Is the sum of xy and yx positive?(1) xy 0(2) x + y 0a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'C'. Can you explain this answer?

EduRev

All Courses

Explore Courses UPSC Exam UPSC Test Series Free Notes EduRev Infinity

Open App

GMAT Exam > GMAT Questions > Is the sum of xy and yx positive?(1) xy >...

Join the Discussion on the App

Is the sum of x^y and y^x positive?

(1) xy > 0

(2) x + y > 0

a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Correct answer is option 'C'. Can you explain this answer?

FREE This question is part of

Test: Exponents- 2

Attempt Test

Attempt this Test

Verified Answer

Is the sum of xy and yx positive?(1) xy > 0(2) x + y > 0a)Stat...

Steps 1 & 2: Understand Question and Draw Inferences

To Find: If x^y + y^x > 0

Step 3: Analyze Statement 1 independently

(1) xy > 0

Tells that x and y are of the same sign. Two cases arise:
- x, y > 0
  - In this case x^y, y^x > 0. So, x^y + y^x > 0
- x, y < 0
  - In this case, x^y + y^x may or may not be positive, depending on the values of x and y. Following cases can arise:
  - Both x, y are even → In this case x^y,y^x > 0. So, x^y+y^x > 0
  - Both x and y are odd → In this case x^y,y^x< 0. So, x^y+y^x< 0
  - x is even and y is odd → In this case x^y < 0, y^x > 0. Cannot comment on the value ofx^y+y^x
  - x is odd and y is even → In this case x^y < 0, y^x > 0. Cannot comment on the value of x^y+y^x

Insufficient to answer.

Step 4: Analyze Statement 2 independently

(2) x + y > 0

Considering the constraint x + y > 0, following cases are possible:
- x, y > 0. So, x + y > 0. In this case, x^y, y^x > 0. So, x^y + y^x > 0
- x < 0, y > 0 and |y| > |x|. So, x + y > 0. In this case x^y + y^x may or may not be positive.
  - If y is odd, then x^y < 0 , y^x > 0 as y is positive. In this case, we cannot comment on the value of x^y + y^x
  - If y is even , then x^y > 0 , y^x > 0 as y is positive. In this case, x^y + y^x> 0
- x > 0, y < 0 and |x| > |y|. So, x + y > 0. In this case x^y + y^x may or may not be positive.

Insufficient to answer.

Step 5: Analyze Both Statements Together (if needed)

From Statement 1, xy > 0
From Statement 2, x + y > 0

Statement-1 tells us that x and y have the same signs. Following cases are possible:

If x & y > 0, xy > 0 and x + y > 0. In this case x^y + y^x > 0
If x & y < 0, x+ y < 0. Not possible. (If x & y both are negative, the x + y cannot be > 0)

The only possible case is when x, y > 0 and hence x^y + y^x > 0

Sufficient to answer.

Answer: C

View all questions of this test

View all answers Start learning for free

< Previous Question Next Question >

Explore Courses for GMAT exam

Similar GMAT Doubts

This data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in a leap year or the meaning of the word counterclockwis e), you must indicate whether -Q.If x and y are positive integers, is y odd?1. x is odd.2.xy is odd.

View answer

This data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in a leap year or the meaning of the word counterclockwis e), you must indicate whether -Q.How many of the numbers x, y, and z are positive if each of these numbers is less than 10?1. x + y + z = 202.x + y = 14

View answer

Directions: Each Data Sufficiency problem consists of a question and two statements labeled (1) and (2), that provide data. Based on the data given plus your knowledge of mathematics and everyday facts, you must decide whether the data are sufficient for answering the question. The five answer choices are the same for every data sufficiency question.What is the value of positive two-digit integer x?(1) The sum of the two digits is 5.(2) x is prime.

View answer

This data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in a leap year or the meaning of the word counterclockwis e), you must indicate whether -Q.Is the positive integer X divisible by 21?1. When X is divided by 14, the remainder is 42.When X is divided by 15, the remainder is 5

View answer

Directions: The data sufficiency problem consists of a question and two statements, labeled (1)and (2), in which certain data are given. You have to decide whether the data given in thestatements are sufficient for answering the question. Using the data given in the statements plusyour knowledge of mathematics and everyday facts (such as the number of days in July or themeaning of counterclockwis e), you must indicate whetherQ.1. x is positive2.

View answer

Top Courses for GMATView all

GMAT Focus Edition Mock Test Series 2024

Top Courses for GMAT

View all

Is the sum of xy and yx positive?(1) xy > 0(2) x + y > 0a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'C'. Can you explain this answer?

Share with a Friend

Answer this doubt

Question Description
Is the sum of xy and yx positive?(1) xy > 0(2) x + y > 0a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'C'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Is the sum of xy and yx positive?(1) xy > 0(2) x + y > 0a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Is the sum of xy and yx positive?(1) xy > 0(2) x + y > 0a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'C'. Can you explain this answer?.

Solutions for Is the sum of xy and yx positive?(1) xy > 0(2) x + y > 0a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT. Download more important topics, notes, lectures and mock test series for GMAT Exam by signing up for free.

Here you can find the meaning of Is the sum of xy and yx positive?(1) xy > 0(2) x + y > 0a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of Is the sum of xy and yx positive?(1) xy > 0(2) x + y > 0a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'C'. Can you explain this answer?, a detailed solution for Is the sum of xy and yx positive?(1) xy > 0(2) x + y > 0a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of Is the sum of xy and yx positive?(1) xy > 0(2) x + y > 0a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice Is the sum of xy and yx positive?(1) xy > 0(2) x + y > 0a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice GMAT tests.

Explore Courses for GMAT exam