Y = |X+3| + |x-4|
Let Y = 7
7 = |X+3| + |x-4|
now testing borderlines,
test 1 -
X > 4, say X = 5
7 = 8 + 1 (false)
X < 4, say X = 3
7 = 6+1 (trues)
X = 2, 7 = 5+2 (true)
Not taking extreme value for x < 4 , say x = -100
7 = 97 + 104 = 201 (not true) hence there is point after which x < 4 doesnt hold true
Hence A is not sufficient
Second borderline, x = -3
for X < - 3, say x = - 4
7 = 1 + 8 (not true)
X > - 3
X = -2
7 = 1 + 6 (true)
X = -1
7 = 2 + 5 (ture)
X = 0,
7 = 3 + 4 (ture)
taking extreme value for x > - 3 say +100
7 = 103 + 96 = 199 (not true)
Hence B alone is not sufficient
Combine A and B, -3 < X < 4 (for x = -2, -1, 0, 1, 2 ,3 ) all confirm the equation
Algebra->Inequalities (Absolute Value)
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Mission2012
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|a-b| = the DISTANCE between a and b.Mario_87 wrote: if y = |x+3| + |4-x|, does y=7?
1. x < 4
2. x > -3
|a+b| = |a-(-b)| = the DISTANCE between a and -b.
Thus:
|x+3| = the distance between x and -3.
|4-x| = the distance between 4 and x.
y = the SUM of these two distances.
Question stem rephrased:
Is the sum of the two distances equal to 7?
The distance between -3 and 4 is 7.
Thus, if x is BETWEEN these two endpoints, then the sum of the two distances will be EQUAL TO 7:
-3 <--- |x+3| ---> x <---|4-x|---> 4.
Here, |x+3| + |4-x| = the distance between -3 and 4 = 7.
By extension, if x is BEYOND either endpoint -- if x is to the left of -3 or to the right of 4 -- then the sum of the two distances will be GREATER THAN 7.
Statement 1: x < 4
If x=2, then x is between -3 and 4.
If x=-10, then x is to the left of -3.
INSUFFICIENT.
Statement 2: x > -3
If x=2, then x is between -3 and 4.
If x=10, then x is to the right of 4.
INSUFFICIENT.
Statements combined:
-3 < x < 4.
SUFFICIENT.
The correct answer is C.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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