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# If x and y are integers and y=|x+3|+|4-x| , does y=7? (1)

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If x and y are integers and y=|x+3|+|4-x| , does y=7? (1) [#permalink]  07 Aug 2008, 09:38
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If x and y are integers and y=|x+3|+|4-x| , does y=7?

(1) x<4

(2) x>-3
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Re: PowerPrep DS question [#permalink]  07 Aug 2008, 09:38
OA is C, but I have no clue why.
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Re: PowerPrep DS question [#permalink]  07 Aug 2008, 09:44
lumone wrote:
OA is C, but I have no clue why.

Enter X= -2 , -1, 0 , 1, 2, 3 in the expression you always get Y = 7
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Re: PowerPrep DS question [#permalink]  07 Aug 2008, 09:46
Y = (-x-3) + (-4+x)
Y= -7
i think option "1" is correct then
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Re: PowerPrep DS question [#permalink]  07 Aug 2008, 10:19
lumone wrote:
If x and y are integers and y=|x+3|+|4-x| , does y=7?

(1) x<4

(2) x>-3

1) x<4
--> x-4<0 --> 4-x>0
--> |4-x| +ve
|x+3| can be +ve or -ve (x=2 +ve X=-5 -VE)

insuffcient
(2) x>-3 --> x+3>0
means |x+3| = x+3 +ve
but |4-x| can be -ve (-4+x) or +ve ( 4-x)
so insufficient

combine both 4-x>0 and x+3>0
both |x+3| , |4-x| lead positive values
y= |x+3|+|4-x|
= x+3+4-x =7

Clear C.
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Re: PowerPrep DS question [#permalink]  07 Aug 2008, 10:27
Expert's post
lumone wrote:
If x and y are integers and y=|x+3|+|4-x| , does y=7?

(1) x<4

(2) x>-3

Remember that |a - b| is just the distance between a and b on the number line.

Write the question as:

y=|x - (-3)| + |4-x|

In words, this says: "y is equal to the distance from x to -3 plus the distance from x to 4. Draw a number line, draw the points -3 and 4, and put x in the middle. If you add the two distances, you clearly get 7, the distance from -3 to 4. If x is less than -3 or larger than 4, the sum of the distances will be larger than 7. Easy to see if you draw the picture. So we need both statements: C.
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Re: PowerPrep DS question [#permalink]  07 Aug 2008, 10:47
lumone wrote:
x2suresh wrote:
lumone wrote:
If x and y are integers and y=|x+3|+|4-x| , does y=7?

(1) x<4

(2) x>-3

1) x<4
--> x-4<0 --> 4-x>0
--> |4-x| +ve
|x+3| can be +ve or -ve (x=2 +ve X=-5 -VE)

insuffcient
(2) x>-3 --> x+3>0
means |x+3| = x+3 +ve
but |4-x| can be -ve (-4+x) or +ve ( 4-x)
so insufficient

combine both 4-x>0 and x+3>0
both |x+3| , |4-x| lead positive values
y= |x+3|+|4-x|
= x+3+4-x =7

Clear C.

what's ve?

+ve --> positive
-ve --> negative
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Re: PowerPrep DS question [#permalink]  07 Aug 2008, 16:31
lumone wrote:
If x and y are integers and y=|x+3|+|4-x| , does y=7?

(1) x<4

(2) x>-3

to solve this question lets consider three sets of values for x
x<0------I
x>0------II
x=0------III

in region I ,y= 3-x+4+x=7
in region II , y=3+x+4-x=7
in region III , y=3+4=7
hence always irrespective ofd any value of x we get y=7 why require I and II
infact both are individually sufficient
IMO D
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Re: PowerPrep DS question [#permalink]  07 Aug 2008, 16:32
farrukhiq wrote:
Y = (-x-3) + (-4+x)
Y= -7
i think option "1" is correct then

I dont agree with since |-x-3|=x+3
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Re: PowerPrep DS question   [#permalink] 07 Aug 2008, 16:32
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