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Archit3110
Major Poster
31 Dec 2018, 04:03
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MathRevolution
Given
\(\sqrt{(x+1)^2}=x+1\)
or say
\(\sqrt{(x+1)^2} = lx+1l\\
\\
lx+1l= x+1 \\
\\
only for values when x=0 or +/-1\\
\\
so #1:\\
[m]1) x(x-2) = 0\)
x=0 & x=+2
in sufficient
#2
\(2) x(x+2) = 0\)
x=0 & x=-2
in sufficient
from 1 & 2
x=0 sufficient
IMO C
01 Jan 2019, 06:51
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[Math Revolution GMAT math practice question]
(number properties) What is the value of the integer \(n\)?
1) \(n\) is a prime factor of \(21\)
2) \(n\) is a factor of \(49\)
(number properties) What is the value of the integer \(n\)?
1) \(n\) is a prime factor of \(21\)
2) \(n\) is a factor of \(49\)
Updated on: 24 Feb 2021, 03:53
Originally posted by MathRevolution on 02 Jan 2019, 01:42.
Last edited by MathRevolution on 24 Feb 2021, 03:53, edited 1 time in total.
Last edited by MathRevolution on 24 Feb 2021, 03:53, edited 1 time in total.
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MathRevolution
=>
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. We then recheck the question.
The question is equivalent to asking if \(x ≥ -1\) as shown below:
\(\sqrt{(x+1)^2}=x+1\)
\(=> |x+1| = x+1\)
\(=> x ≥ -1\)
Since we have \(1\) variable (\(x\)) and \(0\) equations, D is most likely to be the answer. So, we should consider each condition on its own first.
Condition 1)
\(x(x-2) = 0\)
\(=> x = 0\) or \(x = 2\)
If \(x = 0\), then \(x ≥ -1\) and the answer is ‘yes’.
If \(x = 2\), then \(x ≥ -1\) and the answer is ‘yes’.
Since it gives a unique answer, condition 1) is sufficient.
Condition 2)
\(x(x+2) = 0\)
\(=> x = 0\) or \(x = -2\)
If \(x = 0\), then \(x ≥ -1\) and the answer is ‘yes’.
If \(x = -2\), then \(x < -1\) and the answer is ‘no’.
Since it does not give a unique answer, condition 2) is not sufficient.
Therefore, A is the answer.
Answer: A
If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
