Thread: Prop of Num

hi hesh,

is it a^4 and b^3 ... because otherwise question doesnt make sense. Please qualify

You are correct. I wrote the question wrong

A

1 states n=a^4 b^3
You can tell a, a^2, a^3,a^4 , b, b^2, b^3 , ab, ab^2, ab^3 ...etc are factors of n. You can find out the number but i dont think we need to find it here, as long as we know we can get find all the options,

So 1 holds.

for 2. if you take 70 which has 2 prime factors of 5 and 7, it has other fators such 2, 10, ...which we dont know of....so that wont give us on top of that 2 doesn't tell us n=a^4 b^3
How many different factors does the integer n have?

Hey,

This problem is interesting.

First of all, i agree that A gives us 20 different factors of n so A is sufficient.

Now, B is not sufficient because both 35 and 35*35 have 5,7 as only prime factors but 35 has 4 factors whereas 35*35 has 9 factors.

Though, we should not consider 70 as counterexample since it has also 2 as prime factor which is against the hypothesis of the problem that the only prime factors of n are 5,7.

Answer is A