What is the value of m? (1) |1 - x| = m - 3 (2) |2 - m| = 7

Question

What is the value of m?

(1) |1 - x| = m - 3
(2) |2 - m| = 7

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ShankSouljaBoi · Answer

C

I is insufficient as no info about x is given

II is insufficient as m can be equal to -5 or 9

On combining I and II,
|1-x| = -8 ( when m=-5 ) but distance can be zero or positive only. Hence, this is not a solution.

When m = 9 |1-x| = 6 ---> x will have two values we need not calculate . Only m=9 is the solution. Hence, C is correct

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Kinshook · Answer

Asked: What is the value of m?

(1) |1 - x| = m - 3
m-3>=0
m>=3
NOT SUFFICIENT

(2) |2 - m| = 7
m = 2 + -7
m = -5 or m = 9
NOT SUFFICIENT

(1) + (2)
(1) |1 - x| = m - 3
m-3>=0
m>=3
(2) |2 - m| = 7
m = 2 + -7
m = -5 or m = 9
Since m>3
m = 9
SUFFICIENT

IMO C

CareerGeek · Answer

(1) |1 - x| = m - 3
Note that, least value of modulus is 0
--> m - 3 ≥ 0
--> m ≥ 3 
--> No Definite Value -->  Insufficient

(2) |2 - m| = 7
--> (2 - m) = 7 or -(2 - m) = 7
--> m = 2 - 7 or -2 + m = 7
--> m = -5 or 9 -->  Insufficient

Combining (1) & (2),
m ≥ 3 and m = -5 or 9
Common value of m = 9 ONLY
--> A Unique value -->  Sufficient

Option C

exc4libur · Answer

(1) insufic

|abs value|>=0
m-3>=0, m>=3

(2) insufic

|positive|: 2-m=7, m=-5
|negative|: 2-m=-7, m=9

(1/2) sufic

since m>=3, then m!=-5, so m=9

Ans (C)

rajtare · Answer

1) In sufficient as no information about x is provided 2) if m>2, then 2-m will be <0, thus -(2-m)=7 or m=9 if m<2, then 2-m will be >0, thus 2-m =7, or m=-5 Clearly not sufficient now lets combine equation 1, and 2 if x>1, 1-x will be <0, thus -(1-x) = m-3 or x= m-2, we already know that m has two possible value m=7, and m=-5, in this scenario m=-5 not possible as x>1. hence m=7 if x<1, 1-x will be >0, thus 1-x =m-3 x=4-m, again we know two possible value of m are 7, and 5, in this scenario m=-5 not possible as x<1, hence m=7 since only m=7 satisfy the equation therefore answer should be C.

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What is the value of m? (1) |1 - x| = m - 3 (2) |2 - m| = 7

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