Question

The HCF of two numbers is 12 and their difference is 12. Which of the following can
be the numbers ?
(1) 84, 96
(2) 66, 78
(3) 70, 82
(4) 62,78​

Answer 1

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)

Step-by-step explanation:

therefore, 1) 84 & 96 is your correct answer

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Answer 2

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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)

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