Find all solutions of |||Q| – 7| + Q| = Q ?

Question

Find all solutions of  |||Q|–7|+Q|=Q  ?

Bunuel · Accepted Answer

I've never seen real GMAT question involving triple modulus. Though the above question is not very hard.

|||q|-7|+q|=q

Now, absolute value is always non-negative  |some \ expression|\geq{0} , so as LHS (left hand side) above is an absolute value it must be non-negative then RHS must also be non-negative -->  q\geq{0} , so  |q|=q , so  |||q|-7|+q|=q  becomes:  ||q-7|+q|=q .

||q-7|+q|=q :
If  q\leq{7}  then  |q-7|  becomes  -(q-7)  so  |-q+7+q|=q  -->  q=|7|=7 ;
If  q>{7}  then  |q-7|  becomes  q-7  so  |q-7+q|=q  -->  |2q-7|=q  --> as  q>{7}  then  |2q-7|=2q-7  so  2q-7=q  -->  q=7 .

So, only one solution  q=7 .

krishnasty · Answer

hey guys.... can somebody tell me how to solve such kind of questions ? i am getting confused .. :oops:

Nightmare007 · Answer

Q should always be greater than 0 ; it can't be zero . -> three cases 
case 1 Q <7 solving we get Q = 7 false;
case 2 Q >7 solving we again get Q= 7 false;
case 3 Q = 7 solving we get Q = 7 true,
 so only one solution . i.e. Q = 7

BrushMyQuant · Answer

We need to find all solutions of  |||Q|–7|+Q|=Q ?

Now, Left hand side is modulus of a number and right side is Q
=> Q is non-negative (As modulus of a number is non negative
=> Q ≥ 0
=> |Q| = Q
=> ||Q–7|+Q|=Q
   Now we will have two cases

-   Case 1:  Q - 7 ≥ 0

=> |Q -7 | = Q-7
=> |Q - 7 +Q|=Q
=> | 2Q - 7| = Q
Since Q - 7 ≥ 0 and Q ≥ 0
=> 2Q - 7 ≥ 0
=> | 2Q - 7| = 2Q - 7
=> 2Q - 7 = Q
=> Q = 7
Which satisfies the condition of Q - 7 ≥ 0 and Q ≥ 0
=>  Q = 7 is a solution

-   Case 2:  Q - 7 ≤ 0

=> |Q -7 | = -(Q-7) = -Q + 7

=> |-Q + 7 +Q|=Q

=> |7| = Q

=> Q = 7

Which satisfies the condition of Q - 7 ≤ 0 and Q ≥ 0
=>  Q = 7 is a solution

So,  Answer will be 7 
Hope it helps!

Watch the following video to learn the Basics of Absolute Values

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

bumpbot · Answer

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Find all solutions of |||Q| – 7| + Q| = Q ?

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Now we will have two cases
-Case 1: Q - 7 ≥ 0 => \|Q -7 \| = Q-7 => \|Q - 7 +Q\|=Q => \| 2Q - 7\| = Q Since Q - 7 ≥ 0 and Q ≥ 0 => 2Q - 7 ≥ 0 => \| 2Q - 7\| = 2Q - 7 => 2Q - 7 = Q => Q = 7 Which satisfies the condition of Q - 7 ≥ 0 and Q ≥ 0 => Q = 7 is a solution	-Case 2: Q - 7 ≤ 0 => \|Q -7 \| = -(Q-7) = -Q + 7 => \|-Q + 7 +Q\|=Q => \|7\| = Q => Q = 7 Which satisfies the condition of Q - 7 ≤ 0 and Q ≥ 0 => Q = 7 is a solution

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Find all solutions of |||Q| – 7| + Q| = Q ?

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