Question

Three numbers p, q, and, r are pairwise coprime. If the product of p and q is 629 and the product of q and r is 391 then find the sum of p, q, r.

• A. 147
• B. 77
• C. 67
• D. 123

Answer 1

The correct option is B 77

Given three numbers p, q, and, r are pairwise coprime.
So,
$HCF(p,q)=1HCF(q,r)=1HCF(p,r)=1$

If we have two coprime numbers a and b, then we know that,
$HCF(a,b)=1\Rightarrow HCF(ac,bc)=c$

So,
$HCF(pq,qr)=q$
$\text{Given}pq=629qr=391$

Now we need to find the HCF of 629 and 391.
Applying Euclid's division lemma to numbers 629 and 391,
$629=391\times 1+238391=238\times 1+153238=153\times 1+85153=85\times 1+6885=68\times 1+1768=17\times 4+0$

The remainder has become zero, so the $HCF(629,391)=17\therefore q=17p=\frac{629}{q}=\frac{629}{17}=37r=\frac{391}{q}=\frac{391}{17}=23$

Now, $p+q+r=37+17+23=77$