Aptitude - Numbers - Discussion

Above mentioned are totally absurd. Few of them having tried good but not upto the mark.

Now see this carefully.

We are trying to get our given no. 2^32+1 from the choices given and I tried all d choices. And atlast 2^96+1 is easily broken to get 2^32+1.

Now I take an example to explain it in detail. Since 2^32+1 is completely div by N therefore N<=2^32+1 (less than equal to).

Ex: If 4 is completely div by x then x is always less than or equal to 4.

Now take first option 2^16+1 here it will be completely div N when N<=2^16+1 but wt if N>2^16+1 since value of N is ranging from 0 to 2^32+1 so wt if N>2^16+1 then 2^16+1 is not completely div.

Since we exactly don't know value of N we are checking its range to determine.

Therefore option A is not answer. Now similarly B is not answer not.

Option D is answer because all the range of N completely divides it which is explained how by indiabix.

If you don't understand this answer just try to focus on range of N. And again see my example of 4 completely divided.

@All. Please refer the following.

Formula : (a^3+b^3)=(a+b)(a^2-ab+b^2).
Substitute : (x^3+1^3)=(x+1)(x^2-x*(1)+1^2).

I'm not understanding this problem.

It is being given that (2^32 + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number.

Sol: The given expression is 2^32+1.
This is the form of (a^m + 1).

We use the rule (a^m + 1) / (a^n + 1) when m/n is an odd number

Now check the options:
Option A: (2^16 +1)
32÷16 = 2 (even)

Option B: (2^16-1).
Not in the form (a^n +1).

Option C: (7x2^23).
Not matching the required form.

Option D: (2^96+1).
96÷32 = 3 (odd) correct answer.

I cannot understand, please explain.

I cannot understand how replace (2^96+1) = [ (2^32) ^3].

Hi Dear,

2^32^3 here multiplication of power will take place. So 32x3 = 96 Ok.

But its too complicated procedure.

Is not there more simple procedure to solve this problem?

I can't to understand your explanation. Can you explain clearly and basically................

When we make 2^32 is X,
We try to simplify to get the answer split 2^96 = 2^(32X3)
so it is = X^3
When using the formula for X^3+1, we can identify that number is divisible by 2^32