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# The positive integer x has how many different positive

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Director
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The positive integer x has how many different positive [#permalink]  21 Jan 2006, 13:32
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The positive integer x has how many different positive factors?

1. x is a multiple of the same number of positive integers that 7^5 is

2. x = a^2*b where a and b are different prime numbers.
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This is a tough one. I think D.

From 1) X has the same number of factors as 7^5 has. We can determine the number of factors of 7^5. Hence SUFFICIENT.
From 2) X = a^2*b SUFFICIENT. because factors of x = a, a^2, b, a*b & (X and 1 too!) (sinace a &b are primes)

For eg 12 = 2^2*3 => Facrots = 2, 4, 3, 6, also 12 & 1.

Hence D.
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giddi77 wrote:
This is a tough one. I think D.

From 1) X has the same number of factors as 7^5 has. We can determine the number of factors of 7^5. Hence SUFFICIENT.
From 2) X = a^2*b SUFFICIENT. because factors of x = a, a^2, b, a*b & (X and 1 too!) (sinace a &b are primes)

For eg 12 = 2^2*3 => Facrots = 2, 4, 3, 6, also 12 & 1.

Hence D.

I think the statement (1) is not sufficient because it just provides information about number of factors, but doesn't mention that they are PRIME factors! Hence statement is INSUFFICIENT.

So the answer I think is B!
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I think D is sufficient.

From one we know that 7^5 is the multiple of 1, 7, ......7^5 ie 6. That is all we need. Am I wrong?

From two we know that the factors are 1, a, b, ab, a^2, a^2b. 6.

Just to validate we are getting 6 from both statements. What is wrong here?
Director
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I think its D

a) same no oif multiples as 7^5 means (5+1) factors
b) x=a^2*b means (2+1)*(1+1) factods
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D

St1: there are 6 factors of 7^5. SUFF

St2: Total factors of a^2 *b = (2+1) *(1+1) = 6. SUFF
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Re: DS + wordy [#permalink]  22 Jan 2006, 05:27
bewakoof wrote:
The positive integer x has how many different positive factors?

1. x is a multiple of the same number of positive integers that 7^5 is

2. x = a^2*b where a and b are different prime numbers.

7^5 is a multiple of 1 and 7

What is 1. paraphrased?

I think:

x= b*1*7

b can therefore be 7 or 7^2 etc.

I go for B
Re: DS + wordy   [#permalink] 22 Jan 2006, 05:27
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