aippingw wrote:Here's a problem which is really shaking my confidence. Because I'm thinking that if I can't solve that, I probably didn't get any of the concepts about Prime numbers...

So if you guys could explain it to me I would really appreciate it

(I'm studying with the MGMAT books btw)

If p and q are positive integers and pq=24, what is the value of p ?

1- q/6 is an integer
2- q/2 is an integer

Here's how I solve this problem. And I am wrong but I don't get why

Pq=24, therefore pq prime box is {2,2,2,3}

1- q/6 so q prime box is {2,3}. Therefore p prime box is {2,2} so p could either be 2, 4 (2*2) or 1. I think I got this one right.
==>INSUFFICIENT

2- q/2 so q prime box is {2}. Therefore p prime could is {2,2,3} so p could either be 2,4,6,12.
I know I got it wrong because the Book says that the possible values of P are 2,4,6,8,12,24...

3- Let's not talk about 1 and 2 together since I don't even get them...

Thanks for your help guys

(1). q=6,12, or 24, so we have p=4,2,or 1 ------INSUFFICIENT

(2). q=2,4,6,8,12, or 24, thus p= 12,6,4,3,2------ INSUFFICIENT

(1)and(2)together, q=6,12, or 24, p=4,2,1 ----- INSUFFICIENT

what's the answer? i don't get why P could be 24, either.

I'm not sure but I think the answer is E (I don't have the book in front of me right now)

I just wanna know why. Because I just don't get the explanation. I hate prime numbers, it's so easy but so confusing...

Let me know if you find out any answers

Thx

i think answer is E.

as option A is insufficient
q has 4 values and p has 3 values

option B is insufficient
p and q has many values.

together A and B is insufficient as p and q has 2 values.
so ans is E.

if you need any explanation please let me know.

Thanks for the answer Kel !

I do agree about E as the answer.

I just don't understand what are the values or p and q in either cases + combine. But most important, I don't get WHY the book give those values of q and p as the answers.

And I think that "seanceserene" has the same problem.

So actually, yes if you could explain to me what are the value of p and q for statement 1 and 2 + combine, and WHY, I would really appreciate it

Thanks for your help !

I can't believe I get stuck on this question related to the 1st chapter of the 1st MGMAT study guide... Good for confidence... haha

hey don't feel sad.. DS is very tricky and very very confusing. with practice you will gain confidence.

as per the question:

p & q are positive integers
p*q=24

we have to find the value of p.

lets take first statement: q/6 is an integer
that means q can take 6,12,18,24 as values ( 6/6=1,12/6=2... 24/6=4 are all integers)
now with q=6 p will be 4 (as p*q=24)
with q=12, p will be 2
with q=18, p will be 1.33 , which is not an integer so q=18 and p=1.33 is ruled out.
with q=24, p will be 1

so from option "A" we get 3 values of q and p. so this is insufficient. we need to find only one value of p not 3.

lets take second statement:

q/2 is an integer

so q can take 2,4,6,8,10,12,14,16,18,20,22,24
with q=2 p will be 12 (integer)
with q=4 p will be 6 (integer)
with q=6 p will be 4 (int)
with q=8 p will be 3 (int)
with q=10, p will not be an integer so ruled out
similarly doing for the rest of the values of q we find that p will have 12,6,4,3,2,1 values.
so this is also insufficient.

taking together

compare the values of q from option "A" and option "B" and take only common values of q.
by doing so, we get q=6 ,12 and 24
and p=4,2 and 1
still we get 3 values of p so insufficient.

if still u have any queries let me know.

Thank you so much for your answer !!

however too things:

1- Is there a way to solve this problem with prime numbers ? I was thinking of a Venn Diagram or smth like that.

2- In my orginal post I actually made a mistake. The second proposition was actually p/2. So now the answer that the study guide gives me makes sense. And it works with your method too.

But I was wondering if there was another method than plugging numbers ?

Once again thank you so much for your answer !

If p and q are positive integers and pq=24, what is the value of p ?

1- q/6 is an integer
2- q/2 is an integer


First, note that p=24/q

(1) q is a multiple of 6 i.e. q= 6m for some positive integer m

Thus p= 4/m and p could be any divisor of 4

(2) q is a multiple of 2 i.e. q=2k for some positive integer k
Thus p= 12/k meaning k could be any divisor of 12

(T) Every divisor of 4 is a divisor of 12, so all we know is that p could be any divisor of 4

If p x q = 24, what number is p?

1. q / 6

for 6 to be a factor of q, q must equal = 6, 12,18,24
take those numbers ( 6,2,18,24) and figure what p must equal to get a product of 24.

so, if q = 6, 12, 18,24
p must equal = 4, 2, (cant work with 18), or 1

- - - - - - we have multiple possibilities, therefore, insuf.

2. p / 2
so for p to be divisible (or a factor of) 2 - p could equal, 2,4,6,8,10,12,14,16,18,20,22,24 (you can reduce this if you know that you can't possibly get 16 X ? = 24...) so really, p must equal either 2,4,6,8, 12, or 24

if p = 2,4,6,8, 12, or 24 ****ALSO NOTE, FOR P TO BE DIVISIBLE BY 2 - P MUST BE EVEN****
q must = 12,6,3, or 24


- - - - - - again, insuf. bc multiple possibilities.

together,
so, if q = 6, 12, 18,24
p must equal = 4, 2, or 1

if p = 2,4,6,8, 12, or 24
q must = 12,6,3, or 24


1. combined for q - we have, either 6 and 12
2. we know p must be even (from number 2) - and also combined - or what numbers work with 6 and 12 to get a product of 24.... p must equal either 4 or 2.... so again, insuf.

any time we have multiple answers for an integer we are trying to solve, that becomes insuf.

Quick answer to DS questions requires paraphrasing of the question.

In this case, it is stated that pq=24. The official question is what is p?

However, it is better to paraphrase 'What is q"? because if you know q you will also know the value of p.

(1) for pq=24 and q/6 is an integer, q can be 6, 12, 18 and 24 so Statement 1 is INSUFFICIENT
(2) for pr=24 and q/2 is an integer we have more than two values so Statement 2 is INSUFFICIENT as well.

If you combine two statements (which is the intersection between S1 and S2 because if q/6 is an integer than q/2 is an integer as well) we have more than two possible values for q so therefore the answer to the questions is E