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It is given that 2^32 + 1 is exactly divisible by a certain number. Wh

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It is given that 2^32 + 1 is exactly divisible by a certain number. Wh  [#permalink]

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New post Updated on: 17 Jan 2015, 15:27
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It is given that 2^32 + 1 is exactly divisible by a certain number. Which one of the following is also divisible by the same number ?

a. 2^96 + 1
b. 2^16 - 1
c. 2^16 + 1
d. 7 * 2^33
e. 2^64 + 1

Originally posted by subhamoycomputer on 17 Jan 2015, 12:42.
Last edited by Bunuel on 17 Jan 2015, 15:27, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: It is given that 2^32 + 1 is exactly divisible by a certain number. Wh  [#permalink]

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New post 17 Jan 2015, 12:54
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subhamoycomputer wrote:
Guys I got stuck at this question... Need help.....

It is given that 2^32 + 1 is exactly divisible by a certain number. Which one of the following is also divisible by the same number ?

a. 2^96 + 1
b. 2^16 - 1
c. 2^16 + 1
d. 7 * 2^33
e. 2^64 + 1


a³ + b³ =(a+b)(a² -ab +b²)
Now, let (2^32 + 1) be (a+b)
a³ + b³ = (2^96 + 1)

Now, as mentioned in formula above,
a³ + b³ is always divisible by (a+b)
So any factor of (a+b) is a factor of (a³ + b³)

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Re: It is given that 2^32 + 1 is exactly divisible by a certain number. Wh  [#permalink]

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New post 17 Jan 2015, 21:38
Bunuel Isnt there any other approach to solve this question, other than the one described above?? Thanks.
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Re: It is given that 2^32 + 1 is exactly divisible by a certain number. Wh  [#permalink]

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New post 21 Jan 2015, 18:19
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\((a+b)^3 = (a+b)(a^2 - ab + b^2)\)

\((a-b)^3 = (a-b)(a^2 + ab + b^2)\)

I was told in some earlier posts that the above cube expansions are out of scope of GMAT.
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Re: It is given that 2^32 + 1 is exactly divisible by a certain number. Wh  [#permalink]

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New post 14 Sep 2018, 02:21
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: It is given that 2^32 + 1 is exactly divisible by a certain number. Wh &nbs [#permalink] 14 Sep 2018, 02:21
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