# GMAT Challenging Question 10

#### Algebra PS | Modulus, Absolute value Practice

This GMAT 700 800 level problem solving practice question tests your understanding of absolute values of numbers. It also tests your ability to find values for which the expression will be positive and for those for which it will be negative and determine for what values will the expression be maximum and when it will be minimum.

#### When will the value of the expression be minimum?

S = 1 + $$frac{\text{|a|}}{\text{a}}$ + $\frac{\text{2|b|}}{\text{b}}$ + $\frac{\text{3|ab|}}{\text{ab}}$ − $\frac{\text{4|c|}}{\text{c}}$ The value of the expression will be minimum if we make as many terms negative as possible. Higher the magnitude of the terms made negative, lower the value of the expression. c has to be positive for S to be minimum. The last term will then be -4. If ab is negative, then $\frac{\text{3|ab|}}{\text{ab}}$ = -3 If ab has to be negative, one of a or b has to be positive and the other has to be negative. Possibility 1: If a > 0 and b < 0, $\frac{\text{|a|}}{\text{a}}$ = 1 and $\frac{\text{2|b|}}{\text{b}}$ = -2. The value of the expression is 1 + 1 - 2 - 3 - 4 = -7. Possibility 2: If a < 0 and b > 0, $\frac{\text{|a|}}{\text{a}}$ = -1 and $\frac{\text{2|b|}}{\text{b}}$ = 2. The value of the expression is 1 - 1 + 2 - 3 - 4 = -5. Therefore, the minimum value is -7 #### Step 3: Compute the difference Maximum value of S = 11. Minimum value of S = -7. The difference is 18. #### Choice E is the correct answer. #### GMAT Online CourseTry it free! Register in 2 easy steps and Start learning in 5 minutes! #### Already have an Account? #### GMAT Live Online Classes Next Batch Sep 21, 2024 Work @ Wizako ##### How to reach Wizako? Mobile:$91) 95000 48484
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