Question

The HCF of two numbers is 12 and their difference is also 12. The numbers are

• A. 12, 84
• B. 84, 96
• C. 64, 76
• D. 100, 112

Answer 1

Answer: (B)

84, 96

Since the HCF of the two numbers is 12 the
numbers are 12a and 12b where a and b are
prime to each other
Given $12a-12b=12$ $\Rightarrow$ $a-b=1$
$\Rightarrow$ a and b are consecutive numbers that are prime
to each other. By inspection we can see that
84, 96 i.e. 12 x 7 and 12 x 8 are the two
numbers satisfying this condition $(8-7=1)$