How to solve these questions

[alokbansal85]

If
6<=|X|<=8
3<=|Y|<=5
1<=|Z|<=2

Then what is the minimum and maximum value of |X+Y+Z| ?

Please tell me the logic of these type of question.

[vikasapkal]

when |X| we know that x could be either X or -X....

now,

For positive value

6≤|X|≤8

6≤X≤8

SO X MIN = 6 and MAX = 8

For negative value

6≤|X|≤8

6≤-X≤8

-6≥X≥-8

-8≤X≤-6

SO X MIN = -8 and MAX = -6

this pattern is for all,

3<=|Y|<=5

for positive

Y MIN = 3 and MAX = 5

for negative

Y MIN = -5 and MAX = -3

1<=|Z|<=2

for positive

Z MIN = 1 and MAX = 2

for negative

Z MIN = -2 and MAX = -1


hence,

MAX

|X+Y+Z| = |8+5+2| = 15

MIN

|X+Y+Z| = |-6-3-1| = 10

Thank you,
Vikas

[alokbansal85]

Thanks Vikas, Please review your min and max value one more time as they are contradicting with you answers.

Request any manhattan guide to reply on this.

Alban

[tommywallach]

Hey Alban,

Vikas' explanation for this question was spot on, except he seems to have screwed up the final minimum value. I'll put it a little more simply:

Absolutely value ranges mean it could be anything in both the positive or negative range, so X can be -8 to -6 or 6 to 8, so the biggest it could be is 8, and the smallest is -8. The biggest Y will be 5, and the smallest Y will be -5. The biggest Z will be 2, and the smallest Z will be -2.

So biggest X + Y + Z = 8 + 5 + 2 = 15
Smallest X + Y + Z = -8 + -5 + -2 = -15

Let me know if that makes sense!

-t

[vikasapkal]

hello, tommywallach

i am very much clear on maximum value
i have query about minimum value...

Question asking min value of |X+Y+Z| not x+y+z....

if we take |-8-5-2| = 15 ----turns out to be positive

if we take |-6-3-1| = 10----turns out to be positive as well...hence i inferred that this is the smallest possible value..

in fact absolute value will be always positive...

you are saying the smallest value is -15...

how the value of |something| will be negative?

am i missing something?

[garima_aries01]

So biggest X + Y + Z = 8 + 5 + 2 = 15
Smallest X + Y + Z = -8 + -5 + -2 = -15

So maximum of |x+y+z| = 15
But minimum of |x+y=z| = 0

We all know that minimum of |something| = 0
So we need to see if there is any combination of x,y,z that makes it zero or any number closest to zero

x= -7
y=5
z=2
|-7+5+2| = 0

[tommywallach]

Hey Alok,

Ha! Totally misread the question up top! Absolute value always shows up very unclear on these darn forums. Apologies!

Absolutely right on Garim's part. Just to explain the top-level strategy:

Absolute values range from 0 --> positive infinity. So when you're seeking the max value, just go for the biggest number you can.

On the other hand, for a minimum, you'll never be able to break below 0, so you need to do your best to create zero. Failing that, you'd aim for whatever you could create that is closest to zero.

Make sense? Sorry again for the confusion!

-t