If a, b, and c are not equal to zero, what is the difference between t

Question

If a, b, and c are not equal to zero, what is the difference between the maximum and minimum value of S?

S=1 + \frac{|a|}{a} + \frac{2|b|}{b} + \frac{3|ab|}{ab} −\frac{4|c|}{c}

A. 12
B. 14
C. 18
D. 20
E. 22

Skywalker18 · Accepted Answer

S=1 + \frac{|a|}{a} + \frac{2|b|}{b} + \frac{3|ab|}{ab} −\frac{4|c|}{c}

To maximize S , a and b need to be positive and c needs to be negative 
s(max) = 1 + 1 + 2 + 3 + 4 = 11
To minimize S , a needs to be positive , b needs to be negative and c needs to be positive 
s(min) = 1 + 1 -2 -3 - 4 = - 7 
Difference between max and min value = 11 - (-7) = 18

Answer C

vivekkumar987 · Answer

IMO:D 
To maximize the equation all the terms should be in positive
So 1+1+2+3+4 = 11 ( we can assume any positive number for a & b and a negative number for c)

To minimize the equation all the terms should be in negative
So 1-1-2-3-4 = -9 ( we can assume any negative number for a & b and a positive number for c)

Therefore 11- (-9) =20

vaibhavpanchal · Answer

S=1+|a|a+2|b|b+3|ab|ab−4|c|c

To maximize S , a and b need to be positive and c needs to be negative
s(max) = 1 + 1 + 2 + 3 + 4 = 11
To minimize S , a needs to be positive , b needs to be negative and c needs to be positive
s(min) = 1 + 1 -2 -3 - 4 = - 7
Difference between max and min value = 11 - (-7) = 18

ENGRTOMBA2018 · Answer

You are missing the fact that when a,b both are <0, then the product ab > 0 and hence |ab| > 0 making your "minimum" sum = 1-1-2+3-4 = -3 , not a minimum. If a, b, and c are not equal to zero, what is the difference between the maximum and minimum value of S? S=1+\frac{|a|}{a}+2\frac{|b|}{b}+3\frac{|ab|}{ab}−4\frac{|c|}{c} 1-1-2+3-4 = -4 and NOT -7 In order to minimize S, you need to have opposite signs for ab in order to make |ab| negative as its coefficient (=3) is the highest. Lets say a>0 and b<0 ---> |ab| = -ab, giving you minimum value = 1+1-2-3-4 = -7 and with a<0, b>0 you get, 1-1+2-3-4 = -5. Thus the minimum value of S = -7 The maximum value of S will be when a>0, b>0 and c<0, S=1+\frac{|a|}{a}+2\frac{|b|}{b}+3\frac{|ab|}{ab}−4\frac{|c|}{c}=1+1+2+3+4 = 11 Thus the difference = 11-(-7)=18 Hence C is the correct answer. Hope this helps.

Beixi88 · Answer

The maximum is where every term is positive:

1 + 1 + 2 + 3 - 4 * -1 -> 1 + 1 + 2 + 3 + 4 = 11

The minimum will be where we have the highest value of negatives. This requires our '3' term to be negative. Since our '3' term requires a and b, we want either a or b to be negative, but not both. Due to this, we have a as our positive and b as our negative:

1 + 1 - 2 - 3 - 4 -> 2 - 9 = -7

The distance between -7 and 11 is 18 (C).

vibhavdwivedi · Answer

The answer is C = 18

Since |x|/x =1 if x>0 and |x|/x = -1 if x<0
to get the  max  of S, pick the value C to be negative and A and B to be positive. 
S = 1+1+2+3+4 => S=11

to get the  min  of S, pick the value C and A to be positive and B to be negative (we can also take  B  to be positive instead of A, but B is related to 2, that is the higher value.

S = 1+1-2-3-4 => S=-7

making the difference of max - min = 11 - (-7) = 18

ghv1996 · Answer

Mistake in your solution:
If a and b are negative, then "-3" becomes "+3" because ab= -a*-b = +ab, so consider 'a' positive
So Smin= 1+1-2-3-4= -7
so, 11-(-7)= 18

Kinshook · Answer

Asked: If a, b, and c are not equal to zero, what is the difference between the maximum and minimum value of S?

\(S=1 + \frac{|a|}{a} + \frac{2|b|}{b} + \frac{3|ab|}{ab} −\frac{4|c|}{c}\)

For Smax: -
a>0; b>0; ab>0; c<0
Smax = 1 + 1 + 2 + 3 + 4 = 11

For Smin: -
a>0; b<0; ab<0; c>0
Smin = 1 + 1 - 2 - 3 - 4 = -7

Smax - Smin = 11 - (-7) = 18

IMO C

padmru · Answer

Hi, Wont the minimum value of S would be at -9?
Minimum Value of S = 1-1-2-3-4 = -9.

Difference = 11 - (-9) = 11 + 9 = 20.

Could someone correct me as to why minimum value of S should be -7 and not -9?

Bunuel · Answer

You're assuming both a and b are negative, which makes ab positive. That means |ab|/ab equals 1, not -1. So the term 3|ab|/ab becomes +3, not -3. That's why your total comes out wrong.

If a, b, and c are not equal to zero, what is the difference between t

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If a, b, and c are not equal to zero, what is the difference between t

Prep Toolkit

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