absolute values - DS Q 21 Section 8

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absolute values - DS Q 21 Section 8

by gmatrant » Sat Nov 03, 2007 10:07 pm
If x and y are integers and y = |x + 3| + |4 – x |, does y equal 7?

(1) x lesser than 4
(2) x greater than -3

OA is C i get the answer as D, what is the right answre,pls confirm

Also if you were asked to prove that y is indeed 7.No options are given. How would you do it mathematically (take it as a PS question).
In absolute values,
if y = |x|, then
y= x
y = -x
How do we do it in the question above.
Source: — Data Sufficiency |

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by moneyman » Sun Nov 04, 2007 10:01 pm
The answer is C

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

Stat 1 - x is lesser than 4 so x can be 3,-3 or even -7 . Substitute these three values in the expression and you will get different value for x=-7.INSUFFICIENT

Stat 2- x is greater than -3 so x can be -2,5 or even 35. Substitute these valuse and you will get 7 for x=-2 but a different value for x=35.INSUFFICIENT

By combining the two statements we know that the possible values for x are -2,-1,0,1,2 and 3. All these values when substituted in the expression would give a value of 7.
Maxx

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by athakkar » Mon Nov 05, 2007 11:56 pm
Nice explanation on absolute values

https://www.manhattangmat.com/strategyseries15.cfm

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by gmatrant » Tue Nov 06, 2007 9:56 am
great link..it was very helpful.. thanks