Inequalities

[shivanigs]

If x^3 y^4= 5,000, is y = 5?


(1) y is a positive integer.
(2) x is an integer.

[niketdoshi123]

If x^3 y^4= 5,000, is y = 5?


(1) y is a positive integer.
(2) x is an integer.

Find the prime factors of 5000
5000 = 5*5*5*5*2*2*2 = 2^3 * 5^4 = x^3 y^4
=> y^4 = 5^4
=> y = ±5
So , if y is a positive integer then only it will be equal to 5.

statement 1:
y is a positive integer .
This statement is sufficient to answer the question.

Statement 2:
x is an integer.
Looking at this statement we should check whether x can be a non integer number.
As the factors are prime numbers and both the prime numbers have different powers. There is no other possibility, which satisfies the equation.

the correct answer is A

[Brent@GMATPrepNow]

If x^3 y^4= 5,000, is y = 5?

(1) y is a positive integer.
(2) x is an integer.

5000 = 5*5*5*5*2*2*2
= (2^3)(5^4)

Statement 1: y is a positive integer.
This one looks promising, but we aren't told whether or not x is an integer.
So, we have the possibility of contradictory cases.
case a: y=5 and x=3. In this case, y equals 5
case b: y=1 and x= the cube root of 5000. In this case, y does not equal 5.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT


Statement 2: x is an integer.
We have the possibility of contradictory cases.
case a: y=5 and x=3. In this case, y equals 5
case b: y=-5 and x=3. In this case, y does not equal 5.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2:
If x and y are both integers and y is a positive integer, it must be the case that x=3 and y=5
SUFFICIENT

Answer = C

Cheers,
Brent

[shatyasree]

I agree with Brent

[sana.noor]

how C is the right choice, what if y=3 and x=5?...

[Atekihcan]

how C is the right choice, what if y=3 and x=5?...

That's not possible as (x^3)*(y^4) = (5^3)*(3^4) = a multiple of 3 but 5000 is not a multiple of 3.