The positive integer x has how many different positive

Question

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.

giddi77 · Answer

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.

giddi77 · Answer

My bad

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!

Bhai · Answer

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? :?:

andy_gr8 · Answer

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

ps_dahiya · Answer

D

St1: there are 6 factors of 7^5. SUFF

St2: Total factors of a^2 *b = (2+1) *(1+1) = 6. SUFF

allabout · Answer

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

The positive integer x has how many different positive

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