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C
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Difficulty:
65%
(hard)
Question Stats:
62% (02:11) correct
38%
(01:54)
wrong
based on 195
sessions
History
Date
Time
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Not Attempted Yet
Any decimal that has only a finite number of nonzero digits is a terminating decimal. If a and b are positive integers and z= \(\frac{b}{2^a×5^{2a+1} }\) is expressed as a terminating decimal, how many zeros will z have between the decimal point and the first nonzero digit to the right of the decimal point?
(1) a = 3
(2) 11 < b < 31
(1) a = 3
(2) 11 < b < 31
26 Feb 2020, 08:08
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rheam25
\(\frac{z=b}{2^a×5^{2a+1} }\) = \(\frac{z=b}{10^a×5^{a+1} }\)
To answer the number of zeros between the decimal and first non0zero digit, we need to know a and b both
Statement 1: a = 3
No information about b hence
NOT SUFFICIENT
Statement 2: 11 < b < 31
No information about a hence
NOT SUFFICIENT
Combining the two statements
Minimum \(\frac{z=12}{10^3×5^{3+1} }\)
Maximum \(\frac{z=30}{10^3×5^{3+1} }\)
But both give us the result of 4 zeros between decimal and first non zero digit after decimal hence
SUFFICIENT
Answer: Option C
16 Oct 2024, 08:58
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