The HCF of two numbers is 12 and their difference is 12. Which of the following can be the numbers?
options:
A] 84,96
B] 66,78
C] 70,82
D] 62,78
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The HCF of two numbers is 12 and their difference is 12. Which of the following can be the numbers?
options:
A] 84,96
B] 66,78
C] 70,82
D] 62,78
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Answer:
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 ⇒ a−b=1
⇒ 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)