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What is the value of 2x/3y? [#permalink]
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20 Oct 2014, 07:05
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Re: What is the value of 2x/3y? [#permalink]
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20 Oct 2014, 13:47
Bunuel wrote: Tough and Tricky questions: Algebra. What is the value of 2x/3y ? (1) x^2/y^2 = 36/25 (2) x^5/y^5 > 1 1) This statement tells us that x is either 6 or 6, and that y is either 5 or 5. This is insufficient because x and y might not both have the same sign. 2) This statement tell us that both x and y have the same sign. This is not sufficient because we don't number values. Together these are sufficient. It doesn't matter if x and y are both positive or both negative. As long as they have the same sign, the value is going to be 4/5 (a negative divided by another negative is a positive, as is a positive divided by a positive).



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Re: What is the value of 2x/3y? [#permalink]
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20 Oct 2014, 22:19
Quote: What is the value of 2x/3y ?
(1) x^2/y^2 = 36/25 (2) x^5/y^5 > 1 Sol: St 1 says x^2/y^2 = 36/25 or we have x/y=6/5 or 6/5 So 2x/3y value will be same So St1 is sufficient St 2 gives you ratio of x>y and there are many numbers possible for ex x=2 and y=1 or x=1000, y=2...Value of 2x/3y will change. Ans A
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Re: What is the value of 2x/3y? [#permalink]
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20 Oct 2014, 22:33
WoundedTiger wrote: Quote: What is the value of 2x/3y ?
(1) x^2/y^2 = 36/25 (2) x^5/y^5 > 1 Sol: St 1 says x^2/y^2 = 36/25 or we have x/y=6/5 or 6/5 So 2x/3y value will be same So St1 is sufficient St 2 gives you ratio of x>y and there are many numbers possible for ex x=2 and y=1 or x=1000, y=2...Value of 2x/3y will change. Ans A Oops...I missed the case where x=6,y=5 or x=6 and y=5.. St 1 is not sufficient St 2 is important here we have that \((x^5y^5)/y^5 >0\) so we have 2 cases x^5y^5 >0 and y^5>0 Both x and y have same sign or x^5y^5<0 and y^5<0... y is negative and x<y so x is negative... so we have that x and y have same sign.. Combining we see that x and y have same sign so we can find unique value of 2x/3y Ans C
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What is the ratio of 2x to 3y? [#permalink]
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19 Aug 2015, 15:19
What is the ratio of 2x to 3y?
(1) The ratio of x^2 to y^2 is equal to 36/25.
(2) The ratio of x^5 to y^5 is greater than 1.
Why is Option 1 not sufficient. The answer should always be 6/5 for answer1, as we are taking the square root right??



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Re: What is the value of 2x/3y? [#permalink]
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19 Aug 2015, 15:28



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Re: What is the value of 2x/3y? [#permalink]
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19 Aug 2015, 15:35
Bunuel: Still not able to get , how can x/y = 6/5, as sqrt36=sqrt6^2=6. Right??



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Re: What is the value of 2x/3y? [#permalink]
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19 Aug 2015, 17:59
Shree9975 wrote: Bunuel: Still not able to get , how can x/y = 6/5,as sqrt36=sqrt6^2=6. Right?? If you are unclear about the text in red above, look at it this way, Given, \(\frac{x^2}{y^2}\) = \(\frac{36}{25}\) >> \(\frac{x}{y} = \pm \frac{6}{5}\) Thus, x =6k, y =5k or x=6k, y = 5k , giving you 2 different answers for 2x/3y. Hence this statement is not sufficient. Hope this helps.



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Re: What is the value of 2x/3y? [#permalink]
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19 Aug 2015, 22:09
Engr2012 : Here we are taking square roots of 36 and 25 right?? Here it is written in GMAT square roots always refer to positive roots. squarerootalwayspositive114114.htmlVeritasPrepKarishmaAm i missing anything?? Here



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Re: What is the value of 2x/3y? [#permalink]
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20 Aug 2015, 04:25
Shree9975 wrote: Engr2012 : Here we are taking square roots of 36 and 25 right?? Here it is written in GMAT square roots always refer to positive roots. squarerootalwayspositive114114.htmlVeritasPrepKarishmaAm i missing anything?? Here Yes, what you are missing is the how you define your equation. When you write x^2/y^2 = 36/25 , this equation is of degree 2 in (x/y) and thus you should get 2 solutions (it is a maths rule that you will get n solutions for nth degree equation, be it real or non real solutions!) But if you write the above equation as , (x/y) = \(\sqrt\frac{36}{25}\)] > this equation is 1 degree in (x/y) and hence can only have 1 solution. That is what VeritasPrepKarishma has written at the link posted by you. Hope this clears your doubt.



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Re: What is the value of 2x/3y? [#permalink]
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20 Aug 2015, 07:49
Shree9975 wrote: Engr2012 : Here we are taking square roots of 36 and 25 right?? Here it is written in GMAT square roots always refer to positive roots. squarerootalwayspositive114114.htmlVeritasPrepKarishmaAm i missing anything?? Here When the GMAT provides the square root sign for an even root, such as a square root, fourth root, etc. then the only accepted answer is the positive root. That is: \(\sqrt{9} = 3\), NOT +3 or 3; \(\sqrt[4]{16} = 2\), NOT +2 or 2; Notice though, that in contrast, the equation \(x^2 = 9\) has TWO solutions, +3 and 3. Because \(x^2 = 9\) means that \(x =\sqrt{9}=3\) or \(x=\sqrt{9}=3\).
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What is the ratio of 2x to 3y? (1) The ratio of x2 to y2 is equal to [#permalink]
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20 Mar 2017, 23:32
What is the ratio of \(2x\) to \(3y\)? (1) The ratio of \(x^2\) to \(y^2\) is equal to \(\frac{36}{25}\). (2) The ratio of \(x^5\) to \(y^5\) is greater than 1. Manhattan Challenge Problems Ratios and Exponents 2006, August 21
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What is the ratio of 2x to 3y? (1) The ratio of x2 to y2 is equal to [#permalink]
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20 Mar 2017, 23:59
We need to find 2x:3y = ? (1) x^2 : Y^2 = 36:25 Now, x can be ±6 and y can be ±5; If x and y are of opposite sign, 2x/3y = 12/15; But if x and y are of the same sign, then 2x/3y = 12/15; Hence, Insufficient. (2) x^5/y^5 > 1; This can be true if x and y both are positive or negative. So, we can say both are of same sign. But we don't have any values for x and y. Hence, Insufficient. (1) and (2) together, x = ±6 and y = ±5 and both are of same sign (from point 2). Hence, 2x/3y = 12/15; Sufficient. Answer C.
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Re: What is the value of 2x/3y? [#permalink]
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What is the value of 2x/3y? [#permalink]
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10 Apr 2017, 11:15
Bunuel wrote: Tough and Tricky questions: Algebra. What is the value of 2x/3y ? (1) x^2/y^2 = 36/25 (2) x^5/y^5 > 1 \(\frac{2}{3}*\frac{x}{y}=?\) (1) \((\frac{x}{y})^2=(\frac{6}{5})^2\) \(\frac{x}{y}=±\frac{6}{5}\) => INSUFFICIENT (2) \((\frac{x}{y})^5>1\) \(\frac{x}{y}>1\) => INSUFFICIENT 1 & 2 => \(\frac{x}{y}=\frac{6}{5}\) SUFFICIENT. C.
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Re: What is the value of 2x/3y? [#permalink]
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10 Sep 2017, 13:43
Bunuel wrote: Tough and Tricky questions: Algebra. What is the value of 2x/3y ? (1) x^2/y^2 = 36/25 (2) x^5/y^5 > 1 St 1 X could negative and y could be positive because either possibility would still give you 36/25 St 2 x and y must be positive but no info about the actual values St 1 and st 2 eliminates possibility of x and y being positive and negative must be positive suff C




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