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19 May 2022, 08:30
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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:
45%
(medium)
Question Stats:
63% (01:22) correct
37%
(01:42)
wrong
based on 254
sessions
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If n and p are different positive prime numbers, which of the integers n^4, p^3, and np has (have) exactly 4 positive divisors?
(A) n^4 only
(B) p^3 only
(C) np only
(D) n^4 and np
(E) p^3 and np
(A) n^4 only
(B) p^3 only
(C) np only
(D) n^4 and np
(E) p^3 and np
19 May 2022, 08:44
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IMO E
Lets assume n is 2 and p is 3
now 2^4= 2*2*2*2*1
List of divisors = 1,2,4,8 and 16
Count = 5
p^3 = 3^3 = 3*3*3 =
List of divisors = 1,3,9, and 27
Count = 4
np = 2*3 =6
List of divisors= 1,2,3, and 6
Count=4
Lets assume n is 2 and p is 3
now 2^4= 2*2*2*2*1
List of divisors = 1,2,4,8 and 16
Count = 5
p^3 = 3^3 = 3*3*3 =
List of divisors = 1,3,9, and 27
Count = 4
np = 2*3 =6
List of divisors= 1,2,3, and 6
Count=4
23 Aug 2023, 21:23
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If n and p are different positive prime numbers, which of the integers n^4, p^3, and np has (have) exactly 4 positive divisors?
No. of factors of n^4 = (4+1)=5
No. of factors of p^3 = (3+1)=4
No. of factors of np = (1+1)(1+1)=4
Hence E
No. of factors of n^4 = (4+1)=5
No. of factors of p^3 = (3+1)=4
No. of factors of np = (1+1)(1+1)=4
Hence E
