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

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Bunuel
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What is the value of m? (1) |1 - x| = m - 3 (2) |2 - m| = 7 [#permalink] New post   25 Mar 2020, 02:13
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Question Stats:

50% (01:31) correct 50% (01:46) wrong based on 262 sessions
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What is the value of m?

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


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C
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What is the value of m? (1) |1 - x| = m - 3 (2) |2 - m| = 7 [#permalink] New post   Updated on: 18 Apr 2024, 01:39
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Bunuel wrote:
What is the value of m?

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


Are You Up For the Challenge: 700 Level Questions

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

Originally posted by Kinshook on 25 Mar 2020, 02:24.
Last edited by Bunuel on 18 Apr 2024, 01:39, edited 2 times in total.
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Re: What is the value of m? (1) |1 - x| = m - 3 (2) |2 - m| = 7 [#permalink] New post   Updated on: 25 Mar 2020, 02:25
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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

Originally posted by ShankSouljaBoi on 25 Mar 2020, 02:20.
Last edited by ShankSouljaBoi on 25 Mar 2020, 02:25, edited 1 time in total.
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Re: What is the value of m? (1) |1 - x| = m - 3 (2) |2 - m| = 7 [#permalink] New post   25 Mar 2020, 02:59
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Bunuel wrote:
What is the value of m?

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


(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
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Re: What is the value of m? (1) |1 - x| = m - 3 (2) |2 - m| = 7 [#permalink] New post   22 Jun 2020, 08:47
Bunuel wrote:
What is the value of m?

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


(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)
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What is the value of m? (1) |1 - x| = m - 3 (2) |2 - m| = 7 [#permalink] New post   08 Oct 2022, 16:00
Bunuel wrote:
What is the value of m?

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


Are You Up For the Challenge: 700 Level Questions


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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Re: What is the value of m? (1) |1 - x| = m - 3 (2) |2 - m| = 7 [#permalink] New post   07 Dec 2023, 21:11
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Re: What is the value of m? (1) |1 - x| = m - 3 (2) |2 - m| = 7 [#permalink]
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