asveaass wrote:
If r and s are positive integers, can the fraction r/s be expressed as a decimal with only a finite number of nonzero digits?
1) s is a factor of 100
2) r is a factor of 100
I don't understand the answer explanation in the OG, could someone please explain in detail?
THEORY:Reduced fraction
\frac{a}{b} (meaning that fraction is already reduced to its lowest term) can be expressed as terminating decimal
if and only b (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.)
Questions testing this concept:
does-the-decimal-equivalent-of-p-q-where-p-and-q-are-89566.htmlany-decimal-that-has-only-a-finite-number-of-nonzero-digits-101964.htmlif-a-b-c-d-and-e-are-integers-and-p-2-a3-b-and-q-2-c3-d5-e-is-p-q-a-terminating-decimal-125789.html700-question-94641.htmlis-r-s2-is-a-terminating-decimal-91360.htmlpl-explain-89566.htmlwhich-of-the-following-fractions-88937.htmlBACK TO THE ORIGINAL QUESTION:If r and s are positive integers, can the fraction r/s be expressed as a decimal with only a finite number of nonzero digits?(1) s is a factor of 100. Factors of 100 are: 1, 2, 4, 5, 10, 20, 25, 50 and 100. All these numbers are of the form
2^n5^m (for example 1=2^0*5^0, 2=2^1*5^0, ...), therefore no matter what is the value of r, r/s will always will be terminating decimal. Sufficient.
(2) r is a factor of 100. We need to know about the denominator. Not sufficient.
Answer: A.
Hope it's clear.
_________________
PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory
COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!!
DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
close
67% (01:36) correct
