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by vinay1983 » Sun Oct 06, 2013 8:27 am
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) y is prime

(2) x is prime
Last edited by vinay1983 on Sun Oct 06, 2013 8:48 pm, edited 1 time in total.
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Source: — Data Sufficiency |
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by theCodeToGMAT » Sun Oct 06, 2013 11:08 am
vinay1983 wrote:If x, y, and z are integers greater than 1, and (327)(510)(z) = (58)(914)(xy), then what is the value of x?

(1) y is prime

(2) x is prime
To find --> x

327 * 510 * z / 58 * 914 * y = x

327 = 3 * 109
510 = 2 * 5 * 3 * 17
58 = 2 * 29
914 = 2 * 457


(3 * 109) * (5 * 3 * 17) * Z
________________________ = X
2 * 29 * 457 * y



Statement 1:
y is prime
X can have any value
INSUFFICIENT


Statement 2:
X is prime
y can have any value .. subsequently.. X can have any value out of 109,3,5,17
INSUFFICIENT


Combining...
y = 3 (Out of 109, 5, 3, 17)
Z = 457 * 29 * 2
x = NOT PRIME

I got stuck here...... What is the OA????
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by GMATGuruNY » Sun Oct 06, 2013 11:11 am
I believe that the problem should read as follows:
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
(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.
Last edited by GMATGuruNY on Tue Oct 08, 2013 4:54 am, edited 1 time in total.
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by vinay1983 » Sun Oct 06, 2013 8:49 pm
theCodeToGMAT wrote:
vinay1983 wrote:If x, y, and z are integers greater than 1, and (327)(510)(z) = (58)(914)(xy), then what is the value of x?

(1) y is prime

(2) x is prime
To find --> x

327 * 510 * z / 58 * 914 * y = x

327 = 3 * 109
510 = 2 * 5 * 3 * 17
58 = 2 * 29
914 = 2 * 457


(3 * 109) * (5 * 3 * 17) * Z
________________________ = X
2 * 29 * 457 * y



Statement 1:
y is prime
X can have any value
INSUFFICIENT


Statement 2:
X is prime
y can have any value .. subsequently.. X can have any value out of 109,3,5,17
INSUFFICIENT


Combining...
y = 3 (Out of 109, 5, 3, 17)
Z = 457 * 29 * 2
x = NOT PRIME

I got stuck here...... What is the OA????
Sorry. I am a little out of order
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by lunarpower » Tue Oct 08, 2013 3:36 am
A student pointed me to Mitch's solution on this thread, in particular the part about statement 2.

Mitch --
GMATGuruNY wrote:Statement 2: x is prime
Since x^y is a multiple of 5² and x is prime, x=5 and y=2.
SUFFICIENT.
It's true that x has to be 5. (Since we only care about x, this is all that matters for the problem at hand.)

However, I was wondering how you arrived at y = 2. For instance, why can't y = 3, in which case z = 15? Or y = 4, in which case z = 45? Etc. After all, we are no longer constrained by the requirement that z be prime.
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by GMATGuruNY » Tue Oct 08, 2013 4:59 am
lunarpower wrote:However, I was wondering how you arrived at y = 2. For instance, why can't y = 3, in which case z = 15? Or y = 4, in which case z = 45? Etc. After all, we are no longer constrained by the requirement that z be prime.
Pesky typos! The solution should have indicated that y≥2 (since x^y must be a multiple of 5² and x must be prime). Edited my reply.
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