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

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29,145

13,145

14,145

15,145

answer is A.

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Detailed Solution

If 29 is the HCF the two numbers, then the two numbers will be 29x and 29y.

According to the given condition:

29x + 29y = 174

29(x + y) = 174

x + y = 174/29

= 6

All the possible combinations for x and y can be (1,5), (2,4), (3,3).

Since x and y are co-primes, therefore the only combinations which matches is (1,5)

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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