total of 11 chocolates distributed among them. Hence, we can directly subtract 5 from 11 leaving us with 6 chocolates, which we can try and distribute among the 5 people in such a way as to answer the question.
Using statement I alone, we will not be able to say the exact value of E. As mentioned above, out of the 6 chocolates remaining, 3 can go to E and 3 can go to D. Therefore, E has 4 chocolates. Another combination is, out of the 6 chocolates, 2 can go to E and 2 can go to D (making their total 3) and the remaining 2 can be distributed in any way among the remaining 4 persons. This is evidence enough that, using the first statement alone, we will not be able to find a unique value of E.
Statement II alone - Each of A, B, C and D got distinct number of chocolates.
Let us approach this in a slightly different way. Since everyone has to get at least 1 chocolate, let us give E one chocolate. Now we are left with 10 chocolates, which have to be distributed among A, B C and D such that it satisfies the condition given in the second statement.
10 is an even number. When 4 numbers are added to get an even number as a result, the following combinations are possible
1) All 4 can be even
2) All 4 can be odd
3) 2 numbers can be odd and 2 numbers can be even
However, the first 2 combinations can be ruled out since the sum of the first four even numbers and the sum of the first four odd numbers will exceed 10. Therefore,
A + B + C + D = 10 can only be satisfied by substituting the values 1, 2, 3 and 4 in any order.
If E gets 2 chocolates (which he definitely can ),
then, A+ B + C + D = 9, for which the possible values could be 1,2,3,3 or 1,3,4,1 or 2,2,2,3 and so on. Hence, we see that, as the total gets smaller, some values are bound to repeat.
As such, we can safely say that the only combination of values that satisfies the conditions given in the question statement and statement II is (1,2,3,4). Hence, we can conclude that E gets 1 chocolate. Therefore, the second statement alone is sufficient to answer the question. So, answer option B.
A pertinent point to be noted is that, when you try to solve DS questions using values, you have to be able to back it up using concepts. If you can figure out the concept prior to plugging in values, there's nothing better, because then it means that you would not be plugging random values, but only those values that the concepts dictate.
Hope this helps!
Cheers,
CrackVerbal Academics Team
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