jainrahul1985 wrote:If a, b, c, d and e are 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
OA B
Dividing by a power of 2 results in a terminating decimal:
1/2 = .5
1/2² = .25
1/2³ = .125
etc.
Dividing by a power of 5 results in a terminating decimal:
1/5 = .2
1/5² = .04
1/5³ = .008
etc.
Dividing by a power of 3 results in a non-terminating decimal:
1/3 = .33333...
1/3² = .11111...
1/3³ = .037037037...
Thus, we need to know whether (2^a * 3^b) / (2^c * 3^d * 5^e) will require dividing by a power of 3.
If there are more 3's in the denominator than in the numerator, then (2^a * 3^b) / (2^c * 3^d * 5^e) will require dividing by a power of 3.
Since the number of 3's depends on the sizes of the exponents, the question can be rephrased:
Is b>d?
Statement 1: a>c.
No way to know whether b>d.
Insufficient.
Statement 2: b>d.
Sufficient.
The correct answer is
B.
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