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# If f(n) = 6n^2 + 4n + 8 and g(n) = 4n^2 - 8n - 11, the value of f(x)

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Joined: 03 Mar 2018
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If f(n) = 6n^2 + 4n + 8 and g(n) = 4n^2 - 8n - 11, the value of f(x)  [#permalink]

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17 Apr 2018, 07:35
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95% (hard)

Question Stats:

36% (01:51) correct 64% (02:27) wrong based on 62 sessions

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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) $$x^2 + 6x = 7$$

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Re: If f(n) = 6n^2 + 4n + 8 and g(n) = 4n^2 - 8n - 11, the value of f(x)  [#permalink]

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17 Apr 2018, 17:04
itisSheldon wrote:
If f(n) = 6$$n^2$$+4n+8 and g(n) = 4$$n^2$$-8n-11 , the value of f(x) - g(x) ?

1) g(x) = -15
2) $$x^2$$+6x = 7

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

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Re: If f(n) = 6n^2 + 4n + 8 and g(n) = 4n^2 - 8n - 11, the value of f(x)  [#permalink]

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18 Apr 2018, 07:34
itisSheldon wrote:
If f(n) = 6$$n^2$$+4n+8 and g(n) = 4$$n^2$$-8n-11 , the value of f(x) - g(x) ?

1) g(x) = -15
2) $$x^2$$+6x = 7

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.

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.
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Re: If f(n) = 6n^2 + 4n + 8 and g(n) = 4n^2 - 8n - 11, the value of f(x) &nbs [#permalink] 18 Apr 2018, 07:34
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