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17 Oct 2022, 07:50
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A
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Difficulty:
95%
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Question Stats:
39% (01:29) correct
61%
(02:00)
wrong
based on 116
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How many positive integers less than 1000 have exactly 5 positive divisors?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
17 Oct 2022, 07:59
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( prime ) ^4 will have exactly 5 +ver divisors
prime ; 2,3,5
option A
prime ; 2,3,5
option A
BrentGMATPrepNow
How many positive integers less than 1000 have exactly 5 positive divisors?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
17 Oct 2022, 11:45
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Bookmarks
BrentGMATPrepNow
How many positive integers less than 1000 have exactly 5 positive divisors?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
For an integer n, the number of positive divisors ,d, is given by
\(n = p^x\)
d = x + 1
p is a prime number
Its given that d = 5, so x = 4
Hence we have to find the number of primes such that
0< \(p^4\) < 1000
p = 2 ; \(p^4 \)= 16
p = 3 ; \(p ^ 4\) = 81
p = 5 ; \(p^4\) = 625
Hence the number of integers = 3
IMO A
