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If p, q, and r are positive integers such that q is a factor
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Updated on: 06 Jul 2014, 11:17
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61% (02:25) correct 39% (01:57) wrong based on 233 sessions
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If p, q, and r are positive integers such that q is a factor of r, and r is a multiple of p, which of the following must be an integer? A. (p + q)/r B. (r + p)/q C. p/q D. pq/r E. r(p + q)/pq
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Originally posted by goodyear2013 on 06 Jul 2014, 09:58.
Last edited by Bunuel on 06 Jul 2014, 11:17, edited 1 time in total.
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Re: If p, q, and r are positive integers such that q is a factor
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06 Jul 2014, 11:36
goodyear2013 wrote: If p, q, and r are positive integers such that q is a factor of r, and r is a multiple of p, which of the following must be an integer? A. (p + q)/r B. (r + p)/q C. p/q D. pq/r E. r(p + q)/pq We have that r is a multiple of both q and p. A. (p + q)/r. Not necessarily true. Consider r = 3, and p = q = 1. B. (r + p)/q. Not necessarily true. Consider r = 6, and p = 2 and q=3. C. p/q. Not necessarily true. Consider r = 6, and p = 2 and q=3. D. pq/r. Not necessarily true. Consider r = 3, and p = q = 1. E. \(\frac{r(p + q)}{pq}= \frac{rp+rq}{pq}=\frac{rp}{pq}+\frac{rq}{pq}=\frac{r}{q}+\frac{r}{p}=integer+integer=integer.\) Answer: E.
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Re: If p, q, and r are positive integers such that q is a factor
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08 Jul 2014, 21:40
Let p, q, r be 2, 4, 24 Cross check the conditions given 4 is a factor of 24 ? .......... YES 24 is a multiple of 2? .......... YES Check the options: A: \(\frac{2+4}{24}\) ......... Fail B: \(\frac{24 + 2}{4}\) ......... Fail C: \(\frac{4}{24}\) ............ Fail D: \(\frac{2*4}{24}\) ........... Fail E: \(\frac{24(2+4)}{4*6}\) ................ SuccessAnswer = E
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If p, q, and r are positive integers such that q is a factor
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20 Dec 2014, 10:22
I am not able to get the right answer 1)If q is a factor of r, then r=aq (a any constant ) 2)If r is a multiple of p,then p=br (b any constant) Now checking options 1. (p+q)/r= (br+r/a)/r= b+1/a .................... It can b an Integer if a=1 2. (r+p)/q= (r+br)/(r/a)= a(1+b)............ Always an Integer 3. p/q =rb/(r/a)=b/a ................................ Can be an Integer if b is divisible by a 4. r(p+q)/pq= r(rb+r/a)/(rb*r/a)=(ab+1)/b ............... I think I m doing some basic mistake ,please tell.
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Re: If p, q, and r are positive integers such that q is a factor
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20 Dec 2014, 10:35
veerdonjuan wrote: I am not able to get the right answer 1)If q is a factor of r, then r=aq (a any constant ) 2)If r is a multiple of p,then p=br (b any constant)Now checking options 1. (p+q)/r= (br+r/a)/r= b+1/a .................... It can b an Integer if a=1 2. (r+p)/q= (r+br)/(r/a)= a(1+b)............ Always an Integer 3. p/q =rb/(r/a)=b/a ................................ Can be an Integer if b is divisible by a 4. r(p+q)/pq= r(rb+r/a)/(rb*r/a)=(ab+1)/b ............... I think I m doing some basic mistake ,please tell. r is a multiple of p means r = bp, not p = br.
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Re: If p, q, and r are positive integers such that q is a factor
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20 Dec 2014, 10:44
Thankyou Bunuel !!I think I need good sleep Please tell substituting a value is good (less time consuming & accurate ) approach or assuming variables Bunuel wrote: veerdonjuan wrote: I am not able to get the right answer 1)If q is a factor of r, then r=aq (a any constant ) 2)If r is a multiple of p,then p=br (b any constant)Now checking options 1. (p+q)/r= (br+r/a)/r= b+1/a .................... It can b an Integer if a=1 2. (r+p)/q= (r+br)/(r/a)= a(1+b)............ Always an Integer 3. p/q =rb/(r/a)=b/a ................................ Can be an Integer if b is divisible by a 4. r(p+q)/pq= r(rb+r/a)/(rb*r/a)=(ab+1)/b ............... I think I m doing some basic mistake ,please tell. r is a multiple of p means r = bp, not p = br.
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If p, q, and r are positive integers such that q is a factor
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15 Jun 2017, 02:53
If p, q, and r are positive integers such that q is a factor of r, and r is a multiple of p, which of the following must be an integer?
A. (p+q)/r B. (r+p)/q C. p/q D. pq/r E. r(p+q)/pq



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Re: If p, q, and r are positive integers such that q is a factor
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15 Jun 2017, 03:08
aarushi00 wrote: If p, q, and r are positive integers such that q is a factor of r, and r is a multiple of p, which of the following must be an integer?
A. (p+q)/r B. (r+p)/q C. p/q D. pq/r E. r(p+q)/pq Merging topics. Please refer to the discussion above.
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Re: If p, q, and r are positive integers such that q is a factor
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15 Jun 2017, 03:15
aarushi00 wrote: If p, q, and r are positive integers such that q is a factor of r, and r is a multiple of p, which of the following must be an integer?
A. (p+q)/r B. (r+p)/q C. p/q D. pq/r E. r(p+q)/pq One of the simple way to solve such kind of questions is to use values for different variables given. Lets Assume r = 8 q = 2 p= Either 1 or 4. Need to assume two value since relationship between p & q is not given Let's plug these values A. (p+q)/r = 3/8 = Not an Integer B. (r+p)/q = 12/2 or 9/2 = Not an Integer in 2nd Scenario C. p/q = 1/2 or 2/2 = Not an Integer in 1st Scenario D. pq/r = 2/8 or 8/8 = Not an Integer in 1st Scenario E. r(p+q)/pq = 8.3/3 or 8.6/8 = Integer in Both the Scenarios'. Hence Answer E
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Re: If p, q, and r are positive integers such that q is a factor
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17 Jun 2017, 05:25
goodyear2013 wrote: If p, q, and r are positive integers such that q is a factor of r, and r is a multiple of p, which of the following must be an integer?
A. (p + q)/r B. (r + p)/q C. p/q D. pq/r E. r(p + q)/pq Since q is a factor of r and r is a multiple of p: r/q = integer; r/p = integer. After scanning the choices, we see that we can simplify answer choice E, so let’s do that first: r(p + q)/pq = (rp + rq)/pq = rp/pq + rq/pq = r/q + r/p Since we’ve mentioned that r/q = integer and r/p = integer, r/q + r/p must equal an integer also. Thus, answer choice E is correct. Answer: E
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Re: If p, q, and r are positive integers such that q is a factor
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