Lesson: Integer Properties Strategies

Comment on Integer Properties Strategies

Brent,

Could you help with the Exercise #161 of OG17?

Thanks,
Pedro
gmat-admin's picture

Glad to help!

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?
gmat-admin's picture

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 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.
gmat-admin's picture

Your interpretation is correct; in a set of N consecutive integers, exactly 1 of those integers is divisible by N.

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
gmat-admin's picture

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?
gmat-admin's picture

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?
gmat-admin's picture

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

HI! Could you please help me solve the following question?
https://gmatclub.com/forum/m27-184477.html

Thanks,
Aman
gmat-admin's picture

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

Cheers,
Brent

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.
gmat-admin's picture

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