# Lesson: Integer Properties Strategies

## Comment on Integer Properties Strategies

### Brent,

Brent,

Could you help with the Exercise #161 of OG17?

Thanks,
Pedro Here's my step-by-step solution: https://gmatclub.com/forum/club-x-has-more-than-10-but-fewer-than-40-mem...

Cheers,
Brent

Brent,

Thank you!

Cheers,
Pedro

### why is 51 not a prime number?

why is 51 not a prime number? ### 51 = 3 x 17

51 = 3 x 17
The sum of the digits = 5 + 1 = 6
Since 6 is divisible by 3, we know that 51 is divisible by 3

Cheers,
Brent

### Hi! My question is pertaining

Hi! My question is pertaining to the rule regarding consecutive integers (N consecutive integers ==> 1 number must be divisible by N).... Does this mean that exactly 1 number within the list must be divisible by N, or at least one number (possibly more than 1?) must be divisible by N? I understood it as exactly 1 number must be divisible by N, but I just wanted to confirm. Your interpretation is correct; in a set of N consecutive integers, exactly 1 of those integers is divisible by N.

### Hi Brent,

Hi Brent,

The below question is from MGMAT, need your help in this one. Also if you could suggest more of such questions to practise.

If [x] denotes the least integer greater than or equal to x and [x/2]=0, which of the following could be the value of x ?

-2
-3/2
1/2
1
2 ### Came across this on a

Came across this on a practice test:

What is the tens digit of the positive integer r?
(1) The tens digit of r/10 is 3
(2) The hundredth digit of r 10r is 6

What the best approach for this? ### https://gmatclub.com/forum/if

https://gmatclub.com/forum/if-a-b-and-c-are-integers-and-abc-0-is-a-2-b-149839.html

How can we pick random numbers to prove / disprove the statements here? ### I have shown how we can test

I have shown how we can test numbers in my solution here: https://gmatclub.com/forum/if-a-b-and-c-are-integers-and-abc-0-is-a-2-b-...

Cheers,
Brent

https://gmatclub.com/forum/m27-184477.html

Thanks,
Aman ### Here's my full solution:

Here's my full solution: https://gmatclub.com/forum/m27-184477.html#p2289874

Cheers,
Brent

### Hi Brent, could you help me

Hi Brent, could you help me with this question please? Thank you!! x

If a, b, k, and m are positive integers, is a^k a factor of b^m?
(1) a is a factor of b.
(2) k ≤ m. 