If |r - 6| = 11 and |2q - 12| = 8, what is the minimum possible value

Question

If |r - 6| = 11 and |2q - 12| = 8, what is the minimum possible value of q/r?

A. -5
B. -5/2
C. -2
D. -2/5
E. 2/17

CareerGeek · Answer

|r - 6| = 11
--> r - 6 = ±11
--> r = 6 ± 11
--> r = -5 or 17

|2q - 12| = 8
--> |q - 6| = 4
--> q - 6 = ±4
--> q = 6 ± 4
--> q = 10 or 2

For minimum value of q/r, r = -5 & q = 10
--> q/r = 10/(-5) = -2

Option C

Edwinnguyen · Answer

Q/R min <-> R min Q max (in the scenario we know that Q/R <0) --> OA: C Posted from my mobile device

Archit3110 · Answer

values of r and q = 
|r - 6| = 11 and |2q - 12| = 8
r= -5/17 and q= 10 /2
min value possible of q/r ; 10/-5 ; -2
IMO C

LifeGoesOn · Answer

Opening the modulus with specific conditions :

1) r-6>0 then r>6 and r=11+6=17 ; r-6 <0 then r<6 and -r+6 =11 => r= -5

Similarly opening the modulus for q, we get for q>6 => q=10, and for q<6 => q=2.

Taking the above 4 values into account, the minimum of the ratio should be a negative number.

Hence, The minimum value of q/r would be 10/-5 => -2.

The correct answer is C.

BrushMyQuant · Answer

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

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

Given that |r - 6| = 11 and |2q - 12| = 8 and we need to find the minimum possible value of q/r?

|r - 6| = 11
=> r - 6 = 11 or -11
=> r = 17, -5

|2q - 12| = 8
=> |q - 6| = 4
=> q - 6 = 4 or -4
=> q = 10 or 2

We need to find the minimum value of  \frac{q}{r}  and we have one negative value of r
=> r = -5

=> For q = 10,  \frac{q}{r}  =  \frac{10}{-5}  = -2
=> For q = 2,  \frac{q}{r}  =  \frac{2}{-5}  = -2/5

-2 < -2/5

So,  Answer will be C 
Hope it helps!

Absolute Values Theory and Solved Problems   Playlist Link here

Watch the following video to learn the Basics of Absolute Values

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

Kinshook · Answer

Asked: If |r - 6| = 11 and |2q - 12| = 8, what is the minimum possible value of q/r?

r = 17 or -5
q = 10 or 2

Possible values of q/r = {10/17, 2/17, -2,-2/5}
Minimum possible value of q/r = -2

IMO C

bumpbot · Answer

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If |r - 6| = 11 and |2q - 12| = 8, what is the minimum possible value

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If |r - 6| = 11 and |2q - 12| = 8, what is the minimum possible value

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