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Prime numbers (again and always)

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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Prime numbers (again and always)

by aippingw » Mon Apr 12, 2010 5:07 pm
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
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by seanceserene » Tue Apr 13, 2010 4:56 am
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.
it is not an "alice in wonderland". it is real! i am going to freak GMAT out!
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by aippingw » Tue Apr 13, 2010 5:43 am
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
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by kel2010 » Tue Apr 13, 2010 8:08 am
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.
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by aippingw » Tue Apr 13, 2010 8:13 am
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
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by kel2010 » Wed Apr 14, 2010 8:39 am
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.
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by aippingw » Thu Apr 15, 2010 5:15 am
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 !
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by kevincanspain » Tue Apr 20, 2010 3:51 pm
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
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by Cally627 » Sat Apr 28, 2012 8:40 am
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.
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by ikaplan » Mon Apr 30, 2012 8:42 am
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
"Commitment is more than just wishing for the right conditions. Commitment is working with what you have."
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