Data Sufficiency

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Data Sufficiency

by RiyaR » Mon Sep 22, 2014 9:30 am
If x, y, and z are integers greater than 1, and (327)(3510)(z) = (58)(710)(914)(xy), then what is the value of x?

(1) z is prime

(2) x is prime

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by Matt@VeritasPrep » Mon Sep 22, 2014 9:45 am
RiyaR wrote:If x, y, and z are integers greater than 1, and (327)(3510)(z) = (58)(710)(914)(xy), then what is the value of x?

(1) z is prime

(2) x is prime
Are you sure you've entered this correctly? It doesn't appear to have a solution.

Let's start by simplifying the original equation:

327 * 3510 * z = 58 * 710 * 914 * xy

Now let's try to factor each number.

327 = 3 * 109
3510 = 10 * 351 = 2 * 5 * 3 * 117 = 2 * 5 * 3 * 3 * 39 = 2 * 5 * 3 * 3 * 3 * 13

So 327 * 3510 is really 2 * 3� * 5 * 13 * 109

58 = 2 * 29
710 = 71 * 2 * 5
914 = 2 * 457

So 58 * 710 * 914 is really 2³ * 5 * 29 * 71 * 457

Setting the two equations equal to each other, we have

2 * 3� * 5 * 13 * 109 * z = 2³ * 5 * 29 * 71 * 457 * xy

which reduces (barely) to

3� * 13 * 109 * z = 2² * 29 * 71 * 457 * xy

Unfortunately, S1 is impossible. If z is prime, the LHS and the RHS cannot be equal, since the LHS needs to have ALL of the prime factors on the RHS, so z must be a multiple of 4, 29, 71, AND 457. Since S1 cannot be evaluated, the question can't be answered.

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by Brent@GMATPrepNow » Mon Sep 22, 2014 9:50 am
RiyaR wrote:If x, y, and z are integers greater than 1, and (327)(3510)(z) = (58)(710)(914)(xy), then what is the value of x?

(1) z is prime

(2) x is prime
Are you sure those numbers are correct?
As Matt point out, the question can't be answered.
PLUS, this question requires us to recognize that 457 is prime. Determining whether or not 457 is prime is a painful (time-draining) activity that the GMAT would never have us do.

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by Matt@VeritasPrep » Mon Sep 22, 2014 9:51 am
Eureka!

You meant to type 3²� * 35¹� * z = 5� * 7¹� * 9¹� * xʸ. This is a SERIOUS violation of our policy on properly typing questions, but I'll answer it anyway. :D

3²� * 35¹� * z = 5� * 7¹� * 9¹� * xʸ

is really

3²� * (5*7)¹� * z = 5� * 7¹� * (3*3)¹� * xʸ

or

3²� * 5¹� * 7¹� * z = 5� * 7¹� * 3²� * xʸ

Dividing out common prime factors, we get

5² * z = 3 * xʸ

S1 is SUFFICIENT: since 25z = a multiple of 3, and z is prime, z MUST be 3.
S2 is SUFFICIENT: since 3 * xʸ = a multiple of 25, and x is prime, x MUST be 5.

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by Brent@GMATPrepNow » Mon Sep 22, 2014 9:54 am
Ahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh.

RiyaR, please check your questions once they're posted. I see that you have posted several ambiguous/confusing questions.

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by Brent@GMATPrepNow » Mon Sep 22, 2014 9:57 am
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by GMATGuruNY » Mon Sep 22, 2014 12:00 pm
The problem should read as follows:
If x, y, and z are integers greater than 1, and (3²�)(35¹�)(z) = (5�)(7¹�)(9¹�)(x^y), then what is the value of x?

(1) z is prime

(2) x is prime
(3²�)(35¹�)(z) = (5�)(7¹�)(9¹�)(x^y)

(3²�)(7¹�5¹�)(z) = (5�)(7¹�)(3²)¹�(x^y)

(3²�)(7¹�5¹�)(z) = (5�)(7¹�)(3²�)(x^y)

(5²)(z) = (3)(x^y)

z = (3) * (x^y)/5².
Since z is an INTEGER, the resulting equation implies that z is a multiple of 3 and that x^y is a multiple of 5².

Statement 1: z is prime
Since z is prime and a multiple of 3, z=3.
Thus, (x^y)/5² = 1, implying that x=5 and y=2.
SUFFICIENT.

Statement 2: x is prime
Since x^y is a multiple of 5² and x is prime, x=5 and y≥2.
SUFFICIENT.

The correct answer is D.
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