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If -12 <= x <= 1 and -4 <= y <= 10, sum of minimum and maximum possibl

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Bunuel
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If -12 <= x <= 1 and -4 <= y <= 10, sum of minimum and maximum possibl [#permalink] New post   03 Feb 2020, 02:16
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If \(-12 \leq x \leq 1\) and \(-4 \leq y \leq 10\), sum of minimum and maximum possible value of \(x - |y|\) is

A. -22
B. -21
C. -17
D. 21
E. 22
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B
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Re: If -12 <= x <= 1 and -4 <= y <= 10, sum of minimum and maximum possibl [#permalink] New post   03 Feb 2020, 03:46
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If −12≤x≤1 and −4≤y≤10, sum of minimum and maximum possible value of x−|y|x−|y| is

A. -22
B. -21
C. -17
D. 21
E. 22

Answer - B ->

x min value = -12
|y| min value = 0 (|y| will get rid of negative values of y)

x max value = 1
y max value = 10

min value of (x - |y|) = -12-10 = -22
max value of (x-|y|) = 1 - 0 = 1

Therefore sum of min and max values of (x-|y|) = -22+1 = -21
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Re: If -12 <= x <= 1 and -4 <= y <= 10, sum of minimum and maximum possibl [#permalink] New post   03 Feb 2020, 05:22
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Values of (x, |y|)
Max -> \((1, 10)\)
Min -> \((-12, 0)\)

Max value of \(x - |y| = 1 - |0| = 1\)
Min value of \(x - |y| = -12 - |10| = -22\)

\(Sum = 1 - 22 = -21\)

Option B
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If -12 <= x <= 1 and -4 <= y <= 10, sum of minimum and maximum possibl [#permalink] New post   Updated on: 04 Feb 2020, 21:53
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Explanation:

for minimum value, x=-12, y=10
x−|y| = -12-10 = -22
for maximum value, x=1 , y =0
x−|y| = 1-0 = 1

Sum of maximum & minimum = -22 + 1 = -21

IMO-B

Originally posted by rajatchopra1994 on 03 Feb 2020, 03:30.
Last edited by rajatchopra1994 on 04 Feb 2020, 21:53, edited 1 time in total.
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Re: If -12 <= x <= 1 and -4 <= y <= 10, sum of minimum and maximum possibl [#permalink] New post   03 Feb 2020, 04:53
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Maximum value of (x, |y|) = (1, 10) & minimum value of (x, |y|) = (-12, 0)

Maximum value of x - |y| = 1 - |0| = 1
Minimum value of x - |y| = -12 - |10| = -12 - 10 = -22

Sum of maximum and minimum value = 1 - 22 = -21

Option B
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Re: If -12 <= x <= 1 and -4 <= y <= 10, sum of minimum and maximum possibl [#permalink] New post   03 Feb 2020, 05:25
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minimum value of x−|y| is -12-10 = -22
maximum value of x−|y| is 1-0 = 1
sum = -22+1 = -21

OA:B
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Re: If -12 <= x <= 1 and -4 <= y <= 10, sum of minimum and maximum possibl [#permalink] New post   03 Feb 2020, 06:29
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If −12≤x≤1 and −4≤y≤10, sum of minimum and maximum possible value of x−|y| is

minimum:
x=-12
y=10

-12-10=-22

maximum:
x=1
y=0
1-0=1

sum:
-22+1
=-21

B
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Re: If -12 <= x <= 1 and -4 <= y <= 10, sum of minimum and maximum possibl [#permalink] New post   03 Feb 2020, 08:17
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For the smallest possible value let x = -12 and y = 10 ; -12 - |10| = -22
For the largest possible value let x = 1 and y = 0 ; 1 - |0| = 1
Sum of numbers: -22 + 1 = -21
ANS) B
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Re: If -12 <= x <= 1 and -4 <= y <= 10, sum of minimum and maximum possibl [#permalink] New post   03 Feb 2020, 09:49
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\(x - |y|\) get the minimum value when x minimum and \(|y|\) maximum
=> x = -12, y = 10=> Max \(x - |y| = -12 - |10| = -22\)

\(x - |y|\) get the maximum value when x maximum and \(|y|\) minimum
=> x = 1, y = 0 => Min \(x - |y| = 1 - |0| = 1\)

=> sum of minimum and maximum value of \(x - |y|\) is -21

=> Choice B
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Re: If -12 <= x <= 1 and -4 <= y <= 10, sum of minimum and maximum possibl [#permalink] New post   03 Feb 2020, 18:25
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If −12≤x≤1 and −4≤y≤10, sum of minimum and maximum possible value of x−|y| is ?

