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10 Feb 2023, 14:55
Kudos
Bookmarks
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
72% (02:07) correct
28%
(02:30)
wrong
based on 486
sessions
History
Date
Time
Result
Not Attempted Yet
If a and b are integers and \(5^a - 5^{a-2} = 75*2^b\), what is the value of a + b ?
A. 3
B. 4
C. 5
D. 6
E. 7
A. 3
B. 4
C. 5
D. 6
E. 7
11 Feb 2023, 23:22
Kudos
Bookmarks
Bunuel
\(5^{a-2} (5^2 - 1) = 75*2^b\)
\(5^{a-2} (24) = 5^2 * 3^1 *2^b\)
\(5^{a-2} (8 * 3) = 5^2 * 3^1 *2^b\)
\(5^{a-2}*2^3 = 5^2 *2^b\)
\(2^b = 2^3 \)
\(b = 3\)
\(5^{a-2} = 5^{2}\)
\(a - 2 = 2\)
\(a = 4\)
\(a + b = 3 + 4 = 7\)
Option E
General Discussion
