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Difficulty:
95%
(hard)
Question Stats:
29% (02:12) correct
71%
(02:10)
wrong
based on 49
sessions
History
Date
Time
Result
Not Attempted Yet
What is the largest integer k such that
\(8.1 ×10^{k}\) is less than 0.29% of 0.0031% of 9,000,000,000,000?
A) 2
B) 3
C) 4
D) 5
E) 6
\(8.1 ×10^{k}\) is less than 0.29% of 0.0031% of 9,000,000,000,000?
A) 2
B) 3
C) 4
D) 5
E) 6
24 Mar 2026, 00:57
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kevincan
0.29% of 0.0031% of 9,000,000,000,000.
0.29% can be converted into 29% by multiplying by 100.
0.0031% can be converted into 31% by multiplying by 10000.
From 9,000,000,000,000, we have removed 10^6 to convert the decimal to integers.
So the value becomes 9*10^6.
29*10^-2 * 31 * 10^-2 * 9 * 10^6
= 29 * 31 * 9 * 10^2
= 29*31* 900
approximating we get 30*30*900 = 900*900 = 81* 10^4
The left hand side value is 8.1 * 10^K
converting LHS to resemble the right hand side value. We multiply and divide by 10.
81*10^4 * (10/10) = 8.1 * 10^5
If both LHS = RHS
8.1 * 10^k = 8.1 * 10^5
k = 5.
But the question is LHS less than RHS.
k should be less than 5.
k =4
Option C
25 Mar 2026, 05:27
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Hi, shouldn't it be k = 2? The question asks us for the smallest integer value of k satisfying the equation. k can take any value lesser than 5. Of the given options, 2 is the lowest. However, if the question intended to ask for the LARGEST integer k, then 4 would be the largest possible integer satisfying the equation.
Dereno
