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Intern  Joined: 29 Oct 2013
Posts: 18
If x, y, and z are integers greater than 1, and  [#permalink]

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(3^27)*(5^10)*(z)=(3^28)*(5^8)*(x^y)

z= (3/25)* (x^y)
So x^y should be a multiple of 25 since they're all integers

i. y is prime
This gives us no info about. It could be any integer greater than 1. Insufficient

ii. x is prime
5 is the only prime whose powers are multiples of 25. So the value of y is irrelevant since it is greater than 1. x=5. SUFFICIENT

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Re: If x, y, and z are integers greater than 1, and  [#permalink]

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Hi Bunuel,

I agree, over here I am deflecting out of the scope of GMAT.

In one of the similar questions on GMATClub, I found that you used the concept of log and marked answer as E.

"y" can be log something to base x. So equation is independent of x.

Can we see such ambiguity (unless I am wrong in above scenario) on real GMAT exam?
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Re: If x, y, and z are integers greater than 1, and  [#permalink]

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jeeteshsingh wrote:
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.

Rephrased question: 5^2z = 3x^y

Goal: The goal here is to find a unique value of X

Statement 1: Y is prime. We know that x has to be a power of 5 to balance out the 5^2 on the other equation, but we don't know if z has a 5 as a prime factor, making x potentially greater than 25 (=5^2). Since we don't know the size of x because we y is a prime, this info is insufficient.

Statement 2: X is prime. Now we know that x is prime, so it has to be 5. Any other power of 5 will not be prime. You can pick numbers to prove it to yourself. In this case, x =5 to balance out the 5 on the other side of the equation. Sufficient.
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If x, y, and z are integers greater than 1, and  [#permalink]

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I think there is a typo with the Stem 1. Per the MGMAT, the question is:

If x, y, and z are integers greater than 1, and (3^27)(35^10)(z) = (5^8)(7^10)(9^14)(x^y), then what is the value of x?

(1) z is prime

(2) x is prime

and the OA is D.

niks18 Pls check
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Re: If x, y, and z are integers greater than 1, and  [#permalink]

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jeeteshsingh wrote:
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.

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 3 variables ($$x$$, $$y$$ and $$z$$) and 1 equations, C is most likely to be the answer. So, we should consider 1) & 2) first.

Conditions 1) & 2)
$$3^{27}\cdot 5^{10}\cdot z= 5^8 \cdot 9^{14} \cdot x^y$$
$$⇔5^2\cdot z = 3\cdot x^y$$
$$⇔x=5,y=2,z=3$$ since both are prime number factorization.

Since this question is an integer question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.

Condition 1)
$$x=5,y=2,z=3$$
$$x=10,y=2,z=12$$
The condition 1) only is not sufficient.

Condition 2)
$$x = 5 y = 2, z = 3$$ since $$x$$ is a prime.
After canceling out all corresponding primes from the both sides, we have 5 from the left hand side and so $$x$$ must be 5.
The condition 2) only is sufficient.

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
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Re: If x, y, and z are integers greater than 1, and  [#permalink]

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_________________ Re: If x, y, and z are integers greater than 1, and   [#permalink] 16 Jan 2019, 21:03

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