What is the greatest possible length of
a positive integer less than 1,000?
(A) 10
(B) 9
(C) 8
(D) 7
(E) 6
OA IS B
a positive integer less than 1,000?
(A) 10
(B) 9
(C) 8
(D) 7
(E) 6
OA IS B
To maximize the length of an integer less then 1,000, we should minimize its prime bases.grandh01 wrote:What is the greatest possible length of
a positive integer less than 1,000?
(A) 10
(B) 9
(C) 8
(D) 7
(E) 6
OA IS B
Minimum prime base = 2
So, 2^x < 1,000
or x < 10
Maximum length = 9 for 2^9 = 512
Also, note that 2^9 is not the only integer whose length is 9, for example 2^8 * 3 = 768 < 100 also has the length of 8 + 1 = 9
The correct answer is B.
