Steps 1 & 2: Understand Question and Draw InferencesGiven: The tens digit of N is 9 and the unit’s digit of Np and Nq are 6 and 4 respectively.

To find: The value of N

Let us consider \(N = AB\), where A and B are single-digit numbers and the value of A is 9

Therefore, \(N^p = (AB)^p\)

To find the units digit, we need to focus on the last digit of the number, which is B in the above case. Hence, we can write \(B^p= 6\)

The above expression will hold true in the following cases –

Case I - Value of B = 2, Value of p = 4mCase II - Value of B = 4, Value of p = 2mCase III - Value of B = 6, Value of p = any numberCase IV - Value of B = 8, Value of p = 4mFrom the above cases, we can infer that finding the value of B on the basis of the value of p is possible only when p is an odd number because –

If p is a multiple of 4, B can take values - 2,4,6 or 8

If p is a multiple of 2 but not a multiple of 4 then B can be either 4 or 6

If p is an odd number, B can take only one value - 6

Using the same logic, we can write \(N^q\) as \((AB)6^q\) and \(B^q = 4\).

The above expression will hold true in the following cases –

Case I - Value of B = 2, Value of q = 4m+2Case II - Value of B = 4, Value of q = 2m+1Case III - Value of B = 8, Value of q = 4m+2From the above cases, we can infer that finding the value of B on the basis of the value of q is only possible when q is an odd number because –

If q is an even number, B can be 2 or 8

If q is an odd number, B has to be 4

Step 3: Analyze Statement 1 independentlyStatement 1 says “P is a positive even integer”.

From the inferences that we have drawn, we know if P is an even number, the units digit of N can be 2, 4, or 8

Since Statement 1 leads us to 4 possible values of B, it is clearly not sufficient to arrive at a unique answer.Step 4: Analyze Statement 2 independentlyStatement 2 says that Q is a positive odd integer.

From the inferences that we have drawn, we know if Q is an odd number, the units digit of N has to be 4

Thus N = 94.

Statement 2 is sufficient to get us a unique answer.Step 5: Analyze Both Statements Together (if needed)Since we’ve already got a unique answer in Step 4, this step is not required

Hence Correct Answer: Option B
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