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For any three-digit number, abc
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25 Apr 2021, 11:47
25 Apr 2021, 11:47
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For any three-digit number, \(abc\), \(*abc*=(3^a)(5^b)(7^c)\). What is the value of \((g-f)\) if \(f\) and \(g\) are three-digit numbers for which \(*f*=(3^r)(5^s)(7^t)\) and \(*g*=(25)(*f*)\)?
A. 250
B. 220
C. 200
D. 20
E. 2
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. 250
B. 220
C. 200
D. 20
E. 2
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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For any three-digit number, abc
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26 Apr 2021, 05:56
26 Apr 2021, 05:56
1
Carcass wrote:
For any three-digit number, \(abc\), \(*abc*=(3^a)(5^b)(7^c)\). What is the value of \((g-f)\) if \(f\) and \(g\) are three-digit numbers for which \(*f*=(3^r)(5^s)(7^t)\) and \(*g*=(25)(*f*)\)?
A. 250
B. 220
C. 200
D. 20
E. 2
A. 250
B. 220
C. 200
D. 20
E. 2
In \(*f*=(3^r)(5^s)(7^t)\), Let \(r = 1\), \(s = 1\), \(t = 1\)
\(a = 1\), \(b = 1\), \(c = 1\)
i.e. \(f = 111\)
Now, \(*g*=(25)(*f*) = 5^2(3^r)(5^s)(7^t) = (3^r)(5^{s+2})(7^t)\)
Plug \(r = 1\), \(s = 1\), \(t = 1\)
\(a = 1\), \(b = 1 + 2 = 3\), \(c = 1\)
Therefore, \(g = 131\)
\(g - f = 131 - 111 = 20\)
Hence, option D
gmatclubot
For any three-digit number, abc [#permalink]
26 Apr 2021, 05:56
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