Aptitude - Numbers - Discussion

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It is being given that (2³² + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?

[A].	(2¹⁶ + 1)	[B].	(2¹⁶ - 1)
[C].	(7 x 2²³)	[D].	(2⁹⁶ + 1)

Answer: Option A

Explanation:

Let 2³² = x. Then, (2³² + 1) = (x + 1).

Let (x + 1) be completely divisible by the natural number N. Then,

(2⁹⁶ + 1) = [(2³²)³ + 1] = (x³ + 1) = (x + 1)(x² - x + 1), which is completely divisible by N, since (x + 1) is divisible by N.

Pavi said: (Mon, Jul 26, 2010 01:57:15 AM)

I cannot understand, please explain.

Devi said: (Fri, Sep 17, 2010 03:21:47 AM)

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

Rahul said: (Sun, Sep 26, 2010 04:05:51 AM)

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

A.Athiban Sakthivel said: (Tue, Nov 2, 2010 09:51:49 AM)

But its too complicated procedure. Is not there more simple procedure to solve this problem?

Divya said: (Fri, Nov 19, 2010 02:23:12 AM)

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

Priya said: (Wed, Nov 24, 2010 12:09:09 AM)

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

Mohsin said: (Wed, Dec 15, 2010 10:30:06 AM)

Ohh Its confusing !!!!! I cant understand y take (2^96+1)??????????????????

Mickeey said: (Sat, Dec 18, 2010 01:25:44 PM)

this is some what called as hit and trial method, you have to try the options which are similar to the value (2^32+1) in the question. remaining, you can easily eliminate by seeing. in the above, options A and D are similar to the expression given in the question. suppose the given four options are similar, you have to try all... this is also called as trial and error method...

Anusha said: (Wed, Dec 29, 2010 08:21:24 AM)

Is there any simple procedure?

Jaiveer said: (Wed, Jan 19, 2011 07:57:56 AM)

I could not understand so pls help me for full procedure

Richa said: (Sun, Jan 30, 2011 02:47:37 AM)

Unable to undestand. Kindly help.

Nagaraj said: (Mon, Jan 31, 2011 08:06:49 AM)

It's a simple thing; ((2^96)+1)/((2^32)+1) =((x^3)+1)/(x+1) =(x+1)(x^2-x+1)/(x+1); here easy to delete the (x+1); So we get only a (x^2-x+1)as anatural number;

Karthi said: (Mon, Feb 21, 2011 11:06:06 AM)

Give some explanations to understand clearly.

Rajan said: (Tue, Mar 15, 2011 04:16:33 AM)

Please explain briefly this sum.

Jitendra said: (Sun, Mar 20, 2011 09:09:34 AM)

Please help in another example similar to this.

Arun said: (Tue, Apr 5, 2011 07:18:24 AM)

I understand but I want another example.

Manohar said: (Wed, May 11, 2011 07:09:39 AM)

I cannot understand please explain again.

Mala said: (Mon, Jul 4, 2011 07:15:09 AM)

Its confusing. Is there any simple methods?

Nitesh Jindal said: (Sat, Jul 9, 2011 06:10:57 AM)

It is not comfusing. ok. try to understand the logic here. lets assume 2^32 is x. Now 2^96 = {2^32 }^3 .As 2^32 is x so 2^96 is x^3. Then x^3 +1 is furter solved by formula as a^3 + b^3 = (a+b)(a^2 -ab +b^3) . therefore x^3 + 1 = (x+1)(x^2 - x + 1 )

Neha Garg said: (Mon, Sep 12, 2011 02:03:24 PM)

2^32 means (2 ^4)^8 this will come 6. Because 22=4 222=8 2222= 16 If we multiply 2^5 then again unit digit will b 2, then 4 soon. 6+1= 7 and 2^96 = (2^4)24= 6 6+1 = 7.

Lekha said: (Sat, Sep 24, 2011 08:35:50 PM)

I can't understand. Please explain again. !

Harshita said: (Tue, Feb 7, 2012 05:07:43 PM)

I can't understand. Please explain again.

Aryan Verma said: (Wed, Feb 8, 2012 11:13:28 AM)

@Nagaraj Your Way of making understand is good dear.