Numbers

[shankar.ashwin]

If 'a' and 'b' are positive integers, is (a/b) a terminating decimal?

(1) (b/a) is a terminating decimal
(2) b is not a factor of a

[cans]

A) b=3,a=10. a/b = 10/3 = 3.3333333333 insufficient
(3,3) will be terminating

B) 25/4: 6.25 terminating
10/3. non terminating
Insufficient

A&B) 10/3 will still stand
IMO E

[knight247]

An important thing to remember before getting into the problem is that a Fraction will terminate if and only if the denominator contains either 2 or 5 in some power or both.

(1)b/a is a terminating decimal. This will only happen if the denominator i.e a meets the above mentioned requirement. Try 15/6=5/2 which will terminate and now try 2/5 which will also terminate. But the same thing won't work in case of 17/2 or 17/5 which will terminate but their reciprocals won't. INSUFFICIENT.

(2)b not being a factor of a doesn't give a straight answer. 17/2 where 2 is not a factor or 17 yet the fraction terminates. Can't say the same about 17/3.

Combining both let b=5 and a=2 so it meets both requirements of b/a being a terminating decimal and b not being a factor of a. Yet a/b terminates. Consider b=17 a=2 so b/a is terminating and 2 is not a factor of 17 but 2/17 does not terminate. Hence E