For how many integers pair (x,y) satisfies the result
(1/x)+((1/y)=1/12  Select the correct option:
A) 12 B) 6 C) 29 D) 16 E) 32
Now let’s look at this question from the perspective of number theory.   1/x + 1/y = 1/12   12x + 12y = xy   12x + 12y – xy =0   We need to factorize it and for that we subtract 144 from left and right parts.   12x – xy +12y – 144 = -144   (x-12)(12-y) = -144   (x-12)(y-12) = 144   Now we need to represent 144 as a product of 2 factors and find out our pairs of x and y.   (1*144) (2*72) (3*48) (4*36) (6*24) (8*18) (9*19) and 12*12.   All factor pairs (except 12*12) can be written in reverse order, so we have total 15 positive solutions.   Because we have product, x and y can also take negative values. Using same logic we got 15 negative solutions, but in this case we need to discard (-12)*(-12), because it will give us x=0, y=0. In this point the original equation is undetermined (we can’t divide by zero).   Hence we have total number of integer pairs   15 + 14= 
<gadget id="calculator">  15 + 14</gadget>
<output>29</output>
29   ANSWER:29
<result>C</result>
For how many integers pair (x,y) satisfies the result
(1/x)+((1/y)=1/12