Arithmetic - OG 12

[anirudhbhalotia]

Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 24, 0.82 and 5.096 are three terminating decimals. If r and s are positive integers and the ratio r/s is expressed as a decimal, is r/s a terminating decimal ?

1. 90 < r < 100

2. s = 4


OA - B

[Rahul@gurome]

Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 24, 0.82 and 5.096 are three terminating decimals. If r and s are positive integers and the ratio r/s is expressed as a decimal, is r/s a terminating decimal ?

1. 90 < r < 100
2. s = 4

The trick to answer the question is a fact, which is: Any fraction in its reduced form with a denominator whose prime factors are only 2 and/or 5, is a terminating decimal and if any fraction in its reduced form has a denominator which contains any prime factor other than these two is a recurring decimal.

Thus, whether it is terminating or recurring depends upon the denominator.

Statement 1: 90 < r < 100
We don't know the denominator, s.

Not sufficient

Statement 2: s = 4
Only prime factor of s is 2.
Hence (r/s) is a terminating decimal whatever the value of r is.

Sufficient

The correct answer is B.

[anirudhbhalotia]

Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 24, 0.82 and 5.096 are three terminating decimals. If r and s are positive integers and the ratio r/s is expressed as a decimal, is r/s a terminating decimal ?

1. 90 < r < 100
2. s = 4

The trick to answer the question is a fact, which is: Any fraction in its reduced form with a denominator whose prime factors are only 2 and/or 5, is a terminating decimal and if any fraction in its reduced form has a denominator which contains any prime factor other than these two is a recurring decimal.

Thus, whether it is terminating or recurring depends upon the denominator.

Statement 1: 90 < r < 100
We don't know the denominator, s.

Not sufficient

Statement 2: s = 4
Only prime factor of s is 2.
Hence (r/s) is a terminating decimal whatever the value of r is.

Sufficient

The correct answer is B.

Thanks Rahul!

How do we possibly remember so many different "facts", recall and apply during GMAT!

Can we also say that any no. divided by 4 is a terminating decimal if its not entirely divisible?

[Rahul@gurome]

Can we also say that any no. divided by 4 is a terminating decimal if its not entirely divisible?

Yes, we can.