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# What is the value of x^2 - 6x + 12? (1) (x - 2)(x - 4) = 0 (2) 7x - 3

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Re: What is the value of x^2 - 6x + 12? (1) (x - 2)(x - 4) = 0 (2) 7x - 3 [#permalink]
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Q. What is the value of x^2 - 6x + 12 = (x-3)^2 + 3?

(1) (x - 2)(x - 4) = 0
x=2 or x=4
x=2 --> (2-3)^2 + 3 = 4
x=4 --> (4-3)^2 + 3 = 4
Thus, the value of x^2 - 6x + 12 is 4
SUFFICIENT

(2) 7x - 3 = 25
x=4 --> (4-3)^2 + 3 = 4
Thus, the value of x^2 - 6x + 12 is 4
SUFFICIENT

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Re: What is the value of x^2 - 6x + 12? (1) (x - 2)(x - 4) = 0 (2) 7x - 3 [#permalink]
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the given expression: $$x^2 - 6x + 12$$

statement 1: (x - 2)(x - 4) = 0
from this, we can say x = 2 or 4

if x = 2, then $$x^2 - 6x + 12 = 2^2 - 6*2 + 12 = 4 - 12 + 12 = 4$$
if x = 4, then $$x^2 - 6x + 12 = 4^2 - 6*4 + 12 = 16 - 24 + 12 = 4$$

we can say for either value of x, the expression is equal to 4
hence, statement 1 is sufficient

statement 2: 7x - 3 = 25 implies x = 4
as we have only one value of x, we can determine the value of the given expression
hence, statement 2 is sufficient

option D
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Re: What is the value of x^2 - 6x + 12? (1) (x - 2)(x - 4) = 0 (2) 7x - 3 [#permalink]
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$$x^2-6x+12=x^2-6x+9+3=(x-3)^2+3$$

So our answer depends on the value of $$(x-3)^2$$

(1) $$(x-2)(x-4)=0$$

$$x=2$$ or $$4$$. In both cases, $$(x-3)^2=1$$

So 1 is sufficient

(2) $$7x-3=25$$

So $$x=4$$ and $$(x-3)^2=1$$

2 is sufficient

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Re: What is the value of x^2 - 6x + 12? (1) (x - 2)(x - 4) = 0 (2) 7x - 3 [#permalink]
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Quote:
What is the value of x2−6x+12x2−6x+12?

(1) (x−2)(x−4)=0(x−2)(x−4)=0
(2) 7x−3=25

(1) sufic
x=2: 4-12+12=4
x=4: 16-24+12=4

(2) sufic
7x=28, x=4, sub x, the ans=4

Ans (D)
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What is the value of x^2 - 6x + 12? (1) (x - 2)(x - 4) = 0 (2) 7x - 3 [#permalink]

both statements individually suffice.

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Originally posted by urmi760 on 07 May 2020, 08:25.
Last edited by urmi760 on 26 May 2020, 12:46, edited 1 time in total.
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Re: What is the value of x^2 - 6x + 12? (1) (x - 2)(x - 4) = 0 (2) 7x - 3 [#permalink]
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Kudos
Based on Statement 1: The equation can have only 2 values of x for which (X-2)(x-4)=0 i.e, x=2,4
For both the value of x the original expression X^2 - 6*x + 12 will give the same result as 4 so statement is sufficient to answer the question
Based on statement 2: 7x - 3 = 25 has only 1 solution i.e, x=4 for this x = 4 , the original equation X^2 - 6*x + 12 has the value of 4 hence this statement is also sufficient.

Combining both the conclusion from each statement, D is appropriate choice i.e, each statement is sufficient to answer
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Re: What is the value of x^2 - 6x + 12? (1) (x - 2)(x - 4) = 0 (2) 7x - 3 [#permalink]
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Re: What is the value of x^2 - 6x + 12? (1) (x - 2)(x - 4) = 0 (2) 7x - 3 [#permalink]
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