MGmat number properties

statement B alone is sufficient; IMO

we'll come to this;

5^2 * z = 3 * x^y,

so we get that x^y = 25, 50, 75 or all multiples of 25, knowing that x is prime will show us that 5 is the only possible number that can achieve this; 15, 10 are not prime and cannot do that. So statement B alone is sufficient. Is that the OA??

prindaroy wrote:statement B alone is sufficient; IMO

we'll come to this;

5^2 * z = 3 * x^y,

so we get that x^y = 25, 50, 75 or all multiples of 25, knowing that x is prime will show us that 5 is the only possible number that can achieve this; 15, 10 are not prime and cannot do that. So statement B alone is sufficient. Is that the OA??

Yes the OA is B.. however,what i don't understand is what does x is prime get us? I understand z has to be some multiple of 3. x^y similarly has to be some multiple of 5. but don't we already have the question stem that gives us that.. why do we need statement b?

(3^27)(5^10)(z) = (5^8)(9^14)(x^y)
25z = 3 x^y
z = 3 * x^y / 25 -> x is multiple of 5
(2) alone says that x = 5, hence z = 3 * 5^y / 25, still not enough info cuz y = 2 and y = 4 work too. (1) narrows our choices to y = 2.

Answer is C

PussInBoots wrote:(3^27)(5^10)(z) = (5^8)(9^14)(x^y)
25z = 3 x^y
z = 3 * x^y / 25 -> x is multiple of 5
(2) alone says that x = 5, hence z = 3 * 5^y / 25, still not enough info cuz y = 2 and y = 4 work too. (1) narrows our choices to y = 2.

Answer is C

How did you arrive to this 25z = 3 x^y . Thanks.

PussInBoots wrote:(3^27)(5^10)(z) = (5^8)(9^14)(x^y)
25z = 3 x^y
z = 3 * x^y / 25 -> x is multiple of 5
(2) alone says that x = 5, hence z = 3 * 5^y / 25, still not enough info cuz y = 2 and y = 4 work too. (1) narrows our choices to y = 2.

Answer is C

I do not think y matters because the question only asks for x. So I think B is the correct answer.

Hi Prindaroy,

5^2 * z = 3 * x^y,

so we get that x^y = 25, 50, 75 or all multiples of 25, knowing that x is prime will show us that 5 is the only possible number that can achieve this; 15, 10 are not prime and cannot do that. So statement B alone is sufficient.

You are not considering "3" here?

It seems we all agree that modifying the question
gets us x^y=(5^2)(1/3)z

Condition 1 says y is a prime.
x must be an integer according to the question
thus, z has to be multiple of 3.
z can be 3, 6, 9, 12 and so on
If you plug in 3 in z you get x^y=(5^2). Here x=5
However, if you plug in 12 you get x^y=(5^2)(2^2)=(10^2)
Here x=10 therefore, insufficient.

Condition 2 says x is a prime.
It means that z has to eliminate either 5^2 or 1/3.
We know that z is an integer thus, z cannot
eliminate 5^2. Therefore z has to be 3.
In this case x=5. Hence sufficient.

How does it sound?