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

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agnok
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If x and y are positive, is the ratio of x to y greater than [#permalink] New post  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
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Bunuel
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Re: Ratios [#permalink] New post  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] New post  13 Mar 2016, 06:03
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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] New post  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] New post  24 Apr 2018, 18:40
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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?


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Re: If x and y are positive, is the ratio of x to y greater than [#permalink] New post  20 Feb 2019, 12:28
What would the answer be if it did not have the restriction that x and y > 0?
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Re: If x and y are positive, is the ratio of x to y greater than [#permalink] New post  19 Aug 2020, 17:02
SchruteDwight wrote:
What would the answer be if it did not have the restriction that x and y > 0?


Did you mean if x and y were BOTH integers less than 0? I reckon the answer would be (D) as well. Statement 1 would yield a ratio lesser than 3 and statement 2 would be interpreted the same way as the original question (negatives cancel out).
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Re: If x and y are positive, is the ratio of x to y greater than [#permalink] New post  07 Mar 2023, 03:31
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