inequality

[seyna]

If x > 2 and y < -2, then:
A. x/y > 1
B. x/y < -1
C. x/y < 0 Answer
D. x + y > 0
E. xy > 0

I think the answer is c. but it says d. HHow can d be always true? if x=3 and y=-3, x+y=0 So d can't be always true.

[sarhen]

That is right. C is the correct answer. You may need to check the source of the solution.....could be a typo

[Brent@GMATPrepNow]

If x > 2 and y < -2, then:

A. x/y > 1
B. x/y < -1
C. x/y < 0
D. x + y > 0
E. xy > 0

When posting questions, please use the spoiler function to hide the correct answer. This will allow others to attempt the question without seeing the final answer.

As seyna points out, we can solve this quickly by choosing the x- and y-values that satisfy the given conditions, and see which answer choices can be eliminated.

x = 3 and y = -3 satisfy the given conditions.
Now we'll plug these values into the answer choices and see what happens.

A. x/y > 1 becomes 3/(-3) > 1 becomes -1 > 1 (NOPE)
B. x/y < -1 becomes 3/(-3) < -1 becomes -1 < -1 (NOPE)
C. x/y < 0 becomes 3/(-3) < 0 becomes -1 < 0 (works!)
D. x + y > 0 becomes 3 + (-3) > 0 becomes 0 > 0 (NOPE)
E. xy > 0 becomes (3)(-3) > 0 becomes -9 > 0 (NOPE)

By the process of elimination, the correct answer must be C

Cheers,
Brent

[tomada]

Referring to choice (B), what if x=10 and y= -5? x/y would equal -2, which satisfies the inequality.

If x > 2 and y < -2, then:

A. x/y > 1
B. x/y < -1
C. x/y < 0
D. x + y > 0
E. xy > 0

When posting questions, please use the spoiler function to hide the correct answer. This will allow others to attempt the question without seeing the final answer.

As seyna points out, we can solve this quickly by choosing the x- and y-values that satisfy the given conditions, and see which answer choices can be eliminated.

x = 3 and y = -3 satisfy the given conditions.
Now we'll plug these values into the answer choices and see what happens.

A. x/y > 1 becomes 3/(-3) > 1 becomes -1 > 1 (NOPE)
B. x/y < -1 becomes 3/(-3) < -1 becomes -1 < -1 (NOPE)
C. x/y < 0 becomes 3/(-3) < 0 becomes -1 < 0 (works!)
D. x + y > 0 becomes 3 + (-3) > 0 becomes 0 > 0 (NOPE)
E. xy > 0 becomes (3)(-3) > 0 becomes -9 > 0 (NOPE)

By the process of elimination, the correct answer must be C

Cheers,
Brent

[tomada]

Referring to choice (B), what if x=10 and y= -5? x/y would equal -2, which satisfies the inequality.

If x > 2 and y < -2, then:

A. x/y > 1
B. x/y < -1
C. x/y < 0
D. x + y > 0
E. xy > 0

When posting questions, please use the spoiler function to hide the correct answer. This will allow others to attempt the question without seeing the final answer.

As seyna points out, we can solve this quickly by choosing the x- and y-values that satisfy the given conditions, and see which answer choices can be eliminated.

x = 3 and y = -3 satisfy the given conditions.
Now we'll plug these values into the answer choices and see what happens.

A. x/y > 1 becomes 3/(-3) > 1 becomes -1 > 1 (NOPE)
B. x/y < -1 becomes 3/(-3) < -1 becomes -1 < -1 (NOPE)
C. x/y < 0 becomes 3/(-3) < 0 becomes -1 < 0 (works!)
D. x + y > 0 becomes 3 + (-3) > 0 becomes 0 > 0 (NOPE)
E. xy > 0 becomes (3)(-3) > 0 becomes -9 > 0 (NOPE)

By the process of elimination, the correct answer must be C

Cheers,
Brent

[tomada]

Referring to choice (B), what if x=10 and y= -5? x/y would equal -2, which satisfies the inequality.

If x > 2 and y < -2, then:

A. x/y > 1
B. x/y < -1
C. x/y < 0
D. x + y > 0
E. xy > 0

When posting questions, please use the spoiler function to hide the correct answer. This will allow others to attempt the question without seeing the final answer.

As seyna points out, we can solve this quickly by choosing the x- and y-values that satisfy the given conditions, and see which answer choices can be eliminated.

x = 3 and y = -3 satisfy the given conditions.
Now we'll plug these values into the answer choices and see what happens.

A. x/y > 1 becomes 3/(-3) > 1 becomes -1 > 1 (NOPE)
B. x/y < -1 becomes 3/(-3) < -1 becomes -1 < -1 (NOPE)
C. x/y < 0 becomes 3/(-3) < 0 becomes -1 < 0 (works!)
D. x + y > 0 becomes 3 + (-3) > 0 becomes 0 > 0 (NOPE)
E. xy > 0 becomes (3)(-3) > 0 becomes -9 > 0 (NOPE)

By the process of elimination, the correct answer must be C

Cheers,
Brent

[Brent@GMATPrepNow]

Referring to choice (B), what if x=10 and y= -5? x/y would equal -2, which satisfies the inequality.

That's correct, but let's see what happens when x = 10 and y = -5.
When we plug these values into the answer choices, we get.

A. x/y > 1 becomes 10/(-5) > 1 becomes -2 > 1 (NOPE - ELIMINATE)
B. x/y < -1 becomes 10/(-5) < -1 becomes -2 < -1 (works - keep)
C. x/y < 0 becomes 10/(-5) < 0 becomes -2 < 0 (works - keep)
D. x + y > 0 becomes 10 + (-5) > 0 becomes 5 > 0 (works - keep)
E. xy > 0 becomes (10)(-5) > 0 becomes -50 > 0 (NOPE - ELIMINATE)

Keep in mind we're looking for an answer choice that is ALWAYS true. Since A and E weren't true for the numbers we chose, we'll eliminate them.

Since we still have 3 possible correct answers, we'll need to choose another set of numbers.
How about x = 3 and y = -3.
Now we'll plug these values into the 3 REMAINING answer choices and see what happens.

B. x/y < -1 becomes 3/(-3) < -1 becomes -1 < -1 (NOPE - ELIMINATE)
C. x/y < 0 becomes 3/(-3) < 0 becomes -1 < 0 (works!)
D. x + y > 0 becomes 3 + (-3) > 0 becomes 0 > 0 (NOPE - ELIMINATE)

Now that we've eliminated A, B, D and E, the correct answer must be C

Cheers,
Brent

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Hi tomada,

The original post isn't complete; an Official GMAT question would have included the phrase "which of the following must be true?" at the end of the prompt. Brent has properly explained why the correct answer is the correct answer. When tackling these types of questions, it's important to consider the difference between "what is SOMETIMES true" vs. "what is ALWAYS true." In these situations, plan on finding examples that prove a given answer isn't necessarily true, so that you can eliminate it.

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