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If x and y are positive integers, is 4x – 7y < 0?

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If x and y are positive integers, is 4x – 7y < 0?  [#permalink]

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New post 24 Mar 2019, 13:07
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Question Stats:

56% (01:43) correct 44% (02:07) wrong based on 66 sessions

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If x and y are positive integers, is \(4^x – 7^y < 0\)?

(1) \(16^x + 1 < 49^y\)

(2) \(x > y\)
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Re: If x and y are positive integers, is 4x – 7y < 0?  [#permalink]

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New post 24 Mar 2019, 19:58
If x and y are positive integers, is \(4^x – 7^y < 0\)?

(1) \(16^x + 1 < 49^y\)
Let us modify the statement
\(16^x + 1 < 49^y..........16^x-49^y<-1.......4^{2x}-7^{2y}<-1......(4^x-7^y)(4^x+7^y)<-1\)
Now, x and y are positive, so \(4^x+7^y>0\). This means\(4^x-7^y<0\)
Sufficient

(2) \(x > y\)
x is 100 and y is 1, ans is NO
x is 100 and y is 99, ans is YES
insuff

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Re: If x and y are positive integers, is 4x – 7y < 0?  [#permalink]

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New post 13 May 2019, 02:49
energetics wrote:
If x and y are positive integers, is \(4^x – 7^y < 0\)?

(1) \(16^x + 1 < 49^y\)

(2) \(x > y\)




I) \(2^{4x} +1<7^{2y}\)

x=1, y=1 answer is yes
x=2 y=1 does not satisfy this statement
x=3 y=1 also does not satisfy this statement

Hence we can see that answer is always yes
SUFF.


II)x=2 y=1 answer is No
x=5 y=4 answer is Yes

P.S. Please can this question be moved to the DS forum. Thank you.
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Re: If x and y are positive integers, is 4x – 7y < 0?   [#permalink] 13 May 2019, 02:49
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