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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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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

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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?

Posted from my mobile device

Posted from my mobile device
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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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SchruteDwight
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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