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Math Expert V
Joined: 02 Sep 2009
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What is the value of 2x/3y?  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 62% (01:16) correct 38% (01:29) wrong based on 262 sessions

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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

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

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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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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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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 $$(x^5-y^5)/y^5 >0$$

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

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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;
$$\sqrt{16} = 2$$, 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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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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GMAT 1: 730 Q49 V41 What is the ratio of 2x to 3y? (1) The ratio of x2 to y2 is equal to  [#permalink]

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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.

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

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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.

Manhattan Challenge Problems
Ratios and Exponents
2006, August 21

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

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1
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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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

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

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_________________ Re: What is the value of 2x/3y?   [#permalink] 25 Feb 2019, 05:50
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