For how many different pairs of positive integers (a, b) can the fraction 2/15 be written as the sum 1/a + 1/b ? Pick one:
A) 4
B) 5
C) 8
D) 9
E) 10
(1/a)+(1/b)=215   I. 1/a+1/b=1/15+1/15(a,b)=(15,15)   II. 1/a+1/b=2∗2/15∗2=1/30+3/30(a,b)=10,30)and(30,10)   III.1/a+1/b=2∗3/15∗3=1/45+5/45(a,b)=(45,9)and(9,45)   IV.1/a+1/b=2∗4/15∗4=3/60+5/60(a,b)=(20,12)and(12,20)   Now, we know that the no of different pairs can only be of the form 2k+1. We already have 7 such combinations. Thus, the only value which will satisfy from the given options is 9.   Answer : 9
<result>D</result>
For how many different pairs of positive integers (a, b) can the fraction 2/15 be written as the sum 1/a + 1/b ?