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Sure. Let’s see if @bunuel or @chetan2u have ideas
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remainders-144665.html example 8 is similar and uses binomial distribution
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We can use Fermat’s Theorem here which says
Rem [a^(p-1)/p] = 1 where p is a prime number
=> Rem [2^88/89] = 1
=> Rem [2^89/89] = Rem [2^88/89] * Rem [2/89] = 1*2 = 2

This is what I found online
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Arungmat612 wrote:
We can use Fermat’s Theorem here which says Rem [a^(p-1)/p] = 1 where p is a prime number => Rem [2^88/89] = 1 => Rem [2^89/89] = Rem [2^88/89] * Rem [2/89] = 1*2 = 2

Nice! I don’t think This is tested on the GMAT. You don’t have to know this.
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bb wrote:
I have a feeling there is a quirky formula or solution to this question but I don’t know if this is tested on the GMAT….

Bunuel chetan2u - is this a gmat concept question?

bb,
There are various formulas when it comes to remainder:, Fermat’s remainder theorem, Chinese remainder theorem. Luckily, GMAT doesn’t test them.

Having said that, I believe remainder questions can almost always be solved with pattern. If a question can be answered through a formula, I am sure it must be following some pattern.

Here too it should be the case:
2^1:2,
2^2: 4,
2^3: 8,
2^4: 16,
2^5: 32,
2^6: 64,
2^7: 128 or 128-89 or 39,
2^8: 39*2 or 78
2^9: 78*2-89 or 156-89 or 67
2^10: 67*2-89 or 134-89 or 45
2^11: 45*2 or 90-89 or 1
2^12: 1*2 or 2
So, we are repeating the remainders now and there are 11 different remainders in a pattern.
89=11*8+1
So, 2^89 will have same remainder as 2^1 or 2.

Posted from my mobile device
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bb wrote:
I have a feeling there is a quirky formula or solution to this question but I don’t know if this is tested on the GMAT….

Bunuel chetan2u - is this a gmat concept question?

­
Yes, the question is out of scope for the GMAT. You can solve it either by binomial expansion or using Fermat's Little Theorem (if p is a prime number, then for any integer a, a^p – a will be a multiple of p). Since 89 is prime, then 2^89 - 2 is a multiple of 89. Thus, 2^89 is 2 more than a multiple of 89, making the remainder equal to 2.

Having said that, you absolutely don't need this for the GMAT and you can ignore the above altogether.
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has anyone opted for gmat intensive classes by Anish and CJ
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Are we expecting any new questions if the New GMAT focus prep comes up next month?
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Hey, does anyone have the detailed syllabus for GMAT FE?
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stuts007 wrote:
Hey, does anyone have the detailed syllabus for GMAT FE?

Ya..I have

Which will be better gmat or gre if you are not good in quants??
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I prepped for the GMAT until now (Verbal going very well, Quant not so much, Data sufficiency going very well) -- Are skills transferrable for the GRE or would it require an entirely new practice?
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Hello can someone suggest which book is good for quants and data insights? Jamboree or Kalpan? Or there is some other book?
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Hi, does anyone know if Manhattan prep offers their own free GMAT practice test or do they just redirect you to mba.com ?
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Hi Everyone, anyone have rough plan to Prepare for GMAT FE in 3 months
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Hi all. I’ve been studying for the GMAT Focus Edition for a couple of months now and feel as though I’m running out of material to assess my understanding. I have seen varying reviews about non-official sources and want to make sure the material I am using for the exam is as like for like as possible to the real exam. I’ve been using the GMAT Focus Edition Official guides, the GMAT Club Mock and the GMAT Focus Edition Official Mocks, I’m coming to my last 2 final Official Focus Editions Mocks. Could anyone advise any other material that would be good to use? I’d preferably like to save my official mock exams till when I’m ready for the exam to give a true reflection of my understanding and where I am it before sitting the exam. Any advice/help would be greatly appreciated.
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SryN1998 wrote:
Hi all. I’ve been studying for the GMAT Focus Edition for a couple of months now and feel as though I’m running out of material to assess my understanding. I have seen varying reviews about non-official sources and want to make sure the material I am using for the exam is as like for like as possible to the real exam. I’ve been using the GMAT Focus Edition Official guides, the GMAT Club Mock and the GMAT Focus Edition Official Mocks, I’m coming to my last 2 final Official Focus Editions Mocks. Could anyone advise any other material that would be good to use? I’d preferably like to save my official mock exams till when I’m ready for the exam to give a true reflection of my understanding and where I am it before sitting the exam. Any advice/help would be greatly appreciated.

Hi, even I am using the exact same resources for my prep. Plus forum quiz on the gmat Club. It has a vast pool of Official questions that can be taken in the form of quiz. Hope this helps!

Just out of curiosity.. wat are ur official mock scores like?
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