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The sum of two numbers is 216 and HCF is 27. How many numbers pairs of such numbers are there?
- a)1
- b)2
- c)3
- d)0
Correct answer is option 'B'. Can you explain this answer?
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The sum of two numbers is 216 and HCF is 27. How many numbers pairs of...
Given,
HCF of two numbers = 27
Let, two numbers be 27a and 27b
As, the sum of two numbers is 216
⇒ 27a + 27b = 216
⇒ 27(a + b) = 216
⇒ a + b = 8
So, possible values of (a, b) are (1, 7), (2, 6), (3, 5) and (4, 4)
But the numbers of the pairs (2, 6) and (4, 4) are not co- prime and they will change the HCF.
So, possible pairs are (1, 7) and (3, 5)
∴ Possible number of pairs = 2
HCF of two numbers = 27
Let, two numbers be 27a and 27b
As, the sum of two numbers is 216
⇒ 27a + 27b = 216
⇒ 27(a + b) = 216
⇒ a + b = 8
So, possible values of (a, b) are (1, 7), (2, 6), (3, 5) and (4, 4)
But the numbers of the pairs (2, 6) and (4, 4) are not co- prime and they will change the HCF.
So, possible pairs are (1, 7) and (3, 5)
∴ Possible number of pairs = 2
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The sum of two numbers is 216 and HCF is 27. How many numbers pairs of such numbers are there?a)1b)2c)3d)0Correct answer is option 'B'. Can you explain this answer?
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