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Manager  Joined: 17 Nov 2009
Posts: 219
If x and y are positive, is the ratio of x to y greater than  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 68% (01:29) correct 32% (01:34) wrong based on 225 sessions

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

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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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GRE 1: Q169 V154 Re: If x and y are positive, is the ratio of x to y greater than  [#permalink]

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1
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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Bunuel niks18 amanvermagmat gmatbusters chetan2u

Quote:
If x and y are positive, is the ratio of x to y greater than 3 ?[/b]

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.

Why does this hold true even for decimal values though we are not mentioned that x and y are integers in questions stem?
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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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Yes this is valid for any positive number (integers, decimals, fractions, surds etc)
You can see it like this.

Statement 1: x = 3y+2
Hence x/y = (3y+2)/y = 3+2/y hence>3.
Sufficient

Statement 2: 2x/3y >2: hence multiplying 3/2 both sides of inequality, we get x/y>3.
Sufficient.

Answer D

adkikani wrote:
Bunuel niks18 amanvermagmat gmatbusters chetan2u

Quote:
If x and y are positive, is the ratio of x to y greater than 3 ?[/b]

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.

Why does this hold true even for decimal values though we are not mentioned that x and y are integers in questions stem?

Posted from my mobile device

Posted from my mobile device
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Manager  B
Joined: 03 Sep 2018
Posts: 61
Re: If x and y are positive, is the ratio of x to y greater than  [#permalink]

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What would the answer be if it did not have the restriction that x and y > 0?
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Please consider giving Kudos if my post contained a helpful reply or question. Re: If x and y are positive, is the ratio of x to y greater than   [#permalink] 20 Feb 2019, 13:28
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# If x and y are positive, is the ratio of x to y greater than

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