Is x y ? (1) 9x = 4y (2) x -y

Question

Is x > y ?

(1) 9x = 4y
(2) x > -y

I understand why first statement is insufficient, but not the second one. Please help!

EMPOWERgmatRichC · Answer

Hi MariaVorop,

As simple as this DS question might look, it actually requires a greater degree of thoroughness than most Test Takers realize. TESTing VALUES and a bit of Number Property knowledge will help you to answer this question.

We're asked if X is greater than Y. This is a YES/NO question.

Fact 1: 9X = 4Y

IF...
X = 4
Y = 9
The answer to the question is NO

IF....
X = -4
Y = -9
The answer to the question is YES
Fact 1 is INSUFFICIENT

Fact 2: X > -Y

IF....
X = 4
Y = 9
The answer to the question is NO

IF...
X = 1
Y = 0
The answer to the question is YES
Fact 2 is INSUFFICIENT

Combined, we know....
9X = 4Y, which means that X and Y have the SAME sign (they're either both positive, both negative or both 0)
X > -Y

Given the 3 possible outcomes from Fact 1, we can eliminate certain possibilities from Fact 2....
Both variables cannot be negative (a negative is NOT > than a - )
Both variables cannot be 0 (0 is NOT > 0)

This proves that both variables MUST be positive. 
Since 9X = 4Y, and both variables are positive, Y MUST be > X
The answer to the question is ALWAYS NO
Combined, SUFFICIENT

Final Answer:  C

GMAT assassins aren't born, they're made,
Rich

MariaVorop · Answer

Hi Rich,

thanks for the reply!

In fact 2, did you switch the sign of the inequality x>-y=x<y?
I don't understand where negative sign of y goes?

You wrote that:
IF....
X = 4
Y = 9
The answer to the question is NO

How can y be 9 if it has negative sign?
And actually if we would just plug in in the inequality numbers that you suggested for x and y inequality would actually be true:

4>-9.

I just don't get whether the inequality changes sign or where negative sign of y goes?

IF...
X = 1
Y = 0
The answer to the question is YES
Fact 2 is INSUFFICIENT

Thanks in advance!

best,
Maria

Bunuel · Answer

Is x > y?

(1) 9x = 4y --> if x = 4 and y = 9, then the answer to the question is NO but if x = -4 and y = -9, then the asnwer to the question is YES. Not sufficient.

Notice that above statement implies that x and y have the same sign: both positive, both negative, or both 0.

(2) x > -y --> x + y > 0 --> the sum of two numbers is positive. From this we cannot determine which one is bigger. Not sufficient.

(1)+(2) We have that the sum of two numbers (x and y) is positive AND x and y have the same sign, which means that both must be positive. If both are positive and x/y = 4/9 (from 1), then it must be true that x < y. Sufficient.

Answer: C.

Hope it's clear.

MariaVorop · Answer

Oh, I see. Thank you! 
Best, Maria

EMPOWERgmatRichC · Answer

Hi Maria,

When dealing with a DS question, you can choose how you want to "format" the given information, as long as you're following the "rules" of math.

In Fact 2, we're told that X > -Y

You can write this as....

X > (-1)(Y)

Either way, you MUST choose values for X and Y (remember, they're variables) that fit THIS restriction.

In my two examples, I used....

X = 4
Y = 9

This "fits" the restriction because 4 is > (-1)(9).
In this example, X is NOT > Y and the answer to the question is NO.

In the other example, I used...
X = 1
Y = 0

This also "fits" the restriction because 1 is > (-1)(0)
In this example, X IS > Y and the answer to the question is YES.

GMAT assassins aren't born, they're made,
Rich

Skywalker18 · Answer

(1) 9x = 4y 
=> x = (4/9)y
If x = 4 then y = 9
if x = -4 then y = -9

Not sufficient

(2) x > – y 
=>x + y > 0

Not sufficient

Combining 1 and 2 , we get
Sufficient

Answer C

energetics · Answer

Is x>y?

Plugging in values:

1) 9x=4y
9(4) = 4(9) ✔
9(0) = 4(0) ✘
Depends on values, not sufficient.

2) x > -y
4 > -9 ✘ doesn't fulfill x>y
9 > -4 ✔ fits both 
So it depends on the values again, not sufficient.

3) Take the first example in 1) 9(4) = 4(9) and 2) 4>-9 ... we can definitely say x NOT > y, sufficient.

ManifestDreamMBA · Answer

Statement 1
x = 4y/9
We don't know the value of y to know if x > y
Insufficient

Statement 2
x>-y
But we don't know if y is positive or negative
Insufficient

Combined
x+y>0 (Both add up to a positive number)
9x=4y (Both are positive or both are negative or both are 0)
Sufficient, both are positive numbers and can be solved for

Is x > y ? (1) 9x = 4y (2) x > -y

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