Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: PS: Number property [#permalink]
23 Aug 2009, 07:27

1

This post received KUDOS

I do not think you have to calculate a lot here. The rule is that the fraction terminates if the denominator has ONLY 2 or/and 5 in its prime factorization.

A 10/189...no common factors can be canceled out, and 189 is divisible by 3. The denominator does not have ONLY 2's and 5's since it has 3 in it as well. You can stop here, concluding the fraction does not terminate... B 15/196 - no common factors can be canceled out. 196=2*2*7*7...there is a prime number 7...so the fraction does not terminate.. C 16/225...no common factors can be caceled out. decomposing the denominator 225=25*9=5^2*3^2. Does not terminate since it has 3 in its denominator D 25/144 no common factors can be canceled out. 144= 2*72, and 72 is divisible by 3...so the fraction has 3 in its denominator...does not terminate. E you do not have to check. you know it should be E since it is your last option. But if you want to be sure decompose the denominator and you will get only 2's in it

Re: PS: Number property [#permalink]
07 Sep 2010, 01:37

E. Great question. Be suspicious about 3,7 (more suspicious if the numerator has a factor of 3 or 7). Do not blindly select the answer if the denominator alone has a 3 or 7. If it is 8,4,2,6 then they are usually terminating.

Re: PS: Number property [#permalink]
07 Sep 2010, 04:30

2

This post received KUDOS

Expert's post

TriColor wrote:

Please, explain your answer. Thank you, -----------------------------------------

Q15: Which of the following fractions has a decimal equivalent that is a terminating decimal?

A. 10/189 B. 15/196 C. 16/225 D. 25/144 E. 39/128

THEORY:

Reduced fraction \frac{a}{b} (meaning that fraction is already reduced to its lowest term) can be expressed as terminating decimal if and onlyb (denominator) is of the form 2^n5^m, where m and n are non-negative integers. For example: \frac{7}{250} is a terminating decimal 0.028, as 250 (denominator) equals to 2*5^3. Fraction \frac{3}{30} is also a terminating decimal, as \frac{3}{30}=\frac{1}{10} and denominator 10=2*5.

Note that if denominator already has only 2-s and/or 5-s then it doesn't matter whether the fraction is reduced or not.

For example \frac{x}{2^n5^m}, (where x, n and m are integers) will always be terminating decimal.

(We need reducing in case when we have the prime in denominator other then 2 or 5 to see whether it could be reduced. For example fraction \frac{6}{15} has 3 as prime in denominator and we need to know if it can be reduced.)

the necessary and sufficient condition of terminating decimals is that the denominator's prime factors should only be 2 or 5 or both (form 2^x * 5^y) _________________