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14 Jun 2021, 02:15
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
67% (02:04) correct
33%
(02:01)
wrong
based on 370
sessions
History
Date
Time
Result
Not Attempted Yet
If \(25^5*4^6 = 10^x + a\), and x is an integer, what could be the minimum positive value of a?
(A) 0
(B) 30,000
(C) 30,000,000
(D) 10,000,000,000
(E) 30,000,000,000
(A) 0
(B) 30,000
(C) 30,000,000
(D) 10,000,000,000
(E) 30,000,000,000
14 Jun 2021, 05:34
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25^5*4^5*4
= 100^5*4
= 10^10*(1+3)
= 10^10 + 3*10^10
So, a = 3*10^10.
This is E.
= 100^5*4
= 10^10*(1+3)
= 10^10 + 3*10^10
So, a = 3*10^10.
This is E.
General Discussion
14 Jun 2021, 02:41
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25^5* 4^6 = 10^x + a
(5^2)^5 * (2^2)^6 = 10^x + a
5^10 * 2^12 = 10^x + a
4 * 10^10 = 10^x + a
x = 10 then minimum positive value of 'a' can be 3*10^10 (E) IMO
(5^2)^5 * (2^2)^6 = 10^x + a
5^10 * 2^12 = 10^x + a
4 * 10^10 = 10^x + a
x = 10 then minimum positive value of 'a' can be 3*10^10 (E) IMO
