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# Is (2^(y+z))(3^x)(5^y)(7^z) < (90^y)(14^z)

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Intern
Joined: 14 Mar 2013
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Location: United States
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Is (2^(y+z))(3^x)(5^y)(7^z) < (90^y)(14^z) [#permalink]

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28 Sep 2013, 08:59
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Is (2^(y+z))(3^x)(5^y)(7^z) < (90^y)(14^z)

(1) y and z are positive integers; x = 1
(2) x and z are positive integers; y = 1

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Manager
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Re: Is (2^(y+z))(3^x)(5^y)(7^z) < (90^y)(14^z) [#permalink]

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28 Sep 2013, 10:25
4
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Format the question properly using <Math> tag.

Is$$(2^(^y^+^z^))(3^x)(5^y)(7^z) < (90^y)(14^z)$$

(1) y and z are positive integers; x = 1
(2) x and z are positive integers; y = 1

Lets first break the right hand side of the equation into prime factors
$$(90^y)(14^z) = (2*3^2*5)^y*(2*7)^z = (2^y*3^2^y*5^y)*(2^z*7^z) = 2^(^y^+^z^)*3^2^y*5^y*7^z$$

So now the question becomes:
Is $$2^(^y^+^z^)*3^x*5^y*7^z < 2^(^y^+^z^)*3^2^y*5^y*7^z$$

By Simplifying LHS and RHS, we get:
Is $$3^x < 3^2^y$$

Statement 1:
y and z are positive integers; x = 1
So, x will always be less than 2y because $$y>1$$
Thus, $$3^x < 3^2^y$$ ... SUFFICIENT

Statement 2:
x and z are positive integers; y = 1
If x = 1 then $$3^x < 3^2^y$$
But if x = 2 then $$3^x$$ is not less than $$3^2^y$$ ... Hence INSUFFICIENT

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Re: Is (2^(y+z))(3^x)(5^y)(7^z) < (90^y)(14^z) [#permalink]

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20 Oct 2013, 12:40
TirthankarP wrote:
Format the question properly using <Math> tag.

Is$$(2^(^y^+^z^))(3^x)(5^y)(7^z) < (90^y)(14^z)$$

(1) y and z are positive integers; x = 1
(2) x and z are positive integers; y = 1

Lets first break the right hand side of the equation into prime factors
$$(90^y)(14^z) = (2*3^2*5)^y*(2*7)^z = (2^y*3^2^y*5^y)*(2^z*7^z) = 2^(^y^+^z^)*3^2^y*5^y*7^z$$

So now the question becomes:
Is $$2^(^y^+^z^)*3^x*5^y*7^z < 2^(^y^+^z^)*3^2^y*5^y*7^z$$

By Simplifying LHS and RHS, we get:
Is $$3^x < 3^2^y$$

Statement 1:
y and z are positive integers; x = 1
So, x will always be less than 2y because $$y>1$$
Thus, $$3^x < 3^2^y$$ ... SUFFICIENT

Statement 2:
x and z are positive integers; y = 1
If x = 1 then $$3^x < 3^2^y$$
But if x = 2 then $$3^x$$ is not less than $$3^2^y$$ ... Hence INSUFFICIENT

Kudos plz if my reply helped. Need to unlock G M A T Club Tests

Just a minor question, wont the red portion be contradicting the first statement?

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Manager
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Re: Is (2^(y+z))(3^x)(5^y)(7^z) < (90^y)(14^z) [#permalink]

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20 Oct 2013, 19:07
suk1234 wrote:
Just a minor question, wont the red portion be contradicting the first statement?

While considering the second statement, we should not even think of the first statement.
While solving the question using statement 2 alone, we don't bother what information we got earlier using statement 1.
However, if both statement 1 and 2 alone are not sufficient, then only we have to consider the information from both statement 1 and 2.

Thats the crux of data sufficiency questions.
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Re: Is (2^(y+z))(3^x)(5^y)(7^z) < (90^y)(14^z) [#permalink]

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17 Mar 2016, 06:22
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Re: Is (2^(y+z))(3^x)(5^y)(7^z) < (90^y)(14^z) [#permalink]

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06 Sep 2017, 20:10
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Is (2^(y+z))(3^x)(5^y)(7^z) < (90^y)(14^z)   [#permalink] 06 Sep 2017, 20:10
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# Is (2^(y+z))(3^x)(5^y)(7^z) < (90^y)(14^z)

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