Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 36, 0.72, and 3.005 are terminating decimals.
If a, b, c, d and e are non-negative integers and p = (2^a) (3^b) and q = (2^c) (3^d) (5^e), is
p/q a terminating decimal?
(1) a > c
(2) b > d
Source: MGMAT
OA: B
Can someone explain this?
Terminating decimals
This topic has expert replies
1/3 is non terminating.
1/2 and 1/5 are terminating fraction,
so, b and d will decides terminating of p/q
if b > d then p/q will be terminating decimal.
if b < d then p/q will be non terminating decimal.
Hence, st 1 is not sufficient as discussed above.
st2 is sufficient
Hence B
1/2 and 1/5 are terminating fraction,
so, b and d will decides terminating of p/q
if b > d then p/q will be terminating decimal.
if b < d then p/q will be non terminating decimal.
Hence, st 1 is not sufficient as discussed above.
st2 is sufficient
Hence B
Solution....
P/Q = 2^(a-c) * 3 ^(b-d) * 5^e
and a/b/c/d/e are non-negative integers....
Hence 5^e will always be an integer...i.e. terminating decimal
2^(+- integer ) is always an integer so we dont need information about whether (a-c) > = or < 0
but 3 ^ ( -ve integer ) e.g. 1/3 =0.33333 is not a terminating decimal whereas 3 ^ ( +ve integer ) e.g. 3^2=9 is.
so we need to know something about (b-d)...Hence (B)
P/Q = 2^(a-c) * 3 ^(b-d) * 5^e
and a/b/c/d/e are non-negative integers....
Hence 5^e will always be an integer...i.e. terminating decimal
2^(+- integer ) is always an integer so we dont need information about whether (a-c) > = or < 0
but 3 ^ ( -ve integer ) e.g. 1/3 =0.33333 is not a terminating decimal whereas 3 ^ ( +ve integer ) e.g. 3^2=9 is.
so we need to know something about (b-d)...Hence (B)