Question

The greatest common factor of 65 and z, some unknown positive integer, is 13. there are two possible values for z between 30 and 60. what is the difference between these two values? (a) 11 (b) 12 (c) 13 (d) 14 (e) 15

Answer 1

Z is 52 and the difference between the values 65 and 52 is 13.

Given,

Two numbers : 65 and Z

Greatest common factor of the above numbers = 13

Z is a positive integer.

Possible values of Z is between 30 and 60.

Now,

13 x 5 = 65

So other number must be a multiple of 13 and a number below 5.

That is, 13 x 4 = 52 and 13 x 3 = 39. These are the two numbers between 30 and 60.

Now consider the difference.

65 – 52 = 13

65 – 39 = 26

In the given options we have 13 and 26 is not given in the option.

So the value of Z is 52 and the difference between 65 and 52 is 13.

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