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17 Apr 2018, 08:35
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
45% (02:04) correct
55%
(02:25)
wrong
based on 141
sessions
History
Date
Time
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If \(f(n) = 6n^2 + 4n + 8\) and \(g(n) = 4n^2 - 8n - 11\), the value of \(f(x) - g(x)\) ?
(1) \(g(x) = -15\)
(2) \(x^2 + 6x = 7\)
(1) \(g(x) = -15\)
(2) \(x^2 + 6x = 7\)
17 Apr 2018, 18:04
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itisSheldon
f(x) - g(x)=6\(x^2\)+4x+8 -4\(x^2\)+8x+11
=2\(x^2\)+12x+19
=2(\(x^2\)+6x- 7) +33 ............................. eqn1
1) g(x) = -15 or 4\(x^2\)-8x-11=-15
or 4\(x^2\)-8x+4=0
or 4(\(x^2\)-2x+1)=0
or 4\((x-1)^2\)=0
or x=1......substituting x in eqn1 we will get a definite value of f(x) - g(x).... Thus Sufficient
2) \(x^2\)+6x = 7 or \(x^2\)+6x -7=0 ......substituting this expression in eqn1 we will get a definite value of f(x) - g(x).... Thus Sufficient
Hence the answer is D.
18 Apr 2018, 08:34
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itisSheldon
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.
\(f(x) - g(x)\)
\(= ( 6x^2 +4x+8) - (4x^2-8x-11)\)
\(= 6x^2 + 4x + 8 - 4x^2 +8x +11\)
\(= 2x^2 + 12x + 19\)
The question asks for the value of \(2x^2 + 12x + 19\).
Since we have 1 variable (x) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.
Condition 1) : \(g(x) = -15\)
\(4x^2 - 8x - 11 = -15\)
\(⇔ 4x^2 - 8x + 4 = 0\)
\(⇔ 4( x^2 - 2x + 1 ) = 0\)
\(⇔ 4( x - 1 )^2 = 0\)
\(⇔ x = 1\)
Thus \(f(1) - g(1) = 2*1^2 + 12*1 + 19 = 2 + 12 + 19 = 33\).
Condition 1) is sufficient.
Condition 2) : \(x^2 + 6x = 7\)
\(x^2 + 6x = 7\)
\(⇔ x^2 + 6x - 7 = 0\)
\(⇔ (x-1)(x+7) = 0\)
\(⇔ x = 1\) or \(x = -7\)
\(f(1) - g(1) = 2*1^2 + 12*1 + 19 = 2 + 12 + 19 = 33\)
\(f(-7) - g(-7) = 2*(-7)^2 + 12*(-7) + 19 = 98 - 84 + 19 = 33\).
Since the answer is unique, condition 2) is sufficient.
Therefore, D is the answer.
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.
