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# If x and y are positive, is the ratio of x to y greater than

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Manager
Joined: 17 Nov 2009
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If x and y are positive, is the ratio of x to y greater than [#permalink]

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06 Oct 2010, 07:52
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If x and y are positive, is the ratio of x to y greater than 3 ?

(1) x is 2 more than 3 times y.
(2) The ratio of 2x to 3y is greater than 2
[Reveal] Spoiler: OA

Kudos [?]: 64 [0], given: 17

Math Expert
Joined: 02 Sep 2009
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Re: Ratios [#permalink]

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06 Oct 2010, 07:58
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If x and y are positive, is the ratio of x to y greater than 3 ?

Is $$\frac{x}{y}>3$$? --> since y is positive, we can multiply both sides by it to get: is $$x>3y$$?

(1) x is 2 more than 3 times y --> $$x=3y+2$$ --> directly tells us that $$x$$ is 2 more than $$3y$$. Sufficient.

Or: substitute $$x$$: is $$x>3y$$? --> is $$3y+2>3y$$? --> is $$2>0$$? YES. Sufficient.

(2) The ratio of 2x to 3y is greater than 2 --> $$\frac{2x}{3y}>2$$ --> $$x>3y$$. Sufficient.

Answer: D.
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Re: If x and y are positive, is the ratio of x to y greater than [#permalink]

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13 Mar 2016, 06:03
Whenever we are given a combination of equality and inequality we must substitute that equality in the inequality to obtain the ranges
here statement 2 is obvious;y true
in statement 1 after we substitute x=3y+2 => we get 2>0 => true .
hence the answer is D
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Re: If x and y are positive, is the ratio of x to y greater than [#permalink]

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05 Jan 2018, 02:01
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Re: If x and y are positive, is the ratio of x to y greater than   [#permalink] 05 Jan 2018, 02:01
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# If x and y are positive, is the ratio of x to y greater than

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