The max =x−|y|= 1-|0|= 1
The min= x−|y|= -12 -|-10|= -12-10= -22

--> The sum = 1-22= -21

The answer is B.
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Re: If -12 <= x <= 1 and -4 <= y <= 10, sum of minimum and maximum possibl [#permalink] New post   03 Feb 2020, 20:34
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We are given the ranges -12<=x<=1 and -4<=y<=10 and we are to find the sum of the minimum and maximum possible values of x-|y|
We know the |y| will always be +ve, hence to get the maximum value of x-|y|, |y| must be minimum, and from the given range, y must equal zero while x must be the maximum value of x and this is 1.
so Maximum value of x-|y| = 1-|0| = 1.

For the minimum, |y| must be maximum possible value in the range while x must be the minimum value possible.
hence Minimum value of x-|y| = -12-|10| = -22
Maximum+minimum = 1-22=-21

B is the answer.
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If -12 <= x <= 1 and -4 <= y <= 10, sum of minimum and maximum possibl [#permalink] New post   Updated on: 04 Feb 2020, 02:34
max value will be at x=1&y=0 ; i.e 1 and min value x=-12 and y = 10 ; -22
so sum ; -22+1 ;-21
IMO B

If −12≤x≤1 and −4≤y≤10, sum of minimum and maximum possible value of x−|y| is

A. -22
B. -21
C. -17
D. 21
E. 22

Originally posted by Archit3110 on 03 Feb 2020, 07:48.
Last edited by Archit3110 on 04 Feb 2020, 02:34, edited 1 time in total.
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If -12 <= x <= 1 and -4 <= y <= 10, sum of minimum and maximum possibl [#permalink] New post   Updated on: 04 Feb 2020, 04:02
Quote:
If −12≤x≤1 and −4≤y≤10, sum of minimum and maximum possible value of x−|y| is

A. -22
B. -21
C. -17
D. 21
E. 22


min: -12-|10|=-22
max: 1-|0|=1
sum: -21

Ans (B)

Originally posted by exc4libur on 03 Feb 2020, 07:51.
Last edited by exc4libur on 04 Feb 2020, 04:02, edited 1 time in total.
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Re: If -12 <= x <= 1 and -4 <= y <= 10, sum of minimum and maximum possibl [#permalink] New post   03 Feb 2020, 23:50
If −12≤x≤1 and −4≤y≤10, sum of minimum and maximum possible value of x−|y| is

A. -22
B. -21
C. -17
D. 21
E. 22

x−|y|(max) = x(max) − |y|(min) = 1 − |-4| = - 3
x−|y|(min) = x(min) − |y|(max) = -12 − |10| = - 22

Also,
−12≤x≤1 and
−4≤y≤10 = 4≤|y|≤10 = -10 ≤ -|y| ≤ -4

Adding 2 equations gives
-12-10 ≤ x -|y| ≤ 1-4
-22 ≤ x -|y| ≤ -3

Sum of maximum and minimum = - 22 - 3 = -25
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If -12 <= x <= 1 and -4 <= y <= 10, sum of minimum and maximum possibl [#permalink] New post   04 Feb 2020, 05:58
lnm87 wrote:
If −12≤x≤1 and −4≤y≤10, sum of minimum and maximum possible value of x−|y| is

A. -22
B. -21
C. -17
D. 21
E. 22

x−|y|(max) = x(max) − |y|(min) = 1 − |-4| = - 3
x−|y|(min) = x(min) − |y|(max) = -12 − |10| = - 22

Also,
−12≤x≤1 and
−4≤y≤10 = 4≤|y|≤10 = -10 ≤ -|y| ≤ -4

Adding 2 equations gives
-12-10 ≤ x -|y| ≤ 1-4
-22 ≤ x -|y| ≤ -3

Sum of maximum and minimum = - 22 - 3 = -25


What a pity mistake i have made. |y| can take '0' as minimum value and x -12 :( :roll:
And maximum value of |y| is 10 and x is -12.
Hence -12 - 10 + 1 - 0 = -21
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Re: If -12 <= x <= 1 and -4 <= y <= 10, sum of minimum and maximum possibl [#permalink] New post   17 Jun 2021, 14:16
Hey Bunuel

I am totally off the grid in this one. I am getting -25. My solution is like this.

Max value of X and Y : 1 and 10
Min Value of X and Y : -12 and -4 .

while look at the solutions some have take minimum value of Y as 0. I am not getting it how .
Can you help me with is please.?
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Re: If -12 <= x <= 1 and -4 <= y <= 10, sum of minimum and maximum possibl [#permalink] New post   31 Mar 2024, 16:18
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Re: If -12 <= x <= 1 and -4 <= y <= 10, sum of minimum and maximum possibl [#permalink]
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