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Updated on: 07 Aug 2018, 06:15
Originally posted by EgmatQuantExpert on 20 May 2015, 10:20.
Last edited by EgmatQuantExpert on 07 Aug 2018, 06:15, edited 3 times in total.
Last edited by EgmatQuantExpert on 07 Aug 2018, 06:15, edited 3 times in total.
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
54% (02:47) correct
46%
(02:46)
wrong
based on 1883
sessions
History
Date
Time
Result
Not Attempted Yet
If x and y are numbers such that x < - 10 and y > 6, which of the following expressions is true?
I. |x+4| + | y + 4| + | y-4| + |x – 4| > 32
II. |x – 4| + |y + 4| - | x + 4| - | y – 4| < 0
III. |x + 4| + |y + 4| - |x – 4| - |y – 4| = 0
(A) I only
(B) II only
(C) III only
(D) I and III only
(E) I, II and III
This is Question 3 for the e-GMAT Question Series on Absolute Value.
Provide your solution below. Kudos for participation. Happy Solving!
Best Regards
The e-GMAT Team
I. |x+4| + | y + 4| + | y-4| + |x – 4| > 32
II. |x – 4| + |y + 4| - | x + 4| - | y – 4| < 0
III. |x + 4| + |y + 4| - |x – 4| - |y – 4| = 0
(A) I only
(B) II only
(C) III only
(D) I and III only
(E) I, II and III
This is Question 3 for the e-GMAT Question Series on Absolute Value.
Provide your solution below. Kudos for participation. Happy Solving!
Best Regards
The e-GMAT Team
UJs
Joined: 18 Nov 2013
Last visit: 17 Feb 2018
Posts: 67
Given Kudos: 63
Concentration: General Management, Technology
Schools: Oxford'17 (WL) Insead July'17 (I) Judge'17 (D)
GMAT 1: 690 Q49 V34
20 May 2015, 20:47
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As stated, If x and y are numbers such that x < - 10 and y > 6,
if y > 6 , then
lets solve each
I. |x+4| + | y + 4| + | y-4| + |x – 4| > 32
II. |x – 4| + |y + 4| - | x + 4| - | y – 4| < 0
III. |x + 4| + |y + 4| - |x – 4| - |y – 4| = 0
Ans : D
if y > 6 , then
- | y + 4| = y + 4
| y - 4 | = y - 4
- | x – 4 | = - ( x – 4 )
| x + 4| = - ( x + 4 )
lets solve each
I. |x+4| + | y + 4| + | y-4| + |x – 4| > 32
- -(x+4) + (y + 4) + (y - 4) - (x – 4) > 32
-x -4 + y + 4 + y - 4 -x +4 > 32
-2x +2y > 32
-x + y > 16
-(-10.1) + (6.1) > 16 ; True
II. |x – 4| + |y + 4| - | x + 4| - | y – 4| < 0
- -(x-4) + (y + 4) - (-(x + 4)) - (y-4) < 0
-x +4 + y + 4 +x -4 -y +4 < 0
8 < 0 ; False
III. |x + 4| + |y + 4| - |x – 4| - |y – 4| = 0
- -(x+4) + (y + 4) - (-(x – 4)) - (y - 4) = 0
-x -4 + y + 4 +x -4 -y + 4 = 0
0 = 0 ; True
Ans : D
22 May 2015, 07:17
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Official Explanation
Correct Answer: D
First representing the points x and y on the number line: x < -10 and y > 6.
Then, since the expressions talk about |x+4|, |x-4|, |y+4| and |y-4|, representing these distances on the number line as well.
|x+4| represents the distance of x from -4 on the number line
|x-4| represents the distance of x from 4
|y+4| represents the distance of y from -4
|y-4| represents the distance of y from 4
I. |x+4| + | y + 4| + | y-4| + |x – 4| > 32
From the diagram it’s clear that:
|x+4| > 6
|y + 4| >10
|y – 4| > 2
|x – 4| 14
Adding all these we get Expression 1. Therefore, is true always.
II. |x – 4| + |y + 4| - | x + 4| - | y – 4| < 0
From the diagram, we can see that |x – 4| - |x + 4| = 8
And, |y + 4| - | y – 4| = 8
Adding the 2 equations, we get:
|x – 4| + |y + 4| - | x + 4| - | y – 4| = 16
So, expression 2 is NOT TRUE.
III. |x + 4| + |y + 4| - |x – 4| - |y – 4| = 0
From the diagram, we can see that |x + 4| - |x – 4| = -8
And, |y + 4| - | y – 4| = 8
Adding the 2 equations, we get:
|x + 4| + |y + 4| - |x – 4| - |y – 4| = 0
So, expression 3 is TRUE.
Correct Answer: D
First representing the points x and y on the number line: x < -10 and y > 6.
Then, since the expressions talk about |x+4|, |x-4|, |y+4| and |y-4|, representing these distances on the number line as well.
|x+4| represents the distance of x from -4 on the number line
|x-4| represents the distance of x from 4
|y+4| represents the distance of y from -4
|y-4| represents the distance of y from 4
I. |x+4| + | y + 4| + | y-4| + |x – 4| > 32
From the diagram it’s clear that:
|x+4| > 6
|y + 4| >10
|y – 4| > 2
|x – 4| 14
Adding all these we get Expression 1. Therefore, is true always.
II. |x – 4| + |y + 4| - | x + 4| - | y – 4| < 0
From the diagram, we can see that |x – 4| - |x + 4| = 8
And, |y + 4| - | y – 4| = 8
Adding the 2 equations, we get:
|x – 4| + |y + 4| - | x + 4| - | y – 4| = 16
So, expression 2 is NOT TRUE.
III. |x + 4| + |y + 4| - |x – 4| - |y – 4| = 0
From the diagram, we can see that |x + 4| - |x – 4| = -8
And, |y + 4| - | y – 4| = 8
Adding the 2 equations, we get:
|x + 4| + |y + 4| - |x – 4| - |y – 4| = 0
So, expression 3 is TRUE.
