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24 Dec 2021, 21:27
Kudos
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A
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Difficulty:
15%
(low)
Question Stats:
81% (01:21) correct
19%
(01:02)
wrong
based on 73
sessions
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If r is an integer, and \((1.25)(0.005)(0.00025)(10^r) \)is an integer, what is the least possible value of r?
A) 10
B) 5
C) 0
D) -5
E) -10
A) 10
B) 5
C) 0
D) -5
E) -10
24 Dec 2021, 21:56
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D33T
First, the prompt tells us that these decimals multiplied by some power of 10 are equal to an integer. This tells us that the product will not contain a decimal.
Moving forward, we can simplify these decimals by factoring out a power of 10 from all of them.
\(1.25 = 125 * 10^{-2}\)
\(.005 = 5 * 10^{-3}\)
\(.00025 = 25 * 10^{-5}\)
These powers of 10 exponents can be combined and equal -2 + -3 + -5 = -10.
The equation prompt \((1.25)(0.005)(0.00025)(10^r) \) can thus be simplified to \((125)(5)(25)(10^{-10})(10^r)\) and then further conceptualized as \((integer)(10^{-10})(10^r)\).
For this number to be an integer, the r in \(10^{r}\) must be greater than or equal to 10 so as to counteract the \(10^{-10}\) that was factored out of the decimals.
Answer:
04 Sep 2024, 16:43
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