DS Strategy: If p is an integer, is p/18 an integer?

[nm37]

Hello everyone,

I'm on MGMAT Guide 1 - Number Properties, chapter 8 DS Strategy and I've hit a mental roadblock.

The question reads as follows:

If p is an integer, is p/18 an integer?

(1) 5p/18 is an integer
(2) 6p/18 is an integer

The guide goes on to advise readers to break 18 down into prime chunks (2 x 3 x 3) and create a prime box of p for each statement.

And here is where I blank:

The coefficient of 5 does not provide ANY of the necessary primes to be divisible by 18. Therefore, in order for 5p to be divisible by 18, p must be divisible by two 3's and a 2. There are (at least) two 3's and a 2 in the prime box of p. Thus, this is sufficient.

What am I missing? I just don't understand the logic here.

The author goes on to explain another method for solving, which only confuses me further.

Another way to solve is to test numbers. Think of the smalles possible value of p such that 5p/18 is an integer is 18. The next number for which 5p/18 is an integer is 36

[jnelson0612]

Hello everyone,

I'm on MGMAT Guide 1 - Number Properties, chapter 8 DS Strategy and I've hit a mental roadblock.

The question reads as follows:

If p is an integer, is p/18 an integer?

(1) 5p/18 is an integer
(2) 6p/18 is an integer

The guide goes on to advise readers to break 18 down into prime chunks (2 x 3 x 3) and create a prime box of p for each statement.

And here is where I blank:

The coefficient of 5 does not provide ANY of the necessary primes to be divisible by 18. Therefore, in order for 5p to be divisible by 18, p must be divisible by two 3's and a 2. There are (at least) two 3's and a 2 in the prime box of p. Thus, this is sufficient.

What am I missing? I just don't understand the logic here.

The author goes on to explain another method for solving, which only confuses me further.

Another way to solve is to test numbers. Think of the smalles possible value of p such that 5p/18 is an integer is 18. The next number for which 5p/18 is an integer is 36

Let me try to answer your question by proposing an experiment.

Statement 1 tells us that 5p/18 is an integer. Because statements must be true, please give me some possible values for p in which 5p/18 is an integer. Once you come up with a few, see if you can find a value for p that fits this statement but that is not also divisible by 18.

Do that, please report back, and then we'll take it from there. This is really important stuff to understand and I think that by actually trying some numbers you will be closer to fully understanding this concept.