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If n is an integer, then n is divisible by how many positive [#permalink]
 23 Apr 2003, 17:50
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If n is an integer, then n is divisible by how many positive integers ?
1) n is the product of two different prime numbers
2) n and 2^3 are divisible by the same number of positive integers
Last edited by tzolkin on 24 Apr 2003, 14:27, edited 1 time in total.
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D
Statement one tells that n is divisible by 4 positive integers.
Statement two - 2^3 is divisible by 4 positive integers. 1, 2, 4 and 8
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Is the answer not B?
Because from (1) we could have 1*2 =2 or 2*3 =6.
So there is not consistent answer from (1)
only choice (2) will give answer 4.
Is my explanation not correct?
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sarathk wrote: Is the answer not B?
Because from (1) we could have 1*2 =2 or 2*3 =6.
So there is not consistent answer from (1)
only choice (2) will give answer 4.
Is my explanation not correct?
1 is NOT a prime number. The least prime is 2. Remeber that.
(1) the product of two different primes has 4 distinct positive divisors. OK.
(2) 2^3 has 4 positive divisors, as does n. OK.
Thus, it is D.
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can someone clarify my doubt
n is an integer(given) but its not mentioned if its a positive or a negative integer.
if n is taken as positive u get 4 positive divisors.
but if n is taken as a negative integer then u dont know exactly the positive divisors. if this is true (1) cant answer the problem given.
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Think of this as :
1) if n is the product of 2 prime numbers : eg 2*3=5 or 3*5=15
The product is +ve
2) n and 2^3 are divisible by the same number of positive integers
2^3 = 8, thus divisible by 1, 2, 4, 8 (4 +ve integers)
=> n is divisible by 4 positive integers
say n=6 : 1, 2, 3, 6
or n=-6 : 1, 2, 3, 6 (note - still divisible by positive integers)
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arun wrote: can someone clarify my doubt
n is an integer(given) but its not mentioned if its a positive or a negative integer.
if n is taken as positive u get 4 positive divisors.
but if n is taken as a negative integer then u dont know exactly the positive divisors. if this is true (1) cant answer the problem given.
The product of two primes CANNOT be negative, since the least prime is 2. There are no negative primes. In this connection, n HAS to be positive.
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