Question: If x > 0 and y < 0, which of the following is always true?

(A) x – y > y – x
(B) x + y > 0
(C) xy > 0
(D) y > x
(E) x – y < 0

Correct Answer: A
Solution and Explanation:
Approach Solution 1:

To answer this GMAT question, apply the data that was provided in the question. These issues pertain to many different branches of mathematics. This query relates to algebra. It is challenging to choose the best option due to the way the options are presented. Applicants must be able to understand the proper strategy for getting the desired response. There is only one correct answer out of the five options offered.

Asked: Which of the following is always true if x > 0 and y < 0?

(A) y > x, x > y, and y > 0
y - x < 0
x - y > 0 > y - x
ALWAYS TRUE:

(B) x = 1;
y = - 2;
x + y = -1 < 0
x = 2; y = - 1;
x + y = 1 > 0
NOT ESSENTIALLY TRUE

(C) ALWAYS FALSE
xy > 0
Xy < 0

(D) ALWAYS FALSE
y > x
X > y

(E) x - y < 0
x -y > 0
ALWAYS FALSE

A is the correct answer.

Approach Solution 2:

To answer this GMAT question, apply the data that was provided in the question. These issues pertain to many different branches of mathematics. This query relates to algebra. It is challenging to choose the best option due to the way the options are presented. Applicants must be able to understand the proper strategy for getting the desired response. There is only one correct answer out of the five options offered.

This is a straightforward and effective strategy: X > 0, indicating that X is positive.
Y is negative since Y0.

1. A) – Y – (+X) > + X – ( – Y) > + X + Y >

Positive > Negative = –  X – Y
It is always the case.

There is no need to consider more possibilities because the question only offers one option.

A is the correct answer.

Approach Solution 3:

To answer this GMAT question, apply the data that was provided in the question. These issues pertain to many different branches of mathematics. This query relates to algebra. It is challenging to choose the best option due to the way the options are presented. Applicants must be able to understand the proper strategy for getting the desired response. There is only one correct answer out of the five options offered.

Given to us that x > 0 and y < 0
It has asked to find out which option will always be true.
In A it is given that,
x - y > y - x
=> 2x > 2 y
=> x > y
Yes it is always true because x is positive and y is negative.

In B,
X + y > 0
If y is more negative then this case won’t hold

In C,
Xy > 0
If both are of different sign then no way that xy > 0

In D,
y > x
Y is negative and x is positive, so not possible

In E
x - y < 0
=> x < y
This is not possible by given conditions.

A is the correct answer.

“If x > 0 and y < 0, which of the following is always true? " - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.

To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The problem-solving section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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