SaquibHGREWhiz wrote:
A and B are two positive integers such that their product is 384 and their greatest common divisor is 4. Which of the following is(are) possible value(s) of ‘A + B’?
A. 32
B. 44
C. 60
D. 72
E. 84
F. 100
G. 128
Solution: - We are given positive integers A and B such that \(A\times B=384\)
- GCD of A and B is 4 which means we can assume \(A=4k_1\) and \(B=4k_2\) such that \(k_1\) and \(k_2\) are co-prime i.e., do not have any factor in common apart from 1
- We have \(A\times B=384\)
\(⇒4k_1 \times 4k_2=384\)
\(⇒k_1 \times k_2=\frac{384}{16}\)
\(⇒k_1\times k_2=24\) - Possible values are \(1\times 24=24\) and \(3\times 8=24 \)
- Thus, the value of \(A+B=4k_1+4k_2=4(k_1+k_2)\)
\(=4\times (1+24)\) or \(4\times (3+8)\)
\(= 100\) or \(44\)
Hence the right answers are
Options B and F