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Problem Solving - Inequality

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Problem Solving - Inequality [#permalink] New post 25 Jul 2010, 11:43
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0% (00:00) correct 100% (00:00) wrong based on 0 sessions
How many soultions are possible for the inequality, mod(x-3)+mod(x-4)<1 ?

a. 3
b. 4
c. 0
d. 6
e. Infinitely many
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Re: Problem Solving - Inequality [#permalink] New post 25 Jul 2010, 11:57
EnterMatrix wrote:
How many soultions are possible for the inequality, mod(x-3)+mod(x-4)<1 ?

a. 3
b. 4
c. 0
d. 6
e. Infinitely many


|x-3| + |x-4| < 1 ; take three cases

1.x>4

|x-3| + |x-4| < 1

x-3 +x-4 <1

x<4 not possible as we have assumed x>4

2.3<x<4

|x-3| + |x-4| < 1

x-3 + 4-x < 1 not possible

3. x<3

|x-3| + |x-4| < 1

3-x + 4-x <1

x> 3 not possible

hence 0 solution
Answer is C

PS: Make sure you check the answer against the domain. It should satisfy the domain.
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Re: Problem Solving - Inequality   [#permalink] 25 Jul 2010, 11:57
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