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# If x and y are integers and y = |x+3|+|4-x| , does y equal 7

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Intern
Joined: 23 Sep 2008
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If x and y are integers and y = |x+3|+|4-x| , does y equal 7 [#permalink]  11 Mar 2009, 06:53
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If x and y are integers and y = |x+3|+|4-x| , does y equal 7 ?

1) x < 4
2) x > -3

Also , please explain a little how to solve these types of questions

I am not able to do well in absolute value questions :/
Director
Joined: 01 Aug 2008
Posts: 770
Followers: 3

Kudos [?]: 92 [1] , given: 99

Re: OG DS - absolute value questn [#permalink]  11 Mar 2009, 09:37
1
KUDOS
mavesum wrote:
If x and y are integers and y = |x+3|+|4-x| , does y equal 7 ?

1) x < 4
2) x > -3

Also , please explain a little how to solve these types of questions

I am not able to do well in absolute value questions :/

Case 1: x < 4

substitute x = 3 in the equation. you get y = |3+3| + |4-3| = 6 + 1 = 7 sufficient.
substitute x = -7 you get y = |-7+3| + | 4-(-7)| = |-3|+|11| = 3+ 11 = 14 insufficient.

Case 2: x > -3
substitute x = -1, you get y = |(-1)+3|+|4-(-1)| = |2|+|4+1| = 7. sufficient.
substitute x = 8, you get y = |8+3|+|4-8| = |11|+|-4| = 11+4 = 15 insufficinet.

together x<4 and x > -3 ...

you get sufficient ...

Senior Manager
Joined: 19 Aug 2006
Posts: 256
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Re: OG DS - absolute value questn [#permalink]  11 Mar 2009, 10:48
mavesum wrote:
If x and y are integers and y = |x+3|+|4-x| , does y equal 7 ?

1) x < 4
2) x > -3

Also , please explain a little how to solve these types of questions

I am not able to do well in absolute value questions :/

1. x=-6
y=|-6+3|+|4+6|=13
insuff.

2. x=20
|20+3|+|4-20|=39
insuff.

combine 1) and 2) - the range is -2,-1,0,1,2,3
trying x for any from this range will result in 7
suffic.
Director
Joined: 01 Apr 2008
Posts: 909
Schools: IIM Lucknow (IPMX) - Class of 2014
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Re: OG DS - absolute value questn [#permalink]  14 Mar 2009, 04:51
Answer should be B. What is OA?

here we have three distinct regions:
1) x<-3
2) -3 < x < 4
3) x> 4

For 1), x+3 is -ve and 4-x is positive, so the eq becomes,
y = -3-x+4-x = 1-2x >> no solution

For 2), x+3 is +ve and 4-x is positive,
y = x+3+4-x = 7 >> this range is true.

For 3), x+3 is +ve and 4-x is positive,
y = 7.

Hence, y = 7 for all x>-3.

mavesum wrote:
If x and y are integers and y = |x+3|+|4-x| , does y equal 7 ?

1) x < 4
2) x > -3

Also , please explain a little how to solve these types of questions

I am not able to do well in absolute value questions :/
Re: OG DS - absolute value questn   [#permalink] 14 Mar 2009, 04:51
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