QUESTION:
HCF of two numbers is 11 and their LCM is 385. If the numbers do not differ by more than 50, what is the sum of the two numbers?
A) 132
B) 135
C) 120
D) 364
Answer: A) 132
Explanation:
Product of numbers = LCM x HCF
= 11 x 385 = 4235
Let the numbers be of the form
11m and 11n, such that 'm' and 'n' are co-primes.
=> 11m x 11n = 4235
=> m x n = 35
=> (m,n) can be either of
(1, 35), (35, 1), (5, 7), (7, 5).
=> The numbers can be
(11, 385), (385, 11), (55, 77), (77, 55).
But it is given that the numbers cannot
differ by more than 50.
Hence, the numbers are 55 and 77.
Therefore,
Sum of the two numbers = 55 + 77 = 132
HCF of two numbers is 11 and their LCM is 385. If the numbers do not differ by more than 50, what is the sum of the two numbers?
A) 132
B) 135
C) 120
D) 364
Answer: A) 132
Explanation:
Product of numbers = LCM x HCF
= 11 x 385 = 4235
Let the numbers be of the form
11m and 11n, such that 'm' and 'n' are co-primes.
=> 11m x 11n = 4235
=> m x n = 35
=> (m,n) can be either of
(1, 35), (35, 1), (5, 7), (7, 5).
=> The numbers can be
(11, 385), (385, 11), (55, 77), (77, 55).
But it is given that the numbers cannot
differ by more than 50.
Hence, the numbers are 55 and 77.
Therefore,
Sum of the two numbers = 55 + 77 = 132
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