If x, y, and z are integers greater than 1, and (3^27)(5^10)(z) = (5^8)(9^14)(x^y), then what is the value of x?
(1) y is prime
(2) x is prime
Please let me know the method to approach this question.
I'll post the OA after some discussion!
MGmat number properties
This topic has expert replies
-
- Master | Next Rank: 500 Posts
- Posts: 113
- Joined: Thu Jul 16, 2009 11:23 am
- Thanked: 15 times
- GMAT Score:730
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??
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??
-
- Master | Next Rank: 500 Posts
- Posts: 128
- Joined: Thu Jul 30, 2009 1:46 pm
- Thanked: 1 times
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?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??
- PussInBoots
- Master | Next Rank: 500 Posts
- Posts: 157
- Joined: Tue Oct 07, 2008 5:47 am
- Thanked: 3 times
(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
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
-
- Legendary Member
- Posts: 869
- Joined: Wed Aug 26, 2009 3:49 pm
- Location: California
- Thanked: 13 times
- Followed by:3 members
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
- tienvunguyen
- Junior | Next Rank: 30 Posts
- Posts: 20
- Joined: Thu Jul 30, 2009 6:58 am
- Location: Madison, WI
- Thanked: 1 times
- Followed by:2 members
- GMAT Score:750
I do not think y matters because the question only asks for x. So I think B is the correct answer.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
- viju9162
- Master | Next Rank: 500 Posts
- Posts: 434
- Joined: Mon Jun 11, 2007 9:48 pm
- Location: Bangalore
- Thanked: 6 times
- GMAT Score:600
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?
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?
"Native of" is used for a individual while "Native to" is used for a large group
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?
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?