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# If x is an integer, is |2x - 5| + |3x - 10| = 5 - x ? (1) x

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GMAT Instructor
Joined: 04 Jul 2006
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If x is an integer, is |2x - 5| + |3x - 10| = 5 - x ? (1) x [#permalink]

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15 Feb 2008, 02:42
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If x is an integer, is |2x - 5| + |3x - 10| = 5 - x ?

(1) x is divisible by 2
(2) x is positive

Kudos [?]: 336 [1], given: 0

Senior Manager
Joined: 06 Jul 2006
Posts: 291

Kudos [?]: 75 [0], given: 0

Location: SFO Bay Area
Schools: Berkeley Haas
Re: DS: Absolute Values [#permalink]

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15 Feb 2008, 02:50
Should be A.

St1. Using x = -4 or -2 or 2 or 4 etc....LHS will never be equal to RHS...So it is sufficient.
St2 : Using x> 0, LHS will never be equal to RHS, except when x = 3...Hence not sufficient.

Last edited by suntaurian on 15 Feb 2008, 09:58, edited 1 time in total.

Kudos [?]: 75 [0], given: 0

Director
Joined: 01 Jan 2008
Posts: 618

Kudos [?]: 198 [0], given: 1

Re: DS: Absolute Values [#permalink]

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15 Feb 2008, 07:53
kevincan wrote:
If x is an integer, is |2x - 5| + |3x - 10| = 5 - x ?

(1) x is divisible by 2
(2) x is positive

three intervals: x < 5/2, 5/2 <= x < 10/3 and 10/3 <= x <= 5
two solutions 5/2 and 10/3 -> I can expand on that if necessary

1) sufficient because if x is divisible by 2, it can't be equal to 5/2 or 10/3
2) insuffcient -> can be equal to 5/2, 10/3 or not (for example, 1 or 2)

A is the answer

PS: kevin, great questions (+2)

Kudos [?]: 198 [0], given: 1

Senior Manager
Joined: 06 Jul 2006
Posts: 291

Kudos [?]: 75 [0], given: 0

Location: SFO Bay Area
Schools: Berkeley Haas
Re: DS: Absolute Values [#permalink]

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15 Feb 2008, 09:53
maratikus wrote:
kevincan wrote:
If x is an integer, is |2x - 5| + |3x - 10| = 5 - x ?

(1) x is divisible by 2
(2) x is positive

three intervals: x < 5/2, 5/2 <= x < 10/3 and 10/3 <= x <= 5
two solutions 5/2 and 10/3 -> I can expand on that if necessary

1) sufficient because if x is divisible by 2, it can't be equal to 5/2 or 10/3
2) insuffcient -> can be equal to 5/2, 10/3 or not (for example, 1 or 2)

A is the answer

PS: kevin, great questions (+2)

X is an integer, not a fraction. So i am not sure, if what you have explained is still vaid.

Whats the OA ?

Kudos [?]: 75 [0], given: 0

Director
Joined: 01 Jan 2008
Posts: 618

Kudos [?]: 198 [0], given: 1

Re: DS: Absolute Values [#permalink]

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15 Feb 2008, 10:14
kevincan wrote:
If x is an integer, is |2x - 5| + |3x - 10| = 5 - x ?

(1) x is divisible by 2
(2) x is positive

i don't know what's wrong with me. I miscalculated and didn't read the problem.

the only integer solution is 3

1) sufficient -> x ! = 3
2) insufficient

the answer should be A

Kudos [?]: 198 [0], given: 1

Re: DS: Absolute Values   [#permalink] 15 Feb 2008, 10:14
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# If x is an integer, is |2x - 5| + |3x - 10| = 5 - x ? (1) x

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