What is the value of the integer N?

(1) \(101 < N < 103\); The only number between 101 and 103 is 102. Sufficient.

(2) \(202 < 2N < 206\); Dividing the inequality by 2 we get:

\(101 < N < 103\) and he only number between 101 and 103 is 102; Sufficient.

The answer is D

Thank you for the explanation

This is a 'value' data sufficiency question which means the statements which give us a unique value for N will be sufficient.

Another point to note is that the question states clearly that N is an integer.

Let us now begin the statement analysis:

S1: Only 1 integer value of N is possible= 102. Sufficient. Strike off BCE
S2. This one is tricky, from the looks of it it seems like there are 3 integer values that will satisfy N so a lot of people may head towards eliminating D.
However, the statement says 2N; so we need to break down all the possibilities as = 2*N and the integer value(s) will make the answer much clearer.

Possible integers between 202 and 206:
203= 2* 101.5, can N be equal to 101.5? No. it has to be an integer.
204= 2. 102, can N = 102? yes. let's hold on to this one.
205= 2* 102.5. can N =1-2.5? no. it has to be an integer.

So in essence, option B gives us only one unique value that satisfies the requirement.

Therefore D is the answer.

Solution:

We need to determine the value of N given that it is an integer.

Statement One Alone:

Since the only integer between 101 and 103 is 102, N = 102. Statement one alone is sufficient.

Statement Two Alone:

Dividing the inequality by 2, we see that 101 < N < 103, which is exactly the same as the inequality in statement one. Therefore, statement two alone is also sufficient.

Answer: D

This is a value type of DS question in which we need to find a unique value of N. From the question data, we know that N is an integer, therefore, we need not worry about non-integral values in a range.

From statement I alone, 101<N<103. There is only ONE integral value in this interval and that is 102.
Therefore, N = 102. Statement I alone is sufficient. Answer options B, C and E can be eliminated. Possible answer options are A or D.

From statement II alone, 202<2N<206. Dividing all terms in the inequality by 2, we have 101<N<103, which is the same information given in statement I alone. Clearly, that was sufficient and so is this.
Statement II alone is sufficient. Answer option A can be eliminated.

The correct answer option is D.

Hope that helps!
Aravind B T

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