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May 0510:00 AM PDT
-11:00 AM PDT
GMAT Inequalities is a high-frequency topic in GMAT Quant, but many students struggle because the concepts behave differently from standard algebra. Understanding the right rules, patterns, and edge cases can significantly improve both speed and accuracy.
29 May 2019, 00:19
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
64% (02:01) correct
36%
(01:54)
wrong
based on 104
sessions
History
Date
Time
Result
Not Attempted Yet
29 May 2019, 03:22
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Inequalities is a tricky topic which tests you on your reasoning and number skills in equal measure. The best way to approach an Inequality question is to analyze the question stem.
Here the question stem is relatively easy to break down. We need to prove whether x and y have different signs.
Statement 1 : x + y > 2
Clearly x and y can be of the same signs or of different signs. Anytime you are unsure, do not hesitate to plug in values, especially while working with the statements individually.
x = 2 and y = 1 will give us a NO
x = 4 and y = -1 will give us a YES.
Statement 2 : x + 2y < -1
x = 1 and y = -4 will give us a YES
x = -1 and y = -4 will give us a NO
Takeaway:
Now the tricky part is when you need to combine the two statements. In a DS question, the best way to evaluate statements together is to
1. Substitute one statement into the other
2. Use a mathematical operation or a combination of mathematical operations between the two statements, which lead to answering the main questions. In simpler words, algebraically manipulate the statements to answer the question.
While dealing with Inequalities this process becomes easier, as the only mathematical operation that you can perform between two inequations is ADDITION. Subtraction, multiplication and division can only be done in specific cases (when signs are known). Addition though can be performed anywhere as long as the inequality signs are the same.
The two statements here are:
x + y > 2
x + 2y < -1
Multiplying the second equation by -1 and flipping the sign we get,
x + y > 2
-x - 2y > 1
Adding the two equations we get -y > 3 ----> y < -3, so y will always be negative.
Now we know that -y > 3, adding this to the first statement we get, x > 5, so x will always be positive.
Since x and y are of different signs, combing the statements gives us sufficiency.
Hope this helps!
Aditya
Senior Quant Expert
CrackVerbal
Here the question stem is relatively easy to break down. We need to prove whether x and y have different signs.
Statement 1 : x + y > 2
Clearly x and y can be of the same signs or of different signs. Anytime you are unsure, do not hesitate to plug in values, especially while working with the statements individually.
x = 2 and y = 1 will give us a NO
x = 4 and y = -1 will give us a YES.
Statement 2 : x + 2y < -1
x = 1 and y = -4 will give us a YES
x = -1 and y = -4 will give us a NO
Takeaway:
Now the tricky part is when you need to combine the two statements. In a DS question, the best way to evaluate statements together is to
1. Substitute one statement into the other
2. Use a mathematical operation or a combination of mathematical operations between the two statements, which lead to answering the main questions. In simpler words, algebraically manipulate the statements to answer the question.
While dealing with Inequalities this process becomes easier, as the only mathematical operation that you can perform between two inequations is ADDITION. Subtraction, multiplication and division can only be done in specific cases (when signs are known). Addition though can be performed anywhere as long as the inequality signs are the same.
The two statements here are:
x + y > 2
x + 2y < -1
Multiplying the second equation by -1 and flipping the sign we get,
x + y > 2
-x - 2y > 1
Adding the two equations we get -y > 3 ----> y < -3, so y will always be negative.
Now we know that -y > 3, adding this to the first statement we get, x > 5, so x will always be positive.
Since x and y are of different signs, combing the statements gives us sufficiency.
Hope this helps!
Aditya
Senior Quant Expert
CrackVerbal
General Discussion
Statement 1.
Either both x &y are positive or one of them is +ve, other is -ve
Hence x*y can be +ve or -ve
Insufficient
Statement 2
Either both x &y are -ve or one of them is +ve, other is -ve
Hence x*y can be +ve or -ve
Insufficient
Combining both equations
one of them is +ve and other is -ve
xy<0
Sufficient
IMO C
Either both x &y are positive or one of them is +ve, other is -ve
Hence x*y can be +ve or -ve
Insufficient
Statement 2
Either both x &y are -ve or one of them is +ve, other is -ve
Hence x*y can be +ve or -ve
Insufficient
Combining both equations
one of them is +ve and other is -ve
xy<0
Sufficient
IMO C
