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

Are You Up For the Challenge: 700 Level Questions

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

Posted from my mobile device

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.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards