Problem Solving - Inequality : PS Archive
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Problem Solving - Inequality

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Problem Solving - Inequality [#permalink]

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New post 25 Jul 2010, 10:43
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A
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C
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E

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Question Stats:

0% (00:00) correct 100% (00:38) wrong based on 3 sessions

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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
[Reveal] Spoiler: OA
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Re: Problem Solving - Inequality [#permalink]

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New post 25 Jul 2010, 10:57
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, 10:57
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