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# If the function f is defined for all x by f( x) = ax^2 + bx − 43,

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If the function f is defined for all x by f( x) = ax^2 + bx − 43, [#permalink]

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20 Dec 2015, 03:47
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65% (hard)

Question Stats:

60% (01:01) correct 40% (01:21) wrong based on 159 sessions

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If the function f is defined for all x by f(x) = ax^2 + bx − 43, where a and b are constants, what is the value of f(3)?

(1) f(4) = 41
(2) 3a + b = 17
[Reveal] Spoiler: OA

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Re: If the function f is defined for all x by f( x) = ax^2 + bx − 43, [#permalink]

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20 Dec 2015, 21:04
$$F(3) = a*3^2 + b*3 -43 => 9a+3b-43=?$$

I. f(4)=41 =>
$$16a + 4b - 43 =41 => 16a + 4b = 84 or 4a + b = 21$$
Nothing can be done with this information
Not Sufficient

II. 3a + b = 17
$$f(3) = 3 (3a+b) -43 = 3 * 17 - 43$$
Sufficient

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Re: If the function f is defined for all x by f( x) = ax^2 + bx − 43, [#permalink]

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21 Dec 2015, 21:30
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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If the function f is defined for all x by f(x) = ax^2 + bx − 43, where a and b are constants, what is the value of f(3)?

(1) f(4) = 41
(2) 3a + b = 17

When you modify the original condition and the question, you only need to know 3a+b from f(3)=a(3^2)+b(3)-43=3(3a+b)-43. 3a+b=17 is in 2), which is unique and sufficient. Therefore, the answer is B.

-> Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.
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Re: If the function f is defined for all x by f( x) = ax^2 + bx − 43, [#permalink]

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21 Dec 2015, 22:22
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Expert's post
Bunuel wrote:
If the function f is defined for all x by f(x) = ax^2 + bx − 43, where a and b are constants, what is the value of f(3)?

(1) f(4) = 41
(2) 3a + b = 17

It is one of those trick questions in which if you are not careful, you could fall for the trap and never know it. The impressions that "two unknowns need two equations to solve" and "a quadratic gives two solutions" are often exploited by the test makers. So be very wary about them.

Statement 1 is straight forward here:
f(x) = ax^2 + bx - 43
f(4) = 41 = 16a + 4b - 43
4a + b = 21
a and b could take different values so you cannot find f(3)

Statement 2 gives 3a + b = 17
You need to find f(3) = 9a + 3b - 43
Note that 9a + 3b = 3(3a + b) so you actually have the value of the desired expression.
So though statement 2 gives you an equation, you have enough information to solve for f(3).

It is good to write down what you need in such questions.
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Re: If the function f is defined for all x by f( x) = ax^2 + bx − 43, [#permalink]

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22 Dec 2015, 00:28
1) f(4) =41 f(3) =?

16a+4b-43=41
4a+b=21 .. NS

2) 3a+b =17

f(3) =9a+3b-43
= 3(3a+b)-43
=3*17-43
= 8 ... S

B

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Re: If the function f is defined for all x by f( x) = ax^2 + bx − 43, [#permalink]

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19 Oct 2016, 19:04
I have a little doubt here
statement 1 gives us an equation 16a+4b-43=41 nd from the question stem we have the equation 9a+3b-43=0
why cant be solve the two equation with two unknown to get the resultant value?

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Re: If the function f is defined for all x by f( x) = ax^2 + bx − 43, [#permalink]

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19 Oct 2016, 23:40
AmritaSarkar89 wrote:
I have a little doubt here
statement 1 gives us an equation 16a+4b-43=41 nd from the question stem we have the equation 9a+3b-43=0
why cant be solve the two equation with two unknown to get the resultant value?

How did you get the red part? We don't know the value of f(3) = 9a + 3b - 43, that's what we are asked to find out.
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Re: If the function f is defined for all x by f( x) = ax^2 + bx − 43, [#permalink]

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20 Oct 2016, 10:38
At first this Q looks like having 2 variables which necessitates 2 equations for finding a solution. This might make us believe that C could be the answer.

St 1 :
f(x) = ax^2 + bx - 43
f(4) = 41 = 16a + 4b - 43
4a + b - 21 = 0 ..... a and b can have any values.
NSUF

St 2: 3a + b = 17
f(3) = 9a + 3b - 43
= 3(3a + b) - 43
= 3( 17 ) - 43
SUF

Hence B

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Re: If the function f is defined for all x by f( x) = ax^2 + bx − 43, [#permalink]

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20 Oct 2016, 19:24
Bunuel wrote:
AmritaSarkar89 wrote:
I have a little doubt here
statement 1 gives us an equation 16a+4b-43=41 nd from the question stem we have the equation 9a+3b-43=0
why cant be solve the two equation with two unknown to get the resultant value?

How did you get the red part? We don't know the value of f(3) = 9a + 3b - 43, that's what we are asked to find out.

if we put the value of x=3 then don't we get the given equation. Maybe I am totally wrong here, can you please explain?

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Re: If the function f is defined for all x by f( x) = ax^2 + bx − 43, [#permalink]

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20 Oct 2016, 20:48
AmritaSarkar89 wrote:
Bunuel wrote:
AmritaSarkar89 wrote:
I have a little doubt here
statement 1 gives us an equation 16a+4b-43=41 nd from the question stem we have the equation 9a+3b-43=0
why cant be solve the two equation with two unknown to get the resultant value?

How did you get the red part? We don't know the value of f(3) = 9a + 3b - 43, that's what we are asked to find out.

if we put the value of x=3 then don't we get the given equation. Maybe I am totally wrong here, can you please explain?

The question asks to find the value of f(3), which is 9a + 3b - 43. You are equating it to 0, which is wrong.
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Re: If the function f is defined for all x by f( x) = ax^2 + bx − 43, [#permalink]

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19 Dec 2017, 07:10
Bunuel wrote:
If the function f is defined for all x by f(x) = ax^2 + bx − 43, where a and b are constants, what is the value of f(3)?

(1) f(4) = 41
(2) 3a + b = 17

Given
=> f(x)=ax^2+bx-43
=> f(x)=x(ax+b)-43 ----(1)

Therefore
=> f(3)=3(3a+b)-43

So if we can find the value of a & b or (3a+b) we can find f(3)

Statement 1 says f(4)=41
Now f(4)=4(4a+b)-43 from (1)
=> 4(4a+b)-43=41
=> 4(4a+b)=84
=> 4a+b=21
We cannot find the value of a & b or (3a+b)
Therefore NOT sufficient

Statement 2 says (3a+b)=17 =>SUFFICIENT

Therefore 'B"

Thanks

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Re: If the function f is defined for all x by f( x) = ax^2 + bx − 43, [#permalink]

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19 Dec 2017, 21:08
Bunuel wrote:
If the function f is defined for all x by f(x) = ax^2 + bx − 43, where a and b are constants, what is the value of f(3)?

(1) f(4) = 41
(2) 3a + b = 17

f(3) = $$a3^2 + 3b - 43$$
= $$9a + 3b - 43$$
= $$3 (3a + b) - 43$$

Looking at each statement, we see that only Statement (2) will be able to satisfy the equation. Since we have the Value of 3a + b given.

Hence, Negate A, D, C, E

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Re: If the function f is defined for all x by f( x) = ax^2 + bx − 43,   [#permalink] 19 Dec 2017, 21:08
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