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

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Senior Manager
Status: Gathering chakra
Joined: 05 Feb 2018
Posts: 444
If x and y are positive integers, is 4x – 7y < 0?  [#permalink]

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24 Mar 2019, 13:07
1
1
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Difficulty:

55% (hard)

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) $$x > y$$
Math Expert
Joined: 02 Aug 2009
Posts: 8325
Re: If x and y are positive integers, is 4x – 7y < 0?  [#permalink]

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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

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

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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=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.

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