# 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. ### https://gmatclub.com/forum/if

https://gmatclub.com/forum/if-x-and-y-are-integers-greater-than-3-and-15y-11x-305024.html

y=13; is there any quick way to find y=13? Imho,It's a time consuming Once we know that 4(2 – y) is a multiple of 11, we can start testing possible scenarios.
Some possible multiples of 11 include 11, 22, 33,...etc as well as 0, -11, -22,... etc

Important: Since 4 is NOT a multiple of 11, it must be the case that (2 – y) is a multiple of 11.

Now let's test some possible scenarios...

This case, y = -9
However, we're told that y is an integer greater than 3

What about (2 - y) = 22?
This case, y = -20, but we're told that y > 3
At this point, we can see that, if we keep testing bigger and bigger multiples of 11 (33, 44, 55 etc), the corresponding y value will always be negative.

So let's try some smaller multiples of 11

What about (2 - y) = 0?
This case, y = 2, but we're told that y > 3

What about (2 - y) = -11?
This case, y = 13
PERFECT! This satisfies the condition that y > 3

What about (2 - y) = -22?
This case, y = 24
This also satisfies the condition that y > 3

At this point we can see that 13 is the smallest possible y-value such that (2 – y) is a multiple of 11.

So, once we know that (2 – y) is a multiple of 11, we don't have to test many values.

Cheers,
Brent

Thanks

### https://gmatclub.com/forum

https://gmatclub.com/forum/which-of-the-following-integers-can-be-written-as-both-the-131352.html ### Hi Brent,

Hi Brent, 