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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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Difficulty:

35% (medium)

Question Stats:

66% (01:29) correct 34% (01:31) wrong based on 258 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
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Joined: 02 Sep 2009
Posts: 51229

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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.

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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 .
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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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24 Apr 2018, 17:09
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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24 Apr 2018, 18:40
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.

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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Posted from my mobile device
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Re: If x and y are positive, is the ratio of x to y greater than &nbs [#permalink] 24 Apr 2018, 18:40
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