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23 Dec 2013, 07:37
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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:
5%
(low)
Question Stats:
90% (00:53) correct
10%
(01:06)
wrong
based on 1775
sessions
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If k is an integer and 0.0010101*10^k is greater than 1,000, what is the least possible value of k ?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
24 Dec 2013, 03:30
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SOLUTION
If k is an integer and 0.0010101*10^k is greater than 1,000, what is the least possible value of k ?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
No algebraic manipulation is needed for this one. Consider this: when we multiply 0.0010101 by 10^k (where k is a positive integer), decimal point in 0.0010101 moves k decimal places to the right. The product to be more than 1000 we should move decimal point 6 places to the right to get 1010>1000, thus the least value of k is 6.
Answer: E.
If k is an integer and 0.0010101*10^k is greater than 1,000, what is the least possible value of k ?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
No algebraic manipulation is needed for this one. Consider this: when we multiply 0.0010101 by 10^k (where k is a positive integer), decimal point in 0.0010101 moves k decimal places to the right. The product to be more than 1000 we should move decimal point 6 places to the right to get 1010>1000, thus the least value of k is 6.
Answer: E.
General Discussion
25 Dec 2013, 03:34
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My explanation (It's basically the same as Bunuel's)
0.0010101*10^k > 1000
--> (1010.1)*10^-6*10^k >1000*10^0
--> (1010.1)*10^(k-6) >1000*10^0
--> because 1010.1 > 1000, we just need 10^(k-6) >= 10^0 --> k-6 >= 0 --> k >= 6
--> min K = 6.
E is the answer.
Cheer!
0.0010101*10^k > 1000
--> (1010.1)*10^-6*10^k >1000*10^0
--> (1010.1)*10^(k-6) >1000*10^0
--> because 1010.1 > 1000, we just need 10^(k-6) >= 10^0 --> k-6 >= 0 --> k >= 6
--> min K = 6.
E is the answer.
Cheer!
