If |1 - x| = 6 and |2y - 6| = 10, which of the following tcould be the

Question

If |1 - x| = 6 and |2y - 6| = 10, which of the following tcould be the value of xy?

I. -40
II. -14
III. 56

A. I only
B. II only
C. III only
D. I and III only
E. I, II and III

firas92 · Accepted Answer

(1-x) = ±6

x=7 or -5

(2y-6) = ±10
(y-3) = ±5

y=8 or -2

8 x -5=-40
7 x -2=-14
8 x 7 = 56

xy could be I, II or III

Answer is  (E)

Archit3110 · Answer

x can be -5 or 7
y can be -2 or 8
so we get products all three options valid
IMO E

BrushMyQuant · Answer

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

https://www.youtube.com/watch?v=CTzTC-uSAJA

|1 - x| = 6  
=> 1 - x = 6 or 1 - x = -6
=> x = 1-6 or x = 1 + 6
=> x = -5 or x = 7

|2y - 6| = 10  
=> |y - 3| = 5
=> y - 3 = 5 or y - 3 = -5
=> y = 3 + 5 or y = 3 - 5
=> y = 8 or -2

=> Possible values of xy are 
 
 x = -5, y = 8, xy = -5 * 8 = -40 
 x = -5, y = -2, xy = -5 * -2 = 10 
 x = 7, y = 8, xy = 7 * 8 = 56 
 x = 7, y = -2, xy = 7 * -2 = -14

=>  Possible values of xy are -40, -14, 10, 56 
=>   All options are possible

So,  Answer will be E 
Hope it helps!

Watch the following video to MASTER Absolute Values

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

Azeem123 · Answer

X is -5 at x>0 , and x is 7 at x<0 . How is it correct to consider these values in opposite ranges?

Bunuel · Answer

Could you clarify what you mean? The equation |1 - x| = 6 gives two valid solutions: x = -5 and x = 7. There’s no restriction on x > 0 or x < 0 in the question. Both values are acceptable.

BrushMyQuant · Answer

| 1 - x | = 6
=> | x - 1 | = 6

As we have |x - 1| in the equation so we will have two cases 
 
   -   Case 1:  x - 1 ≥ 0, x ≥ 1 
=> |x - 1| = x - 1
=> x - 1 = 6
=> x = 6 + 1 = 7

But condition was x ≥ 1 and 7 ≥ 1 
=>  x = 7 is a  SOLUTION   
  -   Case 2:  x - 1 ≤ 0 => x ≤ 1 
=> |x - 1| = -(x - 1) = 1 - x
=> 1 - x = 6
=> x = 1 - 6 = -5

But condition was x ≤ 1 and - 5 ≤ 1 
=>  x = -5 is a  SOLUTION

Watch  this video  to  MASTER Absolute Values !
Hope it helps!

If |1 - x| = 6 and |2y - 6| = 10, which of the following tcould be the

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As we have \|x - 1\| in the equation so we will have two cases
-Case 1: x - 1 ≥ 0, x ≥ 1 => \|x - 1\| = x - 1 => x - 1 = 6 => x = 6 + 1 = 7 But condition was x ≥ 1 and 7 ≥ 1 => x = 7 is a SOLUTION	-Case 2: x - 1 ≤ 0 => x ≤ 1 => \|x - 1\| = -(x - 1) = 1 - x => 1 - x = 6 => x = 1 - 6 = -5 But condition was x ≤ 1 and - 5 ≤ 1 => x = -5 is a SOLUTION

GMAT Problem Solving (PS) Questions

If |1 - x| = 6 and |2y - 6| = 10, which of the following tcould be the

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards