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What is the value of 2x/3y?

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What is the value of 2x/3y? [#permalink]

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New post 20 Oct 2014, 07:05
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Re: What is the value of 2x/3y? [#permalink]

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New post 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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New post 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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New post 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.. :beat
St 1 is not sufficient

St 2 is important here

we have that \((x^5-y^5)/y^5 >0\)

so we have 2 cases

x^5-y^5 >0 and y^5>0 Both x and y have same sign

or

x^5-y^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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New post 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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New post 19 Aug 2015, 15:28
Shree9975 wrote:
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??


Please refer to the discussion above and ask if anything remains unclear.
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Re: What is the value of 2x/3y? [#permalink]

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New post 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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New post 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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New post 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.
square-root-always-positive-114114.html
VeritasPrepKarishma

Am i missing anything??


Here

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Re: What is the value of 2x/3y? [#permalink]

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New post 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.
square-root-always-positive-114114.html
VeritasPrepKarishma

Am 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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New post 20 Aug 2015, 07:49
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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.
square-root-always-positive-114114.html
VeritasPrepKarishma

Am 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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New post 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.

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Ratios and Exponents
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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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New post 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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New post 21 Mar 2017, 00:10
ziyuen wrote:
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.

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Ratios and Exponents
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Merging topics. Please refer to the discussion above.
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What is the value of 2x/3y? [#permalink]

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New post 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.

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Re: What is the value of 2x/3y? [#permalink]

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New post 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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Re: What is the value of 2x/3y?   [#permalink] 10 Sep 2017, 13:43
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