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Re: Math: Number Theory [#permalink]
19 Nov 2010, 01:18

Quote:

But: Not all number which yield a remainder of 1 or 5 upon division by 6 are prime, so vise-versa of above property is not correct. For example 25 yields a remainder of 1 upon division be 6 and it's not a prime number.

Hope it's clear.

Understood Sir! .. i'll just use it one way; i.e, if i'm told that n is a prime number>3, then i can express it as 6n+1 or 6n+5

I think I just got a bit too excited about it that I forgot to thoroughly test it thru...

Re: Math: Number Theory [#permalink]
03 Jan 2011, 08:42

Bunuel,

For determining last digit of a power for numbers 0, 1, 5, and 6, I am not clear on how to determine the last digit.

Your post says: • Integer ending with 0, 1, 5 or 6, in the integer power k>0, has the same last digit as the base.

What is the last digit of 345^27 ---is the last digit 5? What is the last digit of 216^32----is the last digit 6? What is the last digit of 111^56---is the last digit 1?

Re: Math: Number Theory [#permalink]
01 Feb 2011, 06:29

Hi Folks,

I am having a small confusion between two concepts for which one of my practice Q went wrong. During my elementary school I have studied BODMAS B - Brackets O - Of D- Division M-Mulitplication A- Addition S- Substraction

I tried with this approach and it went wrong, while i was going through this again i happened to see a difference between PEMDAS & BODMAS (Multiplication order is different) .

Can somebody help me to understand which one i should follow.

Re: Math: Number Theory [#permalink]
01 Feb 2011, 06:34

Expert's post

gmat709 wrote:

Hi Folks,

I am having a small confusion between two concepts for which one of my practice Q went wrong. During my elementary school I have studied BODMAS B - Brackets O - Of D- Division M-Mulitplication A- Addition S- Substraction

I tried with this approach and it went wrong, while i was going through this again i happened to see a difference between PEMDAS & BODMAS (Multiplication order is different) .

Can somebody help me to understand which one i should follow.

Thanks Humble GMAT ASPIRANT

The rule mentioned in the initial post is correct.

Anyway: what difference are you talking about? Can you give an example? _________________

Re: Math: Number Theory [#permalink]
27 Feb 2011, 09:04

Any nonzero natural number n can be factored into primes, written as a product of primes or powers of primes. Moreover, this factorization is unique except for a possible reordering of the factors.

Pls give me the example of bold face text because i am not sure what does it exactly means.

Thanks _________________

The proof of understanding is the ability to explain it.

Re: Math: Number Theory [#permalink]
27 Feb 2011, 09:12

Expert's post

GMATD11 wrote:

Any nonzero natural number n can be factored into primes, written as a product of primes or powers of primes. Moreover, this factorization is unique except for a possible reordering of the factors.

Pls give me the example of bold face text because i am not sure what does it exactly means.

Thanks

It's called the fundamental theorem of arithmetic (or the unique-prime-factorization theorem) which states that any integer greater than 1 can be written as a unique product of prime numbers.

For example: 60=2^2*3*5 --> 60 can be written as a product of primes (powers of primes) only in this unique way (you can just reorder the multiples and write 3*2^2*5 or 2^2*5*3 ...). _________________