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Re: If p.q and r are positive integers greater than 1, and p and [#permalink]
26 Dec 2013, 00:40

1

This post received KUDOS

jlgdr wrote:

mau5 wrote:

rajatr wrote:

If p.q and r are positive integers greater than 1, and p and q are factors of r, which of the following must be the factor of r^pq?

I. p+q II. q^p III. p^2 * q^2

A. I only

B. II only

C. III only

D. I and II

E. II and III

We know that p and q are factors of r. Thus, for 2 non-negative integers,m and n, we have : r = pm and r = qn. Now, \(r^{pq} = (pm)^{pq} = (qn)^{pq}\).

Thus, we see that \(q^p\) will always be a factor of the given expression.

Also, from the given problem p,q>2. Thus, the minimum value of p*q = 4.

Thus,\(r^{pq}\) = At-least \(r^4\). Now, as r = pm = qn, thus, \(r^4 = (p*q*m*n)^2 = p^2*q^2*m^2*n^2.\)Thus, \(p^2 * q^2\) is also a factor of the given expression.

E.

What about the first statement?

Cheers J

For this kind of question, I like to plug in numbers.

p = 2 q = 3 r = 6 ==>6^(2*3) = \((6^2)^3 = 36^3\) Clearly, 36 is not divisible by 5 (2+3 =5) Only number ending with 5 or 0 can be divisible by 5 ==> 1st statement is not a "must be true" answer.

Best! _________________

Please +1 KUDO if my post helps. Thank you.

"Designing cars consumes you; it has a hold on your spirit which is incredibly powerful. It's not something you can do part time, you have do it with all your heart and soul or you're going to get it wrong."

Re: If p.q and r are positive integers greater than 1, and p and [#permalink]
25 Apr 2013, 22:35

Expert's post

rajatr wrote:

If p.q and r are positive integers greater than 1, and p and q are factors of r, which of the following must be the factor of r^pq?

I. p+q II. q^p III. p^2 * q^2

A. I only

B. II only

C. III only

D. I and II

E. II and III

We know that p and q are factors of r. Thus, for 2 non-negative integers,m and n, we have : r = pm and r = qn. Now, \(r^{pq} = (pm)^{pq} = (qn)^{pq}\).

Thus, we see that \(q^p\) will always be a factor of the given expression.

Also, from the given problem p,q>2. Thus, the minimum value of p*q = 4.

Thus,\(r^{pq}\) = At-least \(r^4\). Now, as r = pm = qn, thus, \(r^4 = (p*q*m*n)^2 = p^2*q^2*m^2*n^2.\)Thus, \(p^2 * q^2\) is also a factor of the given expression.

Re: If p, q and r are positive integers greater than 1, and p [#permalink]
26 Apr 2013, 00:29

given that p and q are factors of r. so we can picture it this way r=p*q*n (n-some another factor of r) so, r^pq= (p*q*n)^pq

I. p+q .since the question is MUST BE TRUE, we eleminate this option II. (p*q*n)^pq / q^p= integer YES! III.(p*q*n)^pq/ p^2 * q^2 YEs, since we are said that integer p>1 and integer q>1 _________________

Happy are those who dream dreams and are ready to pay the price to make them come true

Re: If p, q and r are positive integers greater than 1, and p [#permalink]
26 Apr 2013, 00:34

LalaB wrote:

given that p and q are factors of r. so we can picture it this way r=p*q*n (n-some another factor of r) so, r^pq= (p*q*n)^pq

Hi LalaB,

this part is incorrect. Consider the case \(r=30\) and its factor \(p=15\) \(q=10\)

According to your statement \(30=10*15*other factor\) As you can see this is not true: no factor of 30 will fit into that equation . (What you say can be true only in some cases....)

Hope this clarifies, let me know _________________

It is beyond a doubt that all our knowledge that begins with experience.

Re: If p.q and r are positive integers greater than 1, and p and [#permalink]
25 Dec 2013, 15:29

mau5 wrote:

rajatr wrote:

If p.q and r are positive integers greater than 1, and p and q are factors of r, which of the following must be the factor of r^pq?

I. p+q II. q^p III. p^2 * q^2

A. I only

B. II only

C. III only

D. I and II

E. II and III

We know that p and q are factors of r. Thus, for 2 non-negative integers,m and n, we have : r = pm and r = qn. Now, \(r^{pq} = (pm)^{pq} = (qn)^{pq}\).

Thus, we see that \(q^p\) will always be a factor of the given expression.

Also, from the given problem p,q>2. Thus, the minimum value of p*q = 4.

Thus,\(r^{pq}\) = At-least \(r^4\). Now, as r = pm = qn, thus, \(r^4 = (p*q*m*n)^2 = p^2*q^2*m^2*n^2.\)Thus, \(p^2 * q^2\) is also a factor of the given expression.

E.

What about the first statement?

Cheers J

gmatclubot

Re: If p.q and r are positive integers greater than 1, and p and
[#permalink]
25 Dec 2013, 15:29

Harvard asks you to write a post interview reflection (PIR) within 24 hours of your interview. Many have said that there is little you can do in this...