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Difficulty:
65%
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Question Stats:
54% (01:30) correct
46%
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wrong
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Which of the following fractions will lead to a terminating decimal?
I. \(\frac{83}{80}\)
II. \(\frac{23}{120}\)
III. \(\frac{33}{480}\)
A. None
B. I only
C. I and II only
D. I and III only
E. I, II, and III
I. \(\frac{83}{80}\)
II. \(\frac{23}{120}\)
III. \(\frac{33}{480}\)
A. None
B. I only
C. I and II only
D. I and III only
E. I, II, and III
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firas92
Current Student
Joined: 16 Jan 2019
Last visit: 02 Dec 2024
Posts: 616
Given Kudos: 142
Location: India
Concentration: General Management
Schools: Tepper '23 (M$) Foster '23 (D)
GMAT 1: 740 Q50 V40
WE:Sales (Other)
Products:
A terminating decimal will have denominator in the 2^a*5^b
\(80 = 2^4*5^1\)
\(120 = 2^3*3^1*5^1\)
\(480 = 2^5*3^1*5^2\) but in this case the numerator is a multiple of 3 so the 3 cancels out and we are left \(2^5*5^2\) in the denominator so its a terminating decimal
I & III only
Answer is (D)
\(80 = 2^4*5^1\)
\(120 = 2^3*3^1*5^1\)
\(480 = 2^5*3^1*5^2\) but in this case the numerator is a multiple of 3 so the 3 cancels out and we are left \(2^5*5^2\) in the denominator so its a terminating decimal
I & III only
Answer is (D)
For a fraction to be terminating, the fraction in its lowest form should have a denominator that should have prime factors consisting of only 2 OR only 5 OR a combination of 2 and 5.
I. \(\frac{83}{80}\)
There is no common factor in Numerator and denominator to reduce the fraction.
Denominator 80 = 2 * 2 * 2 * 2 * 5 -> Only Prime factors of 2 and 5.
Hence, it will lead to a terminating decimal.
II. \(\frac{23}{120}\)
There is no common factor in Numerator and denominator to reduce the fraction.
Denominator 120 = 2 * 2 * 3 * 5 -> There are other factor besides 2 and 5.
Hence, it will NOT lead to a terminating decimal.
III. \(\frac{33}{480}\)
The fraction can be reduced to \(\frac{11}{160}\)
Denominator 160 = 2 * 2 * 2 * 2 * 2 * 5 -> Only Prime factors of 2 and 5.
Hence, it will lead to a terminating decimal.
Answer D
I. \(\frac{83}{80}\)
There is no common factor in Numerator and denominator to reduce the fraction.
Denominator 80 = 2 * 2 * 2 * 2 * 5 -> Only Prime factors of 2 and 5.
Hence, it will lead to a terminating decimal.
II. \(\frac{23}{120}\)
There is no common factor in Numerator and denominator to reduce the fraction.
Denominator 120 = 2 * 2 * 3 * 5 -> There are other factor besides 2 and 5.
Hence, it will NOT lead to a terminating decimal.
III. \(\frac{33}{480}\)
The fraction can be reduced to \(\frac{11}{160}\)
Denominator 160 = 2 * 2 * 2 * 2 * 2 * 5 -> Only Prime factors of 2 and 5.
Hence, it will lead to a terminating decimal.
Answer D
