Absolute Value

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If xy ≠ 0, is x > y?

(1) 4x = 3y

(2) |y - x| = x - y

Ans-C

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Hi shibsriz,

This DS question is perfect for TESTing Values, but recognizing some of the Number Properties that are built into it would certainly help you to solve it.

We're told that X and Y cannot be 0. We're asked: Is X > Y? This is a YES/NO question.

Fact 1: 4X = 3Y

This tells us that the two variables MUST have the same "sign" and are not equal. Let's TEST Values:

X = 3
Y= 4
The answer to the question is NO.

X = -3
Y = -4
The answer to the question is YES.
Fact 1 is INSUFFICIENT

Fact 2: |Y - X| = X - Y

Since the absolute value will end with either a 0 or a positive value, that means X is >= Y.

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

X = 4
Y = 3
The answer to the question is YES.
Fact 2 is INSUFFICIENT

Combined, we know:
1) X and Y have the same "sign" and are different
2) X >= to Y

The only way for BOTH of those facts to be true is when X > Y, so the answer to the question is ALWAYS YES.

Final Answer: C

GMAT assassins aren't born, they're made,
Rich[/spoiler]

[GMATGuruNY]

If xy ≠ 0, is x > y?

(1) 4x = 3y

(2) |y - x| = x - y

Ans-C

Statement 1: 4x=3y
It can be helpful to put one variable in terms of the other:
x = (3/4)y.

Case 1: y=4, x=3
In this case, x<y.

Case 2: y=-4, x=-3
In this case, x>y.

INSUFFICIENT.

Statement 2: |y-x| = x-y
Since the lefthand side must be NONNEGATIVE, so must the righthand side:
x-y≥0
x≥y.
Since it's possible that x=y or that x>y, INSUFFICIENT.

Statements combined:
Statement 2 implies that x=y or that x>y.
Since xy≠0, it's not possible that x=y in statement 1.
Thus, both statements are satisfied only if x>y.
SUFFICIENT.

The correct answer is C.

[[email protected]]

Hi Rich,


Can we also take values where in one of x and y is negative and the other positive?

Thanks

Hi shibsriz,

This DS question is perfect for TESTing Values, but recognizing some of the Number Properties that are built into it would certainly help you to solve it.

We're told that X and Y cannot be 0. We're asked: Is X > Y? This is a YES/NO question.

Fact 1: 4X = 3Y

This tells us that the two variables MUST have the same "sign" and are not equal. Let's TEST Values:

X = 3
Y= 4
The answer to the question is NO.

X = -3
Y = -4
The answer to the question is YES.
Fact 1 is INSUFFICIENT

Fact 2: |Y - X| = X - Y

Since the absolute value will end with either a 0 or a positive value, that means X is >= Y.

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

X = 4
Y = 3
The answer to the question is YES.
Fact 2 is INSUFFICIENT

Combined, we know:
1) X and Y have the same "sign" and are different
2) X >= to Y

The only way for BOTH of those facts to be true is when X > Y, so the answer to the question is ALWAYS YES.

Final Answer: C

GMAT assassins aren't born, they're made,
Rich[/spoiler]

[dddanny2006]

This is my method of solving this
I totally agree with Statement 1 being insufficient.

Now lets look at statement 2.

|y - x| = x - y

Therefore we have y-x=x-y => 2y=2x =>x=y

1=1 2=2 3=3 and thus x is not greater than y when tested against the question stem.So NO and the answer is B

This is simply not fair,,I mean different techniques give us different answers,how is this possible?If I was writing my test today I would answer it as B.How does one get questions like this right?One technique may give you a totally different answer..

Please explain Guru

If xy ≠ 0, is x > y?

(1) 4x = 3y

(2) |y - x| = x - y

Ans-C

Statement 1: 4x=3y
It can be helpful to put one variable in terms of the other:
x = (3/4)y.

Case 1: y=4, x=3
In this case, x<y.

Case 2: y=-4, x=-3
In this case, x>y.

INSUFFICIENT.

Statement 2: |y-x| = x-y
Since the lefthand side must be NONNEGATIVE, so must the righthand side:
x-y≥0
x≥y.
Since it's possible that x=y or that x>y, INSUFFICIENT.

Statements combined:
Statement 2 implies that x=y or that x>y.
Since xy≠0, it's not possible that x=y in statement 1.
Thus, both statements are satisfied only if x>y.
SUFFICIENT.

The correct answer is C.

[dddanny2006]

This is my method of solving this
I totally agree with Statement 1 being insufficient.

Now lets look at statement 2.

|y - x| = x - y

Therefore we have y-x=x-y => 2y=2x =>x=y

1=1 2=2 3=3 and thus x is not greater than y when tested against the question stem.So NO and the answer is B

This is simply not fair,,I mean different techniques give us different answers,how is this possible?If I was writing my test today I would answer it as B.How does one get questions like this right?One technique may give you a totally different answer..

Please explain Guru

Hi shibsriz,

This DS question is perfect for TESTing Values, but recognizing some of the Number Properties that are built into it would certainly help you to solve it.

We're told that X and Y cannot be 0. We're asked: Is X > Y? This is a YES/NO question.

Fact 1: 4X = 3Y

This tells us that the two variables MUST have the same "sign" and are not equal. Let's TEST Values:

X = 3
Y= 4
The answer to the question is NO.

X = -3
Y = -4
The answer to the question is YES.
Fact 1 is INSUFFICIENT

Fact 2: |Y - X| = X - Y

Since the absolute value will end with either a 0 or a positive value, that means X is >= Y.

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

X = 4
Y = 3
The answer to the question is YES.
Fact 2 is INSUFFICIENT

Combined, we know:
1) X and Y have the same "sign" and are different
2) X >= to Y

The only way for BOTH of those facts to be true is when X > Y, so the answer to the question is ALWAYS YES.

Final Answer: C

GMAT assassins aren't born, they're made,
Rich[/spoiler]

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Hi shibsriz,

For Fact 1, we need both variables have to be the "same sign" in order to satisfy the given information.

For Fact 2, we COULD use one positive and one negative, BUT X would have to be the positive and the Y would have to be the negative. As an example, we COULD have used:

X = 3
Y = -2

However, the reverse is NOT possible (we couldn't have a positive X and a negative Y because then the "right side" of the equation would be negative, which wouldn't match the 0 or positive result on the "left side" of the equation).

As it stands, we would NOT need to test negative values in Fact 2, since the two initial tests were enough to prove that Fact 2 was INSUFFICIENT.

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

[[email protected]]

Hi dddanny2006,

In DS questions, you have to be a bit cynical of the given information. There will ALWAYS be at least one result that you can "figure out"; however, DS questions are built to test your THOROUGHNESS, so keep your eyes open for OTHER possibilities.

In this prompt, we're asked "Is X > Y?" This is a YES/NO question.

IF X is greater than Y, then the answer is YES
IF Y is greater than X, then the answer is NO

Is there ANYTHING ELSE TO CONSIDER????....

IF X is EQUAL to Y, then the answer is NO

TESTing Values is a great way to work through the various possibilities (and to make sure that you don't "miss" anything). As it stands, THAT approach (TESTing Values) works on most DS questions (and many Problem Solving questions).

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