For how many ordered pairs (p, q) that are solutions of the system abo

Question

3p-q=9 
 |q|≤14  
For how many ordered pairs  (p, q)  that are solutions of the system above are  p  and  q  both integers?

(A) 8
(B) 9
(C) 14
(D) 28
(E) 29

GMATNinja · Answer

Check out question 5 in the video below for the solution:

https://www.youtube.com/watch?v=JjsHjL7X-vo&t=2906s

Archit3110 · Answer

3p-q=9
p= (9+q)/3
q has to be factor of 3
possible values of q -12,-9,-6,-3,0,3,6,9,12
9 value possible option B

BrushMyQuant · Answer

We need to find how many integer values of p and q satisfy  
  3p-q=9 
 |q|≤14  
 
 |q|≤14 
  => -14 ≤ q ≤ 14 
 
  3p-q=9  
=> 3p = 9 + q
 => p =  \frac{9 + q}{3}

For p to be an integer q has to be a multiple of 3

=> Possible values of q between -14 to 14 and which are multiples of 3 are 
-12, -9, ..., 9, 12
=>  \frac{(12 - (-12))}{3}  + 1  this video  to learn about  Arithmetic Series  ]
= 8 + 1 = 9

So,  Answer will be B 
Hope it helps!

Watch the following video to MASTER Inequality + Absolute value Problems

https://www.youtube.com/watch?v=236auvH8agc

For how many ordered pairs (p, q) that are solutions of the system abo

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