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11 Jun 2018, 06:39
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A
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:
66% (01:44) correct
34%
(00:59)
wrong
based on 35
sessions
History
Date
Time
Result
Not Attempted Yet
11 Jun 2018, 06:39
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Official Solution:
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the question.
Modifying the question:
\(xy < -(x/y)\)
⇔ \(xy^3 < -xy\) (multiplying both sides by \(y^2\))
⇔ \(xy^3 + xy\) < 0
⇔ \(xy(y^2+1)\) < 0
⇔ \(xy < 0\) since \(y^2+1 > 0\)
Condition 1): \(xy < 0\)
Condition 1) is same as the question.
This condition is sufficient.
Condition 2):
Since this condition tells us nothing about \(x\), it is not sufficient.
Therefore, the answer is A.
Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
Answer: A
Answer: A
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the question.
Modifying the question:
\(xy < -(x/y)\)
⇔ \(xy^3 < -xy\) (multiplying both sides by \(y^2\))
⇔ \(xy^3 + xy\) < 0
⇔ \(xy(y^2+1)\) < 0
⇔ \(xy < 0\) since \(y^2+1 > 0\)
Condition 1): \(xy < 0\)
Condition 1) is same as the question.
This condition is sufficient.
Condition 2):
Since this condition tells us nothing about \(x\), it is not sufficient.
Therefore, the answer is A.
Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
Answer: A
Answer: A
ArupRS
23 Feb 2019, 10:20
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