If x^3 y^4= 5,000, is y = 5?
(1) y is a positive integer.
(2) x is an integer.
Inequalities
This topic has expert replies
- niketdoshi123
- Master | Next Rank: 500 Posts
- Posts: 210
- Joined: Thu Mar 08, 2012 11:24 pm
- Thanked: 62 times
- Followed by:3 members
Find the prime factors of 5000shivanigs 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 = 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
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
5000 = 5*5*5*5*2*2*2shivanigs wrote:If x^3 y^4= 5,000, is y = 5?
(1) y is a positive integer.
(2) x is an integer.
= (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
-
- Newbie | Next Rank: 10 Posts
- Posts: 3
- Joined: Thu Aug 16, 2012 2:14 am
-
- Legendary Member
- Posts: 512
- Joined: Mon Jun 18, 2012 11:31 pm
- Thanked: 42 times
- Followed by:20 members
how C is the right choice, what if y=3 and x=5?...
Work hard in Silence, Let Success make the noise.
If you found my Post really helpful, then don't forget to click the Thank/follow me button.
If you found my Post really helpful, then don't forget to click the Thank/follow me button.