Inequalities

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Inequalities

by shivanigs » Sat Aug 11, 2012 8:29 pm
If x^3 y^4= 5,000, is y = 5?


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

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by niketdoshi123 » Sat Aug 11, 2012 8:50 pm
shivanigs wrote: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

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by Brent@GMATPrepNow » Sun Aug 12, 2012 6:39 am
shivanigs wrote: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
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by shatyasree » Thu Aug 16, 2012 3:03 am
I agree with Brent

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by sana.noor » Wed May 08, 2013 9:59 pm
how C is the right choice, what if y=3 and x=5?...
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by Atekihcan » Thu May 09, 2013 2:06 am
sana.noor wrote: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.