If [n] denotes the greatest integer less than or equal to n, is [n] =

Given: [n] denotes the greatest integer less than or equal to n.
eg: [5] = 5
[4.9] = 4
[4.1] = 4

Coming to the given conditions:
S1) Unique value of n can be found. Hence unique value of [n] can be found too. Sufficient
S2) N is between 4 and 5. Therefore by definition, [n] = 4. Sufficient

Answer D.

Solution : [n] = 5 ==> n lies between [5,6).

Statement1 : n=4.5 . No. Sufficient.

Statement2 : n lies in (4,5) . No. Sufficient.

Option D

Re-wording the question, will help in this instance. Basically the question is stating that [n] means we truncate any decimal or fraction n may have. For example [9.01] = 9; [3.99999] =3 and so on.
We need to determine if [n] = 5, or if n is between 5 and 6.
Stmt (1) gives us that n =4.5. Thus, [n] in this case = 4. SUFFICIENT
Stmt (2) gives us that n is between 4 and 5 (if [n]=5, we need n to be between 5 and 6). Again, SUFFICIENT

COrrect answer is D

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.

If [n] denotes the greatest integer less than or equal to n, is [n] = 5?

(1) 5n + 1= 10 + 3n
(2) 4 < n < 5

In the original condition, [1.5]=1, means round down. There is one variable (n) and 2 equations from the 2 conditions, so there is high chance (D) will be our answer.
condition 1), from 2n=9, n=4.5 [4.5]=4, the answer is 'no'. This condition is sufficient.
condition 2), from [4<n<5]=4, the answer is also 'no', making this condition sufficient as well.
The answer becomes (D).

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E

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