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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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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Thankyou Bunuel !!I think I need good sleep
Please tell substituting a value is good (less time consuming & accurate ) approach or assuming variables

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Merging topics. Please refer to the discussion above.
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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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