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
Data Sufficiency
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Are you sure you've entered this correctly? It doesn't appear to have a solution.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
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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Are you sure those numbers are correct?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
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.
Cheers,
Brent
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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.
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.
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.
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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Ahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh.
RiyaR, please check your questions once they're posted. I see that you have posted several ambiguous/confusing questions.
Cheers,
Brent
RiyaR, please check your questions once they're posted. I see that you have posted several ambiguous/confusing questions.
Cheers,
Brent
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The problem should read as follows:
(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.
(3²�)(35¹�)(z) = (5�)(7¹�)(9¹�)(x^y)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�)(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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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
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