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Q.

The HCF of the two numbers is 29 & their sum is 174. The numbers are _________

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a

29,145

b

13,145

c

14,145

d

15,145

answer is A.

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Detailed Solution

Let the two numbers be 29x and 29y. 

Given, 29x + 29y = 174 

29(x + y) = 174 

x + y = 174/29 = 6

Since x and y are co-primes, therefore, possible combinations would be (1,5), (2,4), (3,3)

For (1,5): 29 x = 29 x 1 and 29 y = 29 (5) = 145

Therefore, the required numbers are 29 and 145.

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