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

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

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New post 28 Sep 2013, 07:59
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Question Stats:

56% (01:35) correct 44% (02:05) wrong based on 144 sessions

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

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New post 28 Sep 2013, 09:25
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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

Answer A

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

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New post 20 Oct 2013, 11:40
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

Answer A

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


Just a minor question, wont the red portion be contradicting the first statement?
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Re: Is (2^(y+z))(3^x)(5^y)(7^z) < (90^y)(14^z)  [#permalink]

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New post 20 Oct 2013, 18:07
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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New post 20 Dec 2018, 12:35
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Re: Is (2^(y+z))(3^x)(5^y)(7^z) < (90^y)(14^z) &nbs [#permalink] 20 Dec 2018, 12:35
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