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Difficulty:
45%
(medium)
Question Stats:
59% (01:17) correct
41%
(01:22)
wrong
based on 307
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What is the value of \(x^2 - 6x + 12\)?
(1) \((x - 2)(x - 4) = 0\)
(2) \(7x - 3 = 25\)
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
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What is the value of \(x^2 - 6x + 12\)?
Simplify/Modify
\(x^2 - 6x + 12=x^2-6x+9+3=(x-3)^2+3\)
(1) \((x - 2)(x - 4) = 0\)
So x is either 2 or 4..
a) x=2...\((x-3)^2+3=(2-3)^2+3=1+3=4\)
b) x=4...\((x-3)^2+3=(4-3)^2+3=1+3=4\)
Suff
(2) \(7x - 3 = 25....7x=28...x=4\)
\((x-3)^2+3=(4-3)^2+3=1+3=4\)
Suff
D
_________________
Simplify/Modify
\(x^2 - 6x + 12=x^2-6x+9+3=(x-3)^2+3\)
(1) \((x - 2)(x - 4) = 0\)
So x is either 2 or 4..
a) x=2...\((x-3)^2+3=(2-3)^2+3=1+3=4\)
b) x=4...\((x-3)^2+3=(4-3)^2+3=1+3=4\)
Suff
(2) \(7x - 3 = 25....7x=28...x=4\)
\((x-3)^2+3=(4-3)^2+3=1+3=4\)
Suff
D
_________________
ArunSharma12
Joined: 24 Oct 2015
Last visit: 20 Jul 2022
Posts: 512
Location: India
Schools: IIML-IPMX '22 (A)
GMAT 1: 650 Q48 V31
GMAT 2: 720 Q49 V38 (Online)
GPA: 4
Products:
Quote:
statement 1:
- x = 2: x^2−6x+12 = 4 - 12 + 12 = 4
x= 4: x^2−6x+12 = 16 - 24 + 12 = 4
statement 2:
x = 4
sufficient
Ans: D
GMAT 1: 720 Q49 V40
Posts: 939
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
FINAL ANSWER IS (D)
Posted from my mobile device
(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
FINAL ANSWER IS (D)
Posted from my mobile device
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
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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Products:
\(x^2-6x+12=x^2-6x+9+3=(x-3)^2+3\)
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
Answer is (D)
Posted from my mobile device
_________________
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
Answer is (D)
Posted from my mobile device
_________________
Quote:
(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)
Answer - D,
both statements individually suffice.
Posted from my mobile device
both statements individually suffice.
Posted from my mobile device
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
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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