
A recap on Terminating Decimals:
– To figure out whether the fraction is terminating, bring it down to its lowest form.
– Focus on the denominator – if it is of the form , the fraction is terminating, else it is not.
Keeping this in mind, let’s look at a couple of DS questions on terminating decimals.
Question 1: If ,
,
,
and
are integers and
and
, is
a terminating decimal?
Statement 1:
Statement 2:
Solution:
Given: ,
,
,
and
are integers
Question: Is a terminating decimal?
or is ?
We know that powers of 2 and 5 in the denominator are acceptable for the decimal to be terminating. If there is a power of 3 in the denominator after reducing the fraction, then the decimal in non- terminating. So our question is basically whether the power of 3 in the denominator gets cancelled by the power of 3 in the numerator. If is greater than (or equal to)
, after reducing the fraction to lowest terms, it will have no 3 in the denominator which will make it a terminating decimal. If
is less than
, even after reducing the fraction to its lowest terms, it will have some powers of 3 in the dominator which will make it a non-terminating decimal.
Question: Is ?
Statement 1:
This statement doesn’t tell us anything about the relation between and
. Hence this statement alone is not sufficient.
Statement 2:
This statement tells us that is greater than
. This means that after we reduce the fraction to its lowest form, there will be no 3 in the denominator and it will be of the form
only. Hence it will be a terminating decimal. This statement alone is sufficient.
Answer (B).
Now onto another DS question.
Question 2: If , is it possible to write
as a terminating decimal?
Statement 1: is an integer.
Statement 2: is an integer.
Solution:
Given:
Question: Is a terminating decimal?
Again, will be a terminating decimal if it is of the form
Statement 1: is an integer.
(an integer)
Is a terminating decimal? We don’t know. If
has 3 as a factor,
will be a terminating decimal. Else it will not be. This statement alone is not sufficient.
Statement 2: is an integer.
(an integer)
Is a terminating decimal? We don’t know. If
has 7 as a factor,
will be a terminating decimal. Else it will not be. This statement alone is not sufficient.
Taking both together,
Since and
are integers,
will be a multiple of 6 (and thereby of 3 too) and
will be a multiple of 7. So
will be a terminating decimal.
Answer (C).
Founder, sole curriculum creator and webinar instructor for ANA PREP, Karishma has been working in the test prep industry for almost 20 years now, of which 15+ are in GMAT exam preparation. She is an expert of Quant, Verbal and Data Insights and is known for her simple and elegant solutions. Her venture, ANA PREP, is one of the best GMAT online coaching platforms. Contact her at karishma@anaprep.com