If -8 ≤ a ≤ 1 and -5 ≤ b ≤ 10. Find the sum of minimum and m

Question

If -8 ≤ a ≤ 1 and -5 ≤ b ≤ 10. Find the sum of minimum and maximum value of a - |b|.

A. -19
B. -23
C. -18
D. -22
E. -17

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nick1816 · Answer

Minimum value of a-|b|=-8-|10|=-18
Maximum value of a-|b|= 1-|0|=1
Their Sum= -18+1=-17

ScottTargetTestPrep · Answer

Since |b| is nonnegative:

The maximum value is 1 - 0 = 1.

The minimum value is -8 - 10 = -18.

Thus, the sum of the values is -18 + 1 = -17.

Answer: E

Aprajita760 · Answer

hi,
How in max value , you have put 0 for |b|?

nick1816 · Answer

Because |b| has a non-negative value, you have to minimize the |b| in order to maximize a-|b|. Minimum value |b| is 0.

For example- If a=1 and b=-1
a-|b|=1-|-1|=1-1=0
Value of a-|b| will decrease, if you go on the left side of 0 on the number-line of b

And if a=1 and b=1
a-|b|=1-|1|=1-1=0
Value of a-|b| will decrease, if you go on the right side of 0 on the number-line of b

BrushMyQuant · Answer

↧↧↧ Detailed Video Solution to the Problem ↧↧↧

https://www.youtube.com/watch?v=sQUqopZ5SOA

Minimum Value

To find Min (a - |b|) we need to find the minimum value of a and maximum value of |b|

-8 ≤ a ≤ 1 => Min value of a = -8
-5 ≤ b ≤ 10 => Max value of |b| = |10| = 10

=> Min ( a - |b|) = -8 - 10 = -18

Maximum Value

To find Max (a - |b|) we need to find the maximum value of a and minimum value of |b|

-8 ≤ a ≤ 1 => Max value of a = 1
-5 ≤ b ≤ 10 => Min value of |b| = |0| = 0

=> Max ( a - |b|) = 1 - 0 = 1

=> Sum of Min( a - |b|) and Max( a - |b|) = -18 + 1 = -17

So,  Answer will be E 
Hope it helps!

Watch the following video to MASTER Absolute Values

https://www.youtube.com/watch?v=huFiBk8PaGY

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If -8 ≤ a ≤ 1 and -5 ≤ b ≤ 10. Find the sum of minimum and m

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If -8 ≤ a ≤ 1 and -5 ≤ b ≤ 10. Find the sum of minimum and m

Prep Toolkit

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My Rewards