What is the value of 2x/3y?
(1) x^2/y^2 = 36/25
(2) x^5/y^5 > 1
The OA is the option C.
Why is the first statement not sufficient? Could anyone give me some help, please?
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What is the value of 2x/3y?
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Vincen
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Hello Vjesus12.
Let's take a look at your question. We want to find the value of $$\frac{2x}{3y}=?$$
First of all, we need to assume that x and y are integers.
First Statement
(i) x=6 and y=5, then $$\frac{2x}{3y}=\frac{2\left(6\right)}{3\left(5\right)}=\frac{4}{5}.$$
(ii) x=-6 and y=5, then $$\frac{2x}{3y}=\frac{2\left(-6\right)}{3\left(5\right)}=-\frac{4}{5}.$$
Since we get two different answers, then this statement is not sufficient.
Second Statement
First Statement + Second Statement
(i) x=6 and y=5, then $$\frac{2x}{3y}=\frac{2\left(6\right)}{3\left(5\right)}=\frac{4}{5}.$$
(ii) x=-6 and y=-5, then $$\frac{2x}{3y}=\frac{2\left(-6\right)}{3\left(-5\right)}=\frac{4}{5}.$$
So, we get only one answer. Therefore, using both statements together is sufficient.
I hope it helps.
Let's take a look at your question. We want to find the value of $$\frac{2x}{3y}=?$$
First of all, we need to assume that x and y are integers.
First Statement
Here we can get at least two different cases:(1) x^2/y^2 = 36/25
(i) x=6 and y=5, then $$\frac{2x}{3y}=\frac{2\left(6\right)}{3\left(5\right)}=\frac{4}{5}.$$
(ii) x=-6 and y=5, then $$\frac{2x}{3y}=\frac{2\left(-6\right)}{3\left(5\right)}=-\frac{4}{5}.$$
Since we get two different answers, then this statement is not sufficient.
Second Statement
This statement just tells us that x and y have the same sign. So, x and y can be any value. Therefore, this statement is not sufficient.(2) x^5/y^5 > 1
First Statement + Second Statement
From both statements, we get that x and y have the same sign, therefore we can get just the two following cases:(1) x^2/y^2 = 36/25
(2) x^5/y^5 > 1
(i) x=6 and y=5, then $$\frac{2x}{3y}=\frac{2\left(6\right)}{3\left(5\right)}=\frac{4}{5}.$$
(ii) x=-6 and y=-5, then $$\frac{2x}{3y}=\frac{2\left(-6\right)}{3\left(-5\right)}=\frac{4}{5}.$$
So, we get only one answer. Therefore, using both statements together is sufficient.
I hope it helps.
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Jay@ManhattanReview
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We have to get the value of 2x/3y. If we get the unique value of x/y, we get the answer.VJesus12 wrote:What is the value of 2x/3y?
(1) x^2/y^2 = 36/25
(2) x^5/y^5 > 1
The OA is the option C.
Why is the first statement not sufficient? Could anyone give me some help, please?
Question rephrased: What's the value of x/y?
Let's take each statement one by one.
(1) x^2/y^2 = 36/25
=> x/y = ±6/5. No unique value of x/y; it can be 6/5 or -6/5. Insufficient.
(2) x^5/y^5 > 1
=> x/y > 1. No value of x/y. Insufficient.
(1) and (2) together
From (1), if x/y = 6/5 > 1 and if x/y = -6/5 < 1. From (2), we know that x/y > 1; thus, x/y = 6/5. Sufficient.
The correct answer: C
Hope this helps!
-Jay
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Hi All,
We're asked for the value of 2X/3Y. This question can be solved by TESTing VALUES.
1) (X^2)/(Y^2) = 36/25
IF....
X=6, Y=5, then the answer to the question is 12/15 = 4/5
X=6, Y= -5, then the answer to the question is 12/-15 = -4/5
Fact 1 is INSUFFICIENT
2) X^5/Y^5 > 1
With this inequality, we know that X and Y must be the SAME sign (either both positive or both negative).
IF....
X=6, Y=5, then the answer to the question is 12/15 = 4/5
X=6, Y=1, then the answer to the question is 12/3 = 4
Fact 2 is INSUFFICIENT
Combined, we know...
(X^2)/(Y^2) = 36/25
X^5/Y^5 > 1
Since X and Y must be the SAME sign, we have two immediate examples that 'fit' both Facts....
IF....
X=6, Y=5, then the answer to the question is 12/15 = 4/5
X= -6, Y= -5, then the answer to the question is -12/-15 = 4/5
X and Y could be other values though, but the only pairs of values that fit the first equation will be in the ratio of 6:5. For example....
IF....
X=12, Y=10, then the answer to the question is 24/30 = 4/5
X= -12, Y= -10, then the answer to the question is -24/-30 = 4/5
The answer will ALWAYS be 4/5.
Combined, SUFFICIENT
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
We're asked for the value of 2X/3Y. This question can be solved by TESTing VALUES.
1) (X^2)/(Y^2) = 36/25
IF....
X=6, Y=5, then the answer to the question is 12/15 = 4/5
X=6, Y= -5, then the answer to the question is 12/-15 = -4/5
Fact 1 is INSUFFICIENT
2) X^5/Y^5 > 1
With this inequality, we know that X and Y must be the SAME sign (either both positive or both negative).
IF....
X=6, Y=5, then the answer to the question is 12/15 = 4/5
X=6, Y=1, then the answer to the question is 12/3 = 4
Fact 2 is INSUFFICIENT
Combined, we know...
(X^2)/(Y^2) = 36/25
X^5/Y^5 > 1
Since X and Y must be the SAME sign, we have two immediate examples that 'fit' both Facts....
IF....
X=6, Y=5, then the answer to the question is 12/15 = 4/5
X= -6, Y= -5, then the answer to the question is -12/-15 = 4/5
X and Y could be other values though, but the only pairs of values that fit the first equation will be in the ratio of 6:5. For example....
IF....
X=12, Y=10, then the answer to the question is 24/30 = 4/5
X= -12, Y= -10, then the answer to the question is -24/-30 = 4/5
The answer will ALWAYS be 4/5.
Combined, SUFFICIENT
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
