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# If x and y are non-negative integers, is x>y?

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Joined: 25 Dec 2018
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If x and y are non-negative integers, is x>y?  [#permalink]

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Updated on: 04 Mar 2019, 03:00
3
00:00

Difficulty:

55% (hard)

Question Stats:

61% (01:58) correct 39% (01:57) wrong based on 33 sessions

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If x and y are non-negative integers, is x>y?

(1) $$5^x*3^y=9$$

(2) $$\frac{3^x}{4^y}>\frac{4^y}{3^y}$$

Originally posted by mangamma on 04 Mar 2019, 02:56.
Last edited by Bunuel on 04 Mar 2019, 03:00, edited 1 time in total.
Formatted.
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Re: If x and y are non-negative integers, is x>y?  [#permalink]

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04 Mar 2019, 03:08
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1
mangamma wrote:
If x and y are non-negative integers, is x>y?

(1) $$5^x*3^y=9$$

(2) $$\frac{3^x}{4^y}>\frac{4^y}{3^y}$$

As all we're given are equations, we'll look for a simplification.
This is a Precise approach.

(1) Since 9 = 3^2 = (3^2)(5^0), then x = 0 and y =2.
Sufficient.

(2) Multiplying the common denominator gives (3^x)(3^y)>(4^y)(4^y) which simplifies to 3^(x+y) > 4^(2y). Since 3 is smaller than 4, then for the inequality to be true, the exponent of 3 must be larger. In other words, x+y > 2y and therefore x > y.
Sufficient.

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Re: If x and y are non-negative integers, is x>y?  [#permalink]

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04 Mar 2019, 03:24
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A few good takeaways from this question:

-we can always rewrite integers as their factors, so we can say 9 = 3^2
-we can multiply across inequalities freely (without flipping the sign) when we know the variables are positive
-if a smaller integer is LARGER than a bigger integer and they both have unknown exponents, then the exponent of the smaller integer is obviously "making up" for the difference in value and must be larger than the bigger integer's exponent

The flaw with the question: The statements are incompatible. It cannot be that x = 0 and y = 2, and Statement (2) is true. Because if we plug in x = 0 and y = 2, then Statement (2) reads:

1/16 > 16/9
1/16 is not larger than 16/9

So, while there's good takeaways here, the fact that the statements contradict one another do not make this a great GMAT question.
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Re: If x and y are non-negative integers, is x>y?   [#permalink] 04 Mar 2019, 03:24
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