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08 Oct 2020, 08:15
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
66% (01:22) correct
34%
(01:43)
wrong
based on 146
sessions
History
Date
Time
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Not Attempted Yet
Which of the following fractions has a decimal equivalent that is a terminating decimal?
(A) \(\frac{71}{152}\)
(B) \(\frac{17}{81}\)
(C) \(\frac{117}{152}\)
(D) \(\frac{71}{512}\)
(E) \(\frac{17}{215}\)
(A) \(\frac{71}{152}\)
(B) \(\frac{17}{81}\)
(C) \(\frac{117}{152}\)
(D) \(\frac{71}{512}\)
(E) \(\frac{17}{215}\)
08 Oct 2020, 09:20
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sjuniv32
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 \(2*5^2\). 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 the 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.
BACK TO THE QUESTION:
Only option D (when reduced to its lowest form) has the denominator of the form \(2^n5^m\): \(\frac{71}{512}=\frac{71}{2^9}\).
Answer: D.
Questions testing this concept:
https://gmatclub.com/forum/which-of-the ... 88937.html
https://gmatclub.com/forum/does-the-deci ... 89566.html
https://gmatclub.com/forum/any-decimal-t ... 01964.html
https://gmatclub.com/forum/if-a-b-c-d-an ... 25789.html
https://gmatclub.com/forum/700-question-94641.html
https://gmatclub.com/forum/is-r-s2-is-a- ... 91360.html
https://gmatclub.com/forum/pl-explain-89566.html
https://gmatclub.com/forum/which-of-the- ... 88937.html
General Discussion
25 Oct 2024, 19:27
